Document:

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                                                                  EXHIBIT 4.5(a)

                              INDYMAC BANCORP, INC.
                     FORM OF COMMON STOCK WARRANT AGREEMENT

      COMMON STOCK WARRANT AGREEMENT dated as of _______, ____, between INDYMAC
BANCORP, INC., a Delaware corporation (hereinafter called the "Company"), and
_________, having a corporate trust office in _________, as warrant agent
(hereinafter called the "Warrant Agent").

      WHEREAS, the Company proposes to issue [Class] Purchase Warrants
(hereinafter called the "Warrants") entitling the holders thereof to purchase an
aggregate of ___ shares of Common Stock of the Company (par value $0.01 per
share) (hereinafter called the "Shares") at an initial cash purchase price of
$___ per Share at any time [after ________ and] prior to 5:00 p.m., New York
City time, on ______, ____ (hereinafter called the "expiration date") (unless
extended as provided in Section 9A hereof); and

[IF WARRANTS ARE ATTACHED TO OTHER SECURITIES, INSERT --

      WHEREAS, the Warrants will be offered in Units, each of which consists of
______ and Warrants to purchase ____ Shares; and]

      WHEREAS, the Company desires the Warrant Agent to act on behalf of the
Company, and the Warrant Agent is willing so to act, in connection with the
issuance, registration, transfer, exchange and exercise of Warrants to be issued
from time to time by the Company,

      NOW, THEREFORE, in consideration of the premises and the mutual agreements
herein set forth, the parties hereto agree as follows:

      SECTION 1. APPOINTMENT OF WARRANT AGENT. The Company hereby appoints the
Warrant Agent to act as agent for the Company in accordance with the
instructions hereinafter in this Agreement set forth, and the Warrant Agent
hereby accepts such appointment.

      SECTION 2. FORM OF WARRANT. The text of the Warrants and the form of
election to purchase Shares to be set forth on the reverse thereof shall be
substantially as set forth in Exhibit A attached hereto. Each Warrant shall,
subject to the terms of this Warrant Agreement, entitle the registered holder
thereof to initially purchase the number of Shares specified therein at an
initial exercise price of $___ per Share; provided, however, that the warrant
exercise price and the number of Shares issuable upon exercise of Warrants are
subject to adjustment upon the occurrence of certain events, all as hereinafter
provided. The Warrants shall be executed on behalf of the Company by the manual
or facsimile signature of the present or any future Chairman of the Board,
President or Vice President of the Company, under its seal, affixed or in
facsimile, and by the manual or facsimile signature of the present or any future
Secretary or Assistant Secretary of the Company.

      The Company shall promptly notify the Warrant Agent from time to time in
writing of the number of Warrants to be issued and furnish written instructions
in connection

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therewith signed by an executive officer of the Company; such notification and
instructions may, but need not be, in the form of a general or continuing
authorization to the Warrant Agent. The Warrants shall be dated by the Warrant
Agent as of the date of each initial issuance, and as of the date of issuance
thereof upon any transfer or exchange thereof.

      SECTION 3. COUNTERSIGNATURE AND REGISTRATION. The Warrant Agent shall
maintain books for the transfer and registration of the Warrants. Upon the
initial issuance of the Warrants, the Warrant Agent shall issue and register the
Warrants in the names of the respective registered holders thereof. The Warrants
shall be countersigned by the Warrant Agent (or by any successor to the Warrant
Agent then acting as warrant agent under this Agreement) and shall not be valid
for any purpose unless so countersigned. Such Warrants may be so countersigned,
however, by the Warrant Agent (or by its successor as warrant agent) and be
delivered by the Warrant Agent, notwithstanding that the persons whose manual or
facsimile signatures appear thereon as proper officers of the Company shall have
ceased to be such officers at the time of such countersignature or delivery.
Upon issuance of any Warrant, the Company will present the same, or cause the
same to be presented, to the Warrant Agent for countersignature of such Warrant.

      SECTION 4. TRANSFERS AND EXCHANGES. The Warrant Agent shall transfer, from
time to time, any outstanding Warrants upon the books to be maintained by the
Warrant Agent for that purpose, upon the surrender thereof for transfer properly
endorsed or accompanied by appropriate instructions for transfer. Upon any such
transfer, a new Warrant of like tenor shall be issued to the transferee and the
surrendered Warrant shall be cancelled by the Warrant Agent. All such Warrants
so cancelled shall be delivered by the Warrant Agent to the Company from time to
time. The Warrants may be exchanged at the option of the holder thereof, when
surrendered at the office in ____________ of the Warrant Agent, for another
Warrant, or other Warrants of different denominations, of like tenor and
representing in the aggregate the right to purchase a like number of Shares. The
Warrant Agent is hereby irrevocably authorized to countersign and deliver, in
accordance with the provisions of this Section and Section 3 of this Agreement,
such new Warrants required pursuant to the provisions of this Section, and the
Company, whenever required by the Warrant Agent, will supply the Warrant Agent
with Warrants duly executed on behalf of the Company for such purpose.

[IF THE WARRANTS ARE ATTACHED TO OTHER SECURITIES, INSERT --

      Notwithstanding the foregoing, until ______, the Warrants shall not be
transferable apart from the ______ to which they are attached, any transfer of
the ______ shall be deemed a transfer of the Warrants attached thereto, and any
attempt to transfer the Warrants apart from the ______ shall be void and of no
effect. Each Warrant shall contain a legend to the foregoing effect.]

      SECTION 5. EXERCISE OF WARRANTS. The registered holder of each Warrant
shall have the right, which may be exercised as in such Warrant expressed, to
purchase from the Company (and the Company shall issue and sell to such
registered holder) the number of Shares specified in such Warrants, upon
surrender to the Company, at the office in _________ of the Warrant Agent of
such Warrant, with the form of election to purchase on the reverse thereof duly
filled in and signed, and upon payment to the Warrant Agent for the account of
the Company of

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the warrant exercise price, determined in accordance with the provisions of
Section 9 of this Agreement, for the number of Shares in respect of which such
Warrant is then exercised. Payment of such warrant exercise price may be made in
cash, or by certified check or bank draft or postal or express money order,
payable in United States dollars, to the order of the Warrant Agent. No
adjustment shall be made for any dividends on any Shares issuable upon exercise
of any Warrant. Subject to Section 6, upon such surrender of Warrants, and
payment of the warrant exercise price as aforesaid, the Company shall issue and
cause to be delivered with all reasonable dispatch to or upon the written order
of the registered holder of such Warrants, and in such name or names as such
registered holder may designate, a certificate or certificates for the number of
full Shares so purchased upon the exercise of such Warrants, together with cash,
as provided in Section 9 of this Agreement, in respect of any fraction of a
Share otherwise issuable upon such surrender. Such certificate or certificates
shall be deemed to have been issued and any person so designated to be named
therein shall be deemed to have become a holder of record of such Shares as of
the date of the surrender of such Warrants and payment of the warrant exercise
price as aforesaid; provided, however, that if, at the date of surrender of such
Warrants and payment of such warrant exercise price, the transfer books for the
Shares purchasable upon the exercise of such Warrants shall be closed, no such
surrender of such Warrants and no such payment of such warrant exercise price
shall be effective to constitute the person so designated to be named therein as
the holder of record of such Shares on such date, but shall be effective to
constitute such person as the holder of record of such Shares for all purposes
at the opening of business on the next succeeding day on which the transfer
books for the Shares purchasable upon the exercise of such Warrants shall be
opened, and the certificates for the Shares in respect of which such Warrants
are then exercised shall be issuable as of the date on which such books shall
next be opened, and until such date the Company shall be under no duty to
deliver any certificate for such Shares. The rights of purchase represented by
the Warrants shall be exercisable, at the election of the registered holders
thereof, either as an entirety or from time to time for part only of the Shares
specified therein and, in the event that any Warrant is exercised in respect of
less than all of the Shares specified therein at any time prior to the date of
expiration of the Warrants, a new Warrant or Warrants of like tenor will be
issued for the remaining number of Shares specified in the Warrant so
surrendered, and the Warrant Agent is hereby irrevocably authorized to
countersign and to deliver the required new Warrants pursuant to the provisions
of this Section and of Section 3 of this Agreement, and the Company, whenever
required by the Warrant Agent, will supply the Warrant Agent with Warrants duly
executed on behalf of the Company for such purpose.

      SECTION 6. PAYMENT OF TAXES. The Company will pay any documentary stamp
taxes attributable to the initial issuance of Shares issuable upon the exercise
of Warrants; provided, however, that the Company shall not be required to pay
any tax or taxes which may be payable in respect of any transfer involved in the
issue or delivery of any certificates for Shares in a name other than that of
the registered holder of Warrants in respect of which such Shares are issued and
the Company shall not be required to issue and deliver the certificates for such
Shares unless and until the holder has paid to the Company the amount of any tax
which may be payable in respect of any transfer involved in such issuance or
shall establish to the satisfaction of the Company that such tax has been paid.

      SECTION 7. MUTILATED OR MISSING WARRANTS. In case any of the Warrants
shall be mutilated, lost, stolen or destroyed, the Company will issue and the
Warrant Agent will

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countersign and deliver in exchange and substitution for and upon cancellation
of the mutilated Warrant, or in lieu of and substitution for the Warrant lost,
stolen or destroyed, a new Warrant of like tenor and representing an equivalent
right or interest, but only upon receipt of evidence satisfactory to the Company
and the Warrant Agent of such loss, theft or destruction of such Warrants and
indemnity, if requested, also satisfactory to them. Applicants for such
substitute Warrants shall also comply with such other reasonable regulations and
pay such other reasonable charges as the Company or the Warrant Agent may
prescribe. Any such new Warrant shall constitute an original contractual
obligation of the Company whether or not the allegedly lost, stolen, mutilated
or destroyed Warrant shall be at any time enforceable by anyone.

      SECTION 8. RESERVATION OF SHARES, ETC. Prior to the issuance of any
Warrants there shall have been reserved, and the Company shall at all times
through the expiration date keep reserved, out of its authorized and unissued
Common Stock, a number of Shares sufficient to provide for the exercise of the
rights of purchase represented by the Warrants, and the Transfer Agent for the
Shares and every subsequent Transfer Agent for the Shares issuable upon the
exercise of any of the rights of purchase aforesaid are hereby irrevocably
authorized and directed at all times to reserve such number of authorized and
unissued Shares as shall be requisite for such purpose. The Company will keep a
copy of this Agreement on file with the Transfer Agent for the Shares and with
every subsequent Transfer Agent for the Shares issuable upon the exercise of the
rights of purchase represented by the Warrants. The Warrant Agent is hereby
irrevocably authorized to requisition from time to time from such Transfer Agent
certificates required to honor outstanding Warrants that have been exercised.
The Company will supply such Transfer Agent with duly executed certificates for
such purpose and will itself provide or otherwise make available any cash which
may be issuable as provided in Section 9 of this Agreement. All Warrants
surrendered in the exercise of the rights thereby evidenced or surrendered for
transfer, exchange or partial exercise shall be cancelled by the Warrant Agent
and shall thereafter be delivered to the Company.

      SECTION 9. WARRANT PRICE; ADJUSTMENTS.

      A. The warrant price per share at which Shares shall be purchasable upon
exercise of Warrants (herein called the "warrant exercise price") to and
including the expiration date (unless the expiration date is extended as
provided below in this Section 9A) shall be $___ per share, or, if adjusted as
provided in this Section, shall be such price as so adjusted. The Warrants will
not be exercisable prior to [the close of business on the date of any initial
issuance thereof] [___] and will expire at 5:00 p.m., New York City time, on the
expiration date; provided that the Company reserves the right to, and may, in
its sole discretion, at any time and from time to time, at such time or times as
the Company so determines, extend the expiration date of the Warrants for such
periods of time as it chooses; further provided that in no case may the
expiration date of the Warrants (as extended) be extended beyond five years from
the expiration date set forth above. Whenever the expiration date of the
Warrants is so extended, the Company shall at least 20 days prior to the then
expiration date cause to be mailed to the Warrant Agent and the registered
holders of the Warrants in accordance with the provisions of Section 17 hereof a
notice stating that the expiration date has been extended and setting forth the
new expiration date.

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      B. The above provision is, however, subject to the following:

      (1) The warrant purchase price, the number of Shares purchasable upon
exercise of each Warrant and the number of Warrants outstanding shall be subject
to adjustment as follows:

            (a) In case the Company shall at any time after the date of this
      Agreement (i) pay a dividend, or make a distribution, on the Common Stock
      which is payable in shares of its capital stock (whether shares of Common
      Stock or of capital stock of any other class), (ii) subdivide or
      reclassify its outstanding shares of Common Stock into a greater number of
      securities (including shares of Common Stock), or (iii) combine or
      reclassify its outstanding shares of Common Stock into a smaller number of
      shares (including shares of Common Stock), the number of shares
      purchasable upon exercise of each Warrant immediately prior to the
      occurrence of such event shall be adjusted so that the holder of each
      Warrant shall be entitled to receive upon payment of the warrant purchase
      price the aggregate number of shares of the Company which, if such Warrant
      had been exercised immediately prior to the occurrence of such event, such
      holder would have owned or have been entitled to receive immediately after
      the occurrence of such event. An adjustment made pursuant to this
      subparagraph (a) shall become effective immediately after the record date
      in the case of a dividend and shall become effective immediately after the
      effective date in the case of a subdivision or combination. If, as a
      result of an adjustment made pursuant to this subparagraph (a), the holder
      of any Warrant thereafter exercised shall become entitled to receive
      shares of two or more classes of capital stock of the Company, the Board
      of Directors of the Company (whose determination shall be conclusive)
      shall determine the allocation between or among shares of such classes of
      capital stock. In the event that at any time, as a result of an adjustment
      made pursuant to this subparagraph (a), the holder of any Warrant
      thereafter exercised shall become entitled to receive any shares or other
      securities of the Company other than shares of Common Stock, thereafter
      the number of such other shares so received upon exercise of any Warrant
      shall be subject to adjustment from time to time in a manner and on terms
      as nearly equivalent as practicable to the provisions with respect to the
      shares of Common Stock contained in this paragraph, and other provisions
      of this paragraph 9B(1) with respect to the shares of Common Stock shall
      apply on like terms to any such other shares or other securities.

            (b) [In case the Company shall fix a record date for the issuance of
      rights or warrants to all holders of its Common Stock entitling them (for
      a period expiring within 45 days after such record date) to subscribe for
      or purchase Common Stock at a price per share less than the current market
      price per share of Common Stock (as defined in subparagraph (e) below) at
      such record date, the warrant purchase price shall be determined by
      multiplying the warrant purchase price in effect immediately prior to such
      record date by a fraction, the numerator of which shall be the number of
      Shares of Common Stock outstanding on such record date plus the number of
      Shares of Common Stock which the aggregate offering price of the total
      number of Shares so offered would purchase at such

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      current market price, and the denominator of which shall be the number of
      Shares of Common Stock outstanding on such record date plus the number of
      additional Shares of Common Stock offered for subscription or purchase.
      Such adjustment shall be made successively whenever such a record date is
      fixed, and shall become effective immediately after such record date. In
      determining whether any rights or warrants entitle the holders to
      subscribe for or purchase Shares of Common Stock at less than such current
      market price, and in determining the aggregate offering price of such
      shares, there shall be taken into account any consideration received by
      the Company for such rights or warrants, the value of such consideration,
      if other than cash, to be determined by the Board of Directors of the
      Company. Common Stock owned by or held for the account of the Company or
      any majority owned subsidiary shall not be deemed outstanding for the
      purpose of any adjustment required under this subparagraph (b).]

            (c) [In case the Company shall fix a record date for making a
      distribution to all holders of its Common Stock of evidences of its
      indebtedness or assets (excluding regular quarterly or other periodic or
      recurring cash dividends or distributions and cash dividends or
      distributions paid from retained earnings or referred to in subparagraph
      (a) above) or rights or warrants to subscribe or warrants to purchase
      (excluding those referred to in subparagraph (b) above), then in each such
      case the warrant purchase price shall be determined by multiplying the
      warrant purchase price in effect immediately prior to such record date by
      a fraction (x) the numerator of which shall be such current market price
      (as defined in subparagraph (e) below) per Share of Common Stock on such
      record date, less the then fair market value (as determined in good faith
      by the Board of Directors, whose determination shall be conclusive) of the
      portion of the assets or evidences of indebtedness so distributed or of
      such subscription rights or warrants applicable to one share of the Common
      Stock and (y) the denominator of which shall be the current market price
      per share of the Common Stock on such record date. Such adjustment shall
      be made successively whenever such a record date is fixed and shall become
      effective immediately after such record date. Notwithstanding the
      foregoing, in the event that the Company shall distribute any rights or
      warrants to acquire capital stock ("Rights") pursuant to this subparagraph
      (c), the distribution of separate certificates representing such Rights
      subsequent to their initial distribution (whether or not such distribution
      shall have occurred prior to the date of the issuance of such Warrants)
      shall be deemed to be the distribution of such Rights for purposes of this
      subparagraph (c), provided that the Company may, in lieu of making any
      adjustment pursuant to this subparagraph (c) upon a distribution of
      separate certificates representing such Rights, make proper provision so
      that each holder of such Warrants who exercises such Warrants (or any
      portion thereof) (A) before the record date for such distribution of
      separate certificates shall be entitled to receive upon such exercise
      shares of Common Stock issued with Rights and (B) after such record date
      and prior to the expiration, redemption or termination of such Rights
      shall be entitled to receive upon such exercise, in addition to the shares
      of Common Stock issuable upon such exercise, the same number of such
      Rights as would a holder of the number of shares of Common Stock that such
      Warrants so exercised would have entitled the

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      holder thereof to purchase in accordance with the terms and provisions of
      and applicable to the Rights if such Warrants were exercised immediately
      prior to the record date for such distribution. Common Stock owned by or
      held for the account of the Company or any majority owned subsidiary shall
      not be deemed outstanding for the purpose of any adjustment required under
      this subparagraph (c).]

            (d) After each adjustment of the number of shares purchasable upon
      exercise of each Warrant pursuant to subparagraph 9B(1)(a), the warrant
      exercise price shall be adjusted by multiplying such warrant exercise
      price immediately prior to such adjustment by a fraction of which the
      numerator shall be the number of Shares purchasable upon exercise of each
      Warrant immediately prior to such adjustment, and the denominator of which
      shall be the number of Shares so purchasable immediately thereafter.
      [After each adjustment of the warrant exercise price pursuant to
      subparagraph 9B(1)(b) or (c), the total number of Shares or fractional
      part thereof purchasable upon the exercise of each Warrant shall be
      proportionately adjusted to such number of shares or fractional parts
      thereof as the aggregate warrant exercise price of the number of shares or
      fractional part thereof purchasable immediately prior to such adjustment
      will buy at the adjusted warrant exercise price.]

            (e) [For the purpose of any computation under subparagraphs 9B(1)(b)
      and (c) above, the current market price per Share of Common Stock at any
      date shall be deemed to be the average of the daily closing prices for the
      30 consecutive business days commencing 45 business days before the day in
      question. The closing price for each day shall be (i) if the Common Stock
      is listed or admitted for trading on the New York Stock Exchange, the last
      sale price (regular way), or the average of the closing bid and ask prices
      (regular way), if no sale occurred, of Common Stock, in either case as
      reported on the New York Stock Exchange Composite Tape or, if the Common
      Stock is not listed or admitted to trading on the New York Stock Exchange,
      on the principal national securities exchange on which the Common Stock is
      listed or admitted to trading or, if not listed or admitted to trading on
      any national securities exchange, on the National Market System of the
      National Association of Securities Dealers, Inc. Automated Quotations
      System ("NASDAQ") or, (ii) if not listed or quoted as described in (i),
      the mean between the closing high bid and low asked quotations of Common
      Stock reported by NASDAQ, or any similar system for automated
      dissemination of quotations of securities prices then in common use, if so
      quoted, or (iii) if not quoted as described in clause (ii), the mean
      between the high bid and low asked quotations for Common Stock as reported
      by the National Quotation Bureau Incorporated if at least two securities
      dealers have inserted both bid and asked quotations for Common Stock on at
      least 5 of the 10 preceding days. If none of the conditions set forth
      above is met, the closing price of Common Stock on any day or the average
      of such closing prices for any period shall be the fair market value of
      Common Stock as determined by a member firm of the New York Stock Exchange
      selected by the Company.]

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            (f) (A) Nothing contained herein shall be construed to require an
      adjustment as a result of the issuance of Common Stock pursuant to, or the
      granting or exercise of any rights under, the Company's [List employee and
      shareholder plans, if any, that might otherwise result in adjustments].

                  (A) In addition, no adjustment in the warrant exercise price
            shall be required unless and until the earlier of the following
            shall have occurred: (x) such adjustment would require an increase
            or decrease of at least 1% in the warrant exercise price or (y) a
            period of 3 years shall have elapsed from the date of the occurrence
            of any event requiring any such adjustment pursuant to subparagraphs
            9B(1)(a), (b) or above. All adjustments shall be made to the nearest
            one hundredth of a Share and the nearest cent, and any adjustments
            which by reason of this subparagraph (f) are not required to be made
            shall be carried forward cumulatively and taken into account in any
            subsequent adjustment which (including such carry-forward) is
            required to be made under this subparagraph (f).

            (g) In any case in which this subparagraph 9B(1) shall require that
      an adjustment be made retroactively immediately following a record date,
      the Company may elect to defer (but only until five business days
      following the mailing of the notice described in subparagraph 9B(5) below)
      issuing to the holder of any Warrant exercised after such record date the
      Shares of the Company issuable upon such exercise over and above the
      Shares issuable upon such exercise only on the basis of the warrant
      exercise price prior to adjustment.

            (h) The Company may, at its option, at any time until the expiration
      date, reduce the then current warrant exercise price to any amount deemed
      appropriate by the Board of Directors of the Company for any period not
      exceeding twenty (20) consecutive days (as evidenced in a resolution
      adopted by such Board of Directors), but only upon giving the notices
      required by subparagraph 9(B)(5) twenty (20) days prior to taking such
      action.

            (i) Except as herein otherwise expressly provided, no adjustment in
      the warrant exercise price shall be made by reason of the issuance of
      Shares, or securities convertible into or exchangeable for Shares, or
      securities carrying the right to purchase any of the foregoing or for any
      other reason whatsoever.

            (j) Irrespective of any of the adjustments in the warrant exercise
      price or the number of Shares, Warrant Certificates theretofore issued may
      continue to express the same prices and number of shares as are stated in
      a similar Warrant Certificate issuable initially, or at some subsequent
      time, pursuant to this Agreement and such number of Shares specified
      therein shall be deemed to have been so adjusted.

      (2) No fractional Shares of Common Stock shall be issued upon the exercise
of Warrants. If more than one Warrant shall be exercised at one time by the same
holder, the number of full Shares which shall be issuable upon such exercise
shall be computed on the basis

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of the aggregate number of Shares purchased pursuant to the Warrants so
exercised. Instead of any fractional Share of Common Stock which would otherwise
be issuable upon exercise of any Warrant, the Company shall pay a cash
adjustment in respect of such fraction in an amount equal to the same fraction
of the last sales price (or bid price if there were no sales) per Share of
Common Stock, in either case as reported on the New York Stock Exchange
Composite Tape on the business day which next precedes the day of exercise or,
if the Common Stock is not then listed or admitted to trading on the New York
Stock Exchange, an amount equal to the same fraction of the market price per
share of Common Stock (as determined in a manner described by the Board of
Directors of the Company) at the close of business on the business day which
next precedes the day of exercise.

      (3) In case any of the following shall occur while any Warrants are
outstanding: (a) any reclassification or change of the outstanding Shares of
Common Stock (other than a change in par value, or from par value to no par
value, or from no par value to par value); or (b) any consolidation or merger to
which the Company is a party (other than a consolidation or a merger in which
the Company is the continuing corporation and which does not result in any
reclassification of, or change in, the outstanding shares of Common Stock
issuable upon exercise of the Warrants); or (c) any sale or conveyance to
another corporation of the property of the Company as an entirety or
substantially as an entirety; then the Company, or such successor or purchasing
corporation, as the case may be, shall make appropriate provision by amendment
of this Agreement or otherwise so that the holders of the Warrants then
outstanding shall have the right at any time thereafter, upon exercise of such
Warrants, to purchase the kind and amount of shares of stock and other
securities and property receivable upon such reclassification, change,
consolidation, merger, sale or conveyance as would be received by a holder of
the number of shares of Common Stock issuable upon exercise of such Warrant
immediately prior to such reclassification, change, consolidation, merger, sale
or conveyance. Such provision shall provide for adjustments which shall be as
nearly equivalent as may be practicable to the adjustments provided for in this
Section 9. The above provisions of this subparagraph 9B(3) shall similarly apply
to successive reclassifications, changes, consolidations, mergers, sales or
conveyances.

      (4) Notwithstanding anything to the contrary contained herein, no
adjustment to the warrant exercise price shall decrease such warrant exercise
price below the then par value of the shares of Common Stock.

      (5) Whenever the warrant exercise price then in effect is adjusted as
herein provided, the Company shall mail to each holder of the Warrants at such
holder's address as it shall appear on the books of the Company a statement
setting forth the adjusted warrant exercise price then and thereafter effective
under the provisions hereof, together with the facts, in reasonable detail, upon
which such adjustment is based.

      (6) In case (i) the Company shall declare a dividend (or any other
distribution) on its Common Stock payable otherwise than in cash out of its
current or retained earnings, or (ii) the Company shall authorize the granting
to the holders of its Common Stock of rights to subscribe for or purchase any
shares of capital stock of any class or of any other rights, or (iii) there is
to be any reclassification of the Common Stock of the Company (other than a
subdivision or combination of its outstanding shares of Common Stock), or any
consolidation or

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merger to which the Company is a party and for which approval of any
shareholders of the Company is required, or (iv) any distribution is to be made
on or in respect of the Common Stock in connection with the dissolution,
liquidation or winding up of the Company, then the Company shall mail to each
holder of Warrants at such holder's address as it shall appear on the books of
the Company, at least twenty days (or ten days in any case specified in clause
(i) or (ii) above) prior to the applicable record date hereinafter specified, a
notice stating (x) the record date for such dividend, distribution or rights,
or, if a record is not to be taken, the date as of which the holders of Common
Stock of record to be entitled to such dividend, distribution or rights are to
be determined, or (y) the date on which such reclassification, consolidation,
merger, dissolution, liquidation or winding up is expected to become effective,
and the date as of which it is expected that holders of Common Stock of record
shall be entitled to exchange their shares of Common Stock for securities or
other property deliverable upon such reclassification, consolidation, merger,
dissolution, liquidation or winding up. No failure to mail such notice nor any
defect therein or in the mailing thereof shall affect any such transaction or
any adjustment in the warrant exercise price required by this Section 9.

      SECTION 10. NOTICE TO WARRANTHOLDERS. Nothing contained in this Agreement
or in any of the Warrants shall be construed as conferring upon the holders
thereof the right to vote or to consent or to receive notice as shareholders in
respect of the meetings of shareholders or the election of directors of the
Company or any other matter, or any rights whatsoever as shareholders of the
Company.

      SECTION 11. CERTAIN COVENANTS OF THE COMPANY.

      A. So long as any unexpired Warrants remain outstanding and if required in
order to comply with the Securities Act of 1933, as amended (the "Act"), the
Company covenants and agrees that it will file such post-effective amendments to
the registration statement filed pursuant to the Act with respect to the
Warrants (File No. 333__) (or such other registration statements or
post-effective amendments or supplements) as may be necessary to permit the
Company to deliver to each person exercising a Warrant a prospectus meeting the
requirements of Section 10(a)(3) of the Act and otherwise complying therewith,
and will deliver such a prospectus to each such person. The Company further
covenants and agrees that it will obtain and keep effective all permits,
consents and approvals of governmental agencies and authorities, and will use
its best efforts to take all action which may be necessary to qualify the Shares
for sale under the securities laws of such of the United States, as may be
necessary to permit the free exercise of the Warrants, and the issuance, sale,
transfer and delivery of the Shares issued upon exercise of the Warrants, and to
maintain such qualifications during the entire period in which the Warrants are
exercisable.

      B. The Company covenants and agrees that it shall take all such action as
may be necessary to ensure that all Shares will at the time of delivery of
certificates for such Shares (subject to payment of the warrant exercise price)
be duly and validly authorized and issued and fully paid and nonassessable
Shares, free from any preemptive rights and taxes, liens, charges and security
interests created by or imposed upon the Company.

      C. The Company covenants and agrees that it will take all action which may
be necessary to cause the Shares to be duly listed on the New York Stock
Exchange or any

                                       10
<PAGE>   11

securities exchange on which the other shares of Common Stock of the Company are
listed or on the National Market System of NASDAQ at the dates of exercise of
the Warrants.

      SECTION 12. DISPOSITION OF PROCEEDS, ETC.

      A. The Warrant Agent shall account promptly to the Company with respect to
Warrants exercised and concurrently pay to the Company all moneys received by
the Warrant Agent for the purchase of Shares through the exercise of such
Warrants.

      B. The Warrant Agent shall keep copies of this Agreement available for
inspection by holders of Warrants during normal business hours at its principal
office in the City of _______________, ____.

      SECTION 13. MERGER OR CONSOLIDATION OR CHANGE OF NAME OF WARRANT AGENT.
Any corporation into which the Warrant Agent may be merged or with which it may
be consolidated, or any corporation resulting from any merger or consolidation
to which the Warrant Agent shall be a party, or any corporation succeeding to
the corporate trust business of the Warrant Agent, shall be the successor to the
Warrant Agent hereunder without the execution or filing of any paper or any
further act on the part of any of the parties hereto, provided that such
corporation would be eligible for appointment as a successor Warrant Agent under
the provisions of Section 15 of this Agreement. In case at the time such
successor to the Warrant Agent shall succeed to the agency created by this
Agreement, and if any of the Warrants shall have been countersigned but not
delivered, any such successor to the Warrant Agent may adopt the
countersignature of the original Warrant Agent and deliver such Warrants so
countersigned; and in case at that time any of the Warrants shall not have been
countersigned, any successor to the Warrant Agent may countersign such Warrants
either in the name of the predecessor Warrant Agent or in the name of the
successor Warrant Agent; and in all such cases such Warrant shall have the full
force provided in the Warrants and in this Agreement. In case at any time the
name of the Warrant Agent shall be changed and at such time any of the Warrants
shall have been countersigned but not delivered, the Warrant Agent may adopt the
countersignature under its prior name and deliver Warrants so countersigned; and
in case at that time any of the Warrants shall not have been countersigned, the
Warrant Agent may countersign such Warrants either in its prior name or in its
changed name; and in all such cases such Warrants shall have the full force
provided in the Warrants and in this Agreement.

      SECTION 14. DUTIES OF WARRANT AGENT. The Warrant Agent undertakes the
duties and obligations imposed by this Agreement upon the following terms and
conditions, by all of which the Company and the holders of Warrants, by their
acceptance thereof, shall be bound:

      A. The statements contained herein and in the Warrants shall be taken as
statements of the Company, and the Warrant Agent assumes no responsibility for
the correctness of any of the same except such as describe the Warrant Agent or
action taken or to be taken by it. The Warrant Agent assumes no responsibility
with respect to the distribution of the Warrants except as herein otherwise
provided.

                                       11
<PAGE>   12

      B. The Warrant Agent shall not be responsible for any failure of the
Company to comply with any of the covenants contained in this Agreement or in
the Warrants to be complied with by the Company.

      C. The Warrant Agent may execute and exercise any of the rights or powers
hereby vested in it or perform any duty hereunder either itself or by or through
its attorneys, agents or employees, and the Warrant Agent shall not be
answerable or accountable for any act, default, neglect or misconduct of any
such attorneys, agents or employees or for any loss to the Company resulting
from such neglect or misconduct, provided reasonable care shall have been
exercised in the selection and continued employment thereof.

      D. The Warrant Agent may consult at any time with counsel satisfactory to
it (who may be counsel for the Company), and the Warrant Agent shall incur no
liability or responsibility to the Company or to any holder of any Warrant in
respect of any action taken, suffered or omitted by it hereunder in good faith
and in accordance with the opinion or the advice of such counsel.

      E. The Warrant Agent shall incur no liability or responsibility to the
Company or to any holder of any Warrant for any action taken in reliance on any
notice, resolution, waiver, consent, order, certificate, or other paper,
document or instrument believed by it to be genuine and to have been signed,
sent or presented by the proper party or parties.

      F. The Company agrees to pay to the Warrant Agent agreed upon compensation
for all services rendered by the Warrant Agent in the execution of this
Agreement, to reimburse the Warrant Agent for all expenses, taxes and
governmental charges and other charges of any kind and nature incurred by the
Warrant Agent in the execution of this Agreement and to indemnify the Warrant
Agent and save it harmless against any and all liabilities, including judgments,
costs and reasonable counsel fees, for anything done or omitted by the Warrant
Agent in the execution of this Agreement except as a result of the Warrant
Agent's negligence, bad faith or willful misconduct.

      G. The Warrant Agent shall be under no obligation to institute any action,
suit or legal proceeding or to take any other action likely to involve expense
unless the Company or one or more registered holders of Warrants shall furnish
the Warrant Agent with reasonable security and indemnity for any costs and
expenses which may be incurred, but this provision shall not affect the power of
the Warrant Agent to take such action as the Warrant Agent may consider proper,
whether with or without any such security or indemnity. All rights of action
under this Agreement or under any of the Warrants may be enforced by the Warrant
Agent without the possession of any of the Warrants or the production thereof at
any trial or other proceeding relative thereto, and any such action, suit or
proceeding instituted by the Warrant Agent shall be brought in its name as
Warrant Agent, and any recovery of judgment shall be for the ratable benefit of
the registered holders of the Warrants, as their respective rights or interests
may appear.

      H. The Warrant Agent and any stockholder, director, officer or employee of
the Warrant Agent may buy, sell or deal in any of the Warrants or other
securities of the Company or become pecuniarily interested in any transaction in
which the Company may be

                                       12
<PAGE>   13

interested, or contract with or lend money to or otherwise act as fully and
freely as though it were not Warrant Agent under this Agreement. Nothing herein
shall preclude the Warrant Agent from acting in any other capacity for the
Company or for any other legal entity.

      I. The Warrant Agent shall act hereunder solely as agent and not in a
ministerial capacity, and its duties shall be determined solely by the
provisions hereof. The Warrant Agent shall not be liable for anything which it
may do or refrain from doing in connection with this Agreement except for its
own gross negligence or bad faith.

      SECTION 15. CHANGE OF WARRANT AGENT. The Warrant Agent may resign and be
discharged from its duties under this Agreement by giving to the Company notice
in writing, and to the holders of the Warrants notice by publication, of such
resignation, specifying a date when such resignation shall take effect, which
notice shall be published at the expense of the Company at least once a week for
two consecutive weeks in a newspaper of general circulation in the City of New
York prior to the date so specified. The Warrant Agent may be removed by the
Company by like notice from the Company to the Warrant Agent and the holders of
Warrants at the expense of the Company. If the Warrant Agent shall resign or be
removed or shall otherwise become incapable of acting, the Company shall appoint
a successor to the Warrant Agent. If the Company shall fail to make such
appointment within a period of 30 days after such removal or after it has been
notified in writing of such resignation or incapacity by the resigning or
incapacitated Warrant Agent or by the registered holder of a Warrant (who shall,
with such notice, submit his Warrant for inspection by the Company), then, at
the expense of the Company, the Warrant Agent or the registered holder of any
Warrant may apply to any court of competent jurisdiction for the appointment of
a successor to the Warrant Agent. Any successor Warrant Agent, whether appointed
by the Company or by such a court, shall be a bank or trust company, in good
standing, incorporated under the laws of any State or of the United States of
America, having at the time of its appointment as Warrant Agent a combined
capital and surplus of at least [$100,000,000]. After appointment the successor
Warrant Agent shall be vested with the same powers, rights, duties and
responsibilities as if it had been originally named as Warrant Agent without
further act or deed; but the former Warrant Agent shall deliver and transfer to
the successor Warrant Agent any property at the time held by it hereunder, and
execute and deliver any further assurance, conveyance, act or deed necessary for
the purpose. Failure to file or publish any notice provided for in this Section,
however, or any defect therein, shall not affect the legality or validity of the
resignation or removal of the Warrant Agent or the appointment of the successor
Warrant Agent, as the case may be.

      SECTION 16. IDENTITY OF TRANSFER AGENT. Forthwith upon the appointment of
any Transfer Agent for the Shares or of any subsequent Transfer Agent for Shares
issuable upon the exercise of the rights of purchase represented by the
Warrants, the Company will file with the Warrant Agent a statement setting forth
the name and address of such Transfer Agent.

      SECTION 17. NOTICES. Any notice pursuant to this Agreement to be given or
made by the Warrant Agent or by the registered holder of any Warrant to or on
the Company shall be sufficiently given or made if sent by first-class mail,
postage prepaid, addressed (until another address is filed in writing by the
Company with the Warrant Agent) as follows:

                                       13
<PAGE>   14
                      IndyMac Bancorp, Inc.
                      155 North Lake Avenue
                      Pasadena, California  91101
                      Attn:  Corporate Secretary

Any notice pursuant to this Agreement to be given or made by the Company or by
the registered holder of any Warrant to or on the Warrant Agent shall be
sufficiently given or made if sent by first-class mail, postage prepaid,
addressed (until another address is filed in writing by the Warrant Agent with
the Company) as follows:

                      ----------------------------------

                      ----------------------------------

                      ----------------------------------

      Any notice pursuant to this Agreement to be given or made by the Company
or the Warrant Agent to the registered holder of any Warrant shall be
sufficiently given or made (unless otherwise specifically provided for herein)
if sent by first-class mail, postage prepaid, addressed to said registered
holder at his address appearing on the Warrant register.

      SECTION 18. SUPPLEMENTS AND AMENDMENTS. The parties hereto may from time
to time supplement or amend this Agreement without the approval of any holders
of Warrants in order to cure any ambiguity or to correct or supplement any
provision contained herein which may be defective or inconsistent with any other
provision herein, or to make any other provisions in regard to matters or
questions arising hereunder which the Company and the Warrant Agent may deem
necessary or desirable and which will not materially adversely affect the
interest of the registered holders of the Warrants. The parties hereto may also
modify or amend this Agreement and the terms of the Warrant Certificates with
the consent of the holders of not less than a majority in number of the then
outstanding unexercised Warrant Certificates affected thereby; provided that no
such modification or amendment that accelerates the expiration date, increases
the exercise price or reduces the number of outstanding Warrant Certificates the
consent of the holders of which is required for any such modification or
amendment, may be made without the consent of each holder affected thereby.

      SECTION 19. SUCCESSORS. All the covenants and provisions of this Agreement
by or for the benefit of the Company or the Warrant Agent shall bind and inure
to the benefit of their respective successors and assigns hereunder.

      SECTION 20. LAW GOVERNING. This Agreement and each Warrant issued
hereunder shall be deemed to be a contract made under the laws of the State of
New York and for all purposes shall be construed in accordance with the laws of
said State.

      SECTION 21. BENEFITS OF THIS AGREEMENT. Nothing in this Agreement shall be
construed to give to any person or entity other than the Company and the Warrant
Agent and the holders of Warrants any legal or equitable right, remedy or claim
under this Agreement, but this Agreement shall be for the sole and exclusive
benefit of the Company and the Warrant Agent and the holders of Warrants.

                                       14
<PAGE>   15

      SECTION 22. COUNTERPARTS. This Agreement may be executed in any number of
counterparts, and each of such counterparts shall for all purposes be deemed to
be an original, and all such counterparts shall together constitute but one and
the same instrument.

[IF THE WARRANTS ARE SUBJECT TO ACCELERATION BY THE COMPANY, INSERT --

      SECTION 23. ACCELERATION OF WARRANTS BY THE COMPANY.

      A. At any time on or after __________________, the Company shall have the
right to accelerate any or all Warrants at any time by causing them to expire at
the close of business on the day next preceding a specified date (the
"Acceleration Date"), if the Market Price (as hereinafter defined) of the Common
Stock equals or exceeds ___ percent (___%) of the then effective warrant
exercise price, adjusted as if no changes in such warrant exercise price had
been made pursuant to subsection 9B, on any 20 Trading Days (as hereinafter
defined) within a period of 30 consecutive Trading Days ending no more than five
Trading Days prior to the date on which the Company gives notice to the Warrant
Agent of its election to accelerate the Warrants.

      B. "Market Price" for each Trading Day shall be, if the Common Stock is
listed or admitted for trading on the New York Stock Exchange, the last reported
sale price, regular way (or, if no such price is reported, the average of the
reported closing bid and asked prices, regular way) of Common Stock, in either
case as reported on the New York Stock Exchange Composite Tape or, if the Common
Stock is not listed or admitted to trading on the New York Stock Exchange, on
the principal national securities exchange on which the Common Stock is listed
or admitted to trading or, if not listed or admitted to trading on any national
securities exchange, on the National Market System of NASDAQ or, if not listed
or admitted to trading on any national securities exchange or quoted on the
National Market System of NASDAQ, the average of the closing high bid and low
asked prices in the over-the-counter market, as reported by NASDAQ, or such
other system then in use, or if on any such date the Shares of Common Stock are
not quoted by any such organization, the average of the closing bid and asked
prices as furnished by any New York Stock Exchange firm selected from time to
time by the Company for the purpose. "Trading Day" shall be each Monday through
Friday, other than any day on which securities are not traded in the system or
on the exchange that is the principal market for the Common Stock, as determined
by the Board of Directors of the Company.

      C. In the event of an acceleration of less than all of the Warrants, the
Warrant Agent shall select the Warrants to be accelerated by lot, pro rata or in
such other manner as it deems, in its discretion, to be fair and appropriate.

      D. Notice of an acceleration specifying the Acceleration Date shall be
sent by mailing first class, postage prepaid, to each registered holder of a
Warrant Certificate representing a Warrant accelerated at such holder's address
appearing on the Warrant register not more than 60 days nor less than 30 days
before the Acceleration Date. Such notice of an acceleration also shall be given
no more than 20 days, and no less than 10 days, prior to the

                                       15
<PAGE>   16

mailing of notice to registered holders of Warrants pursuant to this Section, by
publication at least once in a newspaper of general circulation in the City of
New York.

      E. Any Warrant accelerated may be exercised until 5:00 p.m., New York City
time, on the business day next preceding the Acceleration Date. The warrant
exercise price shall be payable as provided in Section 5.]

                                       16
<PAGE>   17
      IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed, all as of the day and year first above written.

                                        INDYMAC BANCORP, INC.

                                        By:
                                            ------------------------------------
                                            Its:
                                                --------------------------------

Attest:

------------------------------------

                                        [WARRANT AGENT]

                                        By:
                                            ------------------------------------
                                            Its:
                                                --------------------------------

Attest:

------------------------------------

                                       17
<PAGE>   18

                                                                       EXHIBIT A

                                [Form of Warrant]

                     Unless extended, Void After 5:00 P.M.,
                    New York City time, _______*_______, ____

[IF THE WARRANTS ARE ATTACHED TO OTHER SECURITIES, INSERT THE FOLLOWING --
[UNTIL ______,] THE WARRANTS REPRESENTED BY THIS CERTIFICATE SHALL NOT BE
TRANSFERABLE APART FROM THE ___ TO WHICH THEY ARE ATTACHED, ANY TRANSFER OF THE
___ SHALL BE DEEMED A TRANSFER OF THE WARRANTS ATTACHED THERETO, AND ANY ATTEMPT
OF TRANSFER THE WARRANTS APART FROM THE ___ SHALL BE VOID AND OF NO EFFECT.]

No. WA                                                Warrant to Purchase ______
                                                          Shares of Common Stock

                                CLASS___ WARRANT

                              INDYMAC BANCORP, INC.

      FOR VALUE RECEIVED, IndyMac Bancorp, Inc. (the "Company"), upon the
surrender [after __________] and prior to 5:00 P.M., New York City time,
_____*_____, ____ (unless extended) of this Warrant for exercise, with the
exercise form on the reverse side hereof duly executed, at the office of
____________, will sell and deliver or cause to be sold and delivered to
______________ or assigns (the "Warrant Holder") a certificate or certificates
for the number of whole shares purchasable, as indicated above, of fully paid
and non-assessable shares of Common Stock ($0.01 par value) of the Company (the
"Shares"), for which this Warrant is exercised, at a price of $___ per Share
(the "Warrant Price"), subject to all the terms, provisions and conditions of a
Common Stock Warrant Agreement dated as of ___________, ____ (the "Warrant
Agreement"), executed by the Company and _____________________ (the "Warrant
Agent"), which Warrant Agreement is hereby incorporated herein by reference and
made a part hereof.

      1. The Warrant Price shall be payable in cash, certified check, bank
draft, postal or express money order or by bank wire transfer, in each case, in
immediately available funds, payable in United States dollars, to the order of
the Warrant Agent. In certain events the Warrant Price and the number of Shares
deliverable on exercise of this Warrant are subject to adjustments, as provided
in the Warrant Agreement. No certificates for a fractional Share will be issued.
As to any fraction of a Share which would otherwise be purchasable on the
exercise of a Warrant, the Company shall pay the cash value thereof determined
as provided in the Warrant Agreement.

      2. This Warrant is issued in accordance with the Warrant Agreement in
which the rights of the Warrant Holders and the terms, provisions and conditions
upon which this

----------
* The expiration date; see page 1 of the Warrant Agreement.

<PAGE>   19

      Warrant has been executed and delivered and may be exercised are more
fully set forth. Every Warrant Holder, by acceptance hereof, assents to all the
terms, provisions and conditions of the Warrant Agreement. A counterpart of the
Warrant Agreement is on file at the office of the Company in Pasadena,
California, and at the office of the Warrant Agent in ____________, ____.

      3. In the event this Warrant shall not be exercised on or before _____*
_____, ____, unless said date is extended as provided for in Section 9A of the
Warrant Agreement, this Warrant shall become void and all rights hereunder shall
cease.

      Reference is made to the further provisions of this Warrant set forth on
the reverse hereof. Such further provisions shall for all purposes have the same
effect as though fully set forth at this place.

      This Warrant shall not be valid for any purpose until it shall have been
countersigned by the Warrant Agent.

----------
* The expiration date; see page 1 of the Warrant Agreement.

                                      A-2
<PAGE>   20

      IN WITNESS WHEREOF, the Company has caused this Warrant to be executed in
its name and on its behalf by the facsimile signatures of its duly authorized
officers and a facsimile of its seal.

Dated:______________, ________

                                        INDYMAC BANCORP, INC.

                                        By:
                                            ------------------------------------
                                            Its:
                                                 -------------------------------

Attest:

------------------------------------

Countersigned:

------------------------------------

------------------------------------

By:
    --------------------------------

                                      A-3
<PAGE>   21

                              [REVERSE OF WARRANT]

      4. Subject to the provisions of paragraph 3 contained on the face of this
Warrant, (a) this Warrant, with or without other Warrants, upon surrender at the
office of the Warrant Agent, may be exchanged for another Warrant or Warrants of
like tenor in denominations entitling the Warrant Holder to purchase a like
aggregate number of Shares, but only to the extent provided in the Warrant
Agreement, or (b) this Warrant may be transferred at the office of the Warrant
Agent by the Warrant Holder or his assigns, in person or by attorney duly
authorized in writing, but only in the manner provided in the Warrant Agreement
and upon surrender of this Warrant. If this Warrant shall be exercised in part,
the Warrant Holder shall be entitled to receive, upon surrender hereof, another
Warrant or Warrants of like tenor for the number of whole Shares not purchased
upon such exercise.

      5. No Warrant Holder shall be entitled to vote or receive dividends or be
deemed the holder of Shares of the Company for any purpose, nor shall anything
contained in the Warrant Agreement or herein be construed to confer upon the
Warrant Holder, as such, any of the rights of a stockholder of the Company or
any right to vote for the election of directors of the Company, or upon any
matter submitted to stockholders at any meeting thereof, or to give or withhold
consent to any action (whether upon any recapitalization, issue of securities,
reclassification of securities, consolidation, merger, conveyance or otherwise)
or to receive notice of meetings or other action affecting stockholders (except
for notices as provided for in the Warrant Agreement), or to receive dividends
or subscription rights or otherwise, until this Warrant shall have been
exercised and the Shares purchasable on the exercise hereof shall have become
deliverable as provided in the Warrant Agreement.

      6. Every holder of a Warrant, by accepting this Warrant, consents and
agrees with the Company, the Warrant Agent and with every subsequent holder of
this Warrant that until this Warrant is transferred on the books of the Warrant
Agent, the Company and the Warrant Agent may treat the registered holder hereof
as the absolute owner hereof for all purposes notwithstanding any notice to the
contrary.

      7. The Company represents and warrants that the Shares to be issued by it
as provided in the Warrant Agreement have been duly authorized and, when so
issued in accordance with the Warrant Agreement, will be validly issued,
fully-paid and non-assessable. The Company represents and warrants that it has
authority to execute and deliver the Warrant Agreement and the Warrants
thereunder, but the Warrant Agent makes no representation with respect thereto,
or with respect to the validity or sufficiency of the Warrants, the Warrant
Agreement or the Shares.

                                      A-4
<PAGE>   22

                                FORM OF EXERCISE

                    (Form of exercise to be executed by the Warrant Holder
                                   at the time of exercise)

To
   -------------------------------------

                               , Warrant
-------------------------------
Agent:

      The undersigned, holder of the within Warrant, (1) exercises his right to
purchase _________ of the Shares of Common Stock ($0.01 par value) of IndyMac
Bancorp, Inc., which the undersigned is entitled to purchase under the terms of
the within Warrant, and (2) makes payment in full for the number of Shares of
Common Stock so purchased by payment of $________ in cash.

      Please issue the certificate for Shares of Common Stock (and any new
Warrants in the case of a partial exercise) as follows:

                   -------------------------------------------
                               Print or Type Name

                   -------------------------------------------
                   Social Security or other Identifying Number

--------------------------------------------------------------------------------
                                 Street Address

--------------------------------------------------------------------------------
City                                 State                              Zip Code

and deliver it (together with any new Warrants in the case of a partial
exercise) to the above address unless a different address is indicated below.

Dated:
       ----------------

                                        ----------------------------------------
                                                        Signature

                                        (Signature must conform in all respects
                                        to name of holder as specified on the
                                        face of the Warrant)

                                      A-5
<PAGE>   23

To be used only for special
instructions for delivery.

Deliver to:

                   -------------------------------------------
                               Print or Type Name

--------------------------------------------------------------------------------
                   Social Security or other Identifying Number

--------------------------------------------------------------------------------
                                 Street Address

--------------------------------------------------------------------------------
City                                 State                              Zip Code

                                      A-6
<PAGE>   24

                                   ASSIGNMENT

                      (Form of assignment to be executed if
                   Warrant Holder desires to transfer Warrant)

      FOR VALUE RECEIVED, ____________________ hereby sells, assigns and
transfers unto ______________

                   -------------------------------------------
                               Print or Type Name

--------------------------------------------------------------------------------
                   Social Security or other Identifying Number

--------------------------------------------------------------------------------
                                 Street Address

--------------------------------------------------------------------------------
City                                 State                              Zip Code

                   -------------------------------------------
                   Social Security or other Identifying Number

the right represented by the within Warrant to purchase ________ Shares of
Common Stock ($0.01 par value) of IndyMac Bancorp, Inc. to which the within
Warrant relates and appoints _____________ attorney to transfer such right on
the books of the Warrant Agent with full power of substitution in the Premises.

Dated:
       ---------------------------------

                                        ----------------------------------------
                                                        Signature

                                        (Signature must conform in all respects
                                        to name of holder as specified on the
                                        face of the Warrant)

Signature Guaranteed

----------------------------------

                                      A-7<PAGE>   1

                                 EXHIBIT 4.5(b)

                              INDYMAC BANCORP, INC.
                  FORM OF WARRANT AGREEMENT FOR PREFERRED STOCK
                              OR DEPOSITING SHARES

        THIS WARRANT AGREEMENT dated as of ___________, __, between IndyMac
Bancorp, Inc., a Delaware corporation (hereinafter called the "Company,") and
____________, having a corporate trust office in ______________, as warrant
agent (herein called the "Warrant Agent").

        WHEREAS, the Company proposes to sell [if Warrants are sold with other
securities -- [title of such other securities being offered] (the "Offered
Securities") with] warrant certificates evidencing one or more warrants (the
"Warrants" or individually a "Warrant") representing the right to purchase
[title of Preferred Stock or Depositary Shares purchasable through exercise of
Warrants] (the "Warrant Securities"), such warrant certificates and other
warrant certificates issued pursuant to this Agreement being herein called the
"Warrant Certificates"; and

        WHEREAS, the Company desires the Warrant Agent to act on behalf of the
Company in connection with the issuance, exchange, exercise and replacement of
the Warrant Certificates, and in this Agreement wishes to set forth, among other
things, the form and provisions of the Warrant Certificates and the terms and
conditions on which they may be issued, exchanged, exercised and replaced;

        NOW THEREFORE, in consideration of the premises and of the mutual
agreements herein contained, the parties hereto agree as follows:

        *Complete or modify the provisions of this Form as appropriate to
reflect the terms of the Warrants, Warrant Securities and Offered Securities.

                                    ARTICLE I

                       ISSUANCE OF WARRANTS AND EXECUTION
                      AND DELIVERY OF WARRANT CERTIFICATES.

        SECTION 1.01 Issuance of Warrants. [If Warrants alone - Upon issuance,
each Warrant Certificate shall evidence one or more Warrants.] [If Offered
Securities and Warrants -- Warrants shall be [initially] issued in connection
with the issuance of the Offered Securities [but shall be separately
transferable on and after ______ (the "Detachable Date")] [and shall not be
separately transferable] and each Warrant Certificate shall evidence one or more
Warrants.] Each Warrant evidenced thereby shall represent the right, subject to
the provisions contained herein and therein, to purchase one Warrant Security.
[If Offered Securities and Warrants -- Warrant Certificates shall be initially
issued in units with the Offered Securities and each Warrant Certificate
included in such a unit shall evidence ___ Warrants for each [ ___ principal
amount] [___ shares] of Offered Securities included in such unit.]

        SECTION 1.02 Execution and Delivery of Warrant Certificates. Each
Warrant Certificate, whenever issued, shall be in registered form substantially
in the form set forth in

                                       1
<PAGE>   2

Exhibit A hereto, shall be dated ___ and may have such letters, numbers, or
other marks of identification or designation and such legends or endorsements
printed, lithographed or engraved thereon as the officers of the Company
executing the same may approve (execution thereof to be conclusive evidence of
such approval) and as are not inconsistent with the provisions of this
Agreement, or as may be required to comply with any law or with any rule or
regulation made pursuant thereto or with any rule or regulation of any stock
exchange on which the Warrants may be listed, or to conform to usage. The
Warrant Certificates shall be signed on behalf of the Company by the Chairman of
the Board, the President or a Vice President of the Company and by the Treasurer
or one of the Assistant Treasurers or the Secretary or one of the Assistant
Secretaries of the Company under its corporate seal reproduced thereon. Such
signatures may be manual or facsimile signatures of such authorized officers and
may be imprinted or otherwise reproduced on the Warrant Certificates. The seal
of the Company may be in the form of a facsimile thereof and may be impressed,
affixed, imprinted or otherwise reproduced on the Warrant Certificates.

        No Warrant Certificate shall be valid for any purpose, and no Warrant
evidenced thereby shall be exercisable, until such Warrant Certificate has been
countersigned by the manual or facsimile signature of the Warrant Agent. Such
signature by the Warrant Agent upon any Warrant Certificate executed by the
Company shall be conclusive evidence that the Warrant Certificate so
countersigned has been duly issued hereunder.

        In case any officer of the Company who shall have signed any of the
Warrant Certificates either manually or by facsimile signature shall cease to be
such officer before the Warrant Certificates so signed shall have been
countersigned and delivered by the Warrant Agent, such Warrant Certificates may
be countersigned and delivered notwithstanding that the person who signed such
Warrant Certificates ceased to be such officer of the Company; and any Warrant
Certificate may be signed on behalf of the Company by such persons as, at the
actual date of the execution of such Warrant Certificate, shall be the proper
officers of the Company, although at the date of the execution of this Agreement
any such person was not such officer.

        The term "holder" or "holder of a Warrant Certificate" as used herein
shall mean any person in whose name any Warrant Certificate shall be registered
upon the books to be maintained by the Warrant Agent for that purpose [If
Offered Securities and Warrants are not immediately detachable -- or upon the
register of the Offered Securities prior to the Detachable Date. Prior to the
Detachable Date, the Company will, or will cause the Registrar of the Offered
Securities to, make available at all times to the Warrant Agent such information
as to holders of the Offered Securities with Warrants as may be necessary to
keep the Warrant Agent's records up to date].

        SECTION 1.03 Issuance of Warrant Certificates. Warrant Certificates
evidencing the right to purchase up to ___ Warrant Securities (except as
provided in Sections 2.03(c), 3.02 and 4.01) may be executed by the Company and
delivered to the Warrant Agent upon the execution of this Warrant Agreement or
from time to time thereafter. The Warrant Agent shall, upon receipt of Warrant
Certificates duly executed on behalf of the Company, countersign Warrant
Certificates evidencing Warrants representing the right to purchase up to ___
Warrant Securities and shall deliver such Warrant Certificates to or upon the
order of the Company. Subsequent to such original issuance of the Warrant
Certificates, the Warrant Agent shall countersign a Warrant

                                       2
<PAGE>   3

Certificate only if the Warrant Certificate is issued in exchange or
substitution for one or more previously countersigned Warrant Certificates or in
connection with their transfer, as hereinafter provided.

                                   ARTICLE II

                           WARRANT PRICE, DURATION AND
                              EXERCISE OF WARRANTS.

        SECTION 2.01 Warrant Price. During the period from ___________________,
through and including ___________________, the exercise price of each Warrant
will be $_______. During the period from _______________________, through and
including ________________, the exercise price of each Warrant will be
_________________________. Such purchase price of Warrant Securities is referred
to in this Agreement as the "Warrant Price". No adjustment shall be made for any
dividends on any Warrant Securities issuable upon exercise of any Warrant.

        SECTION 2.02 Duration of Warrants. Each Warrant may be exercised in
whole at any time, as specified herein, on or after [the date thereof]
[_____________] and at or before 5 P.M., New York City time, on ________________
or such later date as the Company may designate, by notice to the Warrant Agent
and the holders of Warrant Certificates mailed to their addresses as set forth
in the record books of the Warrant Agent (the "Expiration Date"). Each Warrant
not exercised at or before 5 P.M., New York City time, on the Expiration Date
hall become void, and all rights of the holder of the Warrant Certificate
evidencing such Warrant under this Agreement shall cease.

        SECTION 2.03 Exercise of Warrants.

               (a) During the period specified in Section 2.02, any whole number
of Warrants may be exercised by providing certain information as set forth on
the reverse side of the Warrant Certificate and by paying in full, in [lawful
money of the United States of America] [in cash or by certified check or
official bank check or by bank wire transfer, in each case,] [by bank wire
transfer] [in immediately available funds] the Warrant Price for each Warrant
exercised to the Warrant Agent at its corporate trust office [or at
___________________], provided that such exercise is subject to receipt within
five business days of such [payment] [wire transfer] by the Warrant Agent of the
Warrant Certificate with the form of election to purchase Warrant Securities set
forth on the reverse side of the Warrant Certificate properly completed and duly
executed. The date on which payment in full of the Warrant Price is received by
the Warrant Agent shall, subject to receipt of the Warrant Certificate as
aforesaid, be deemed to be the date on which the Warrant is exercised. The
Warrant Agent shall deposit all funds received by it in payment of the Warrant
Price in an account of the Company maintained with it and shall advise the
Company by telephone at the end of each day on which a [payment] [wire transfer]
for the exercise of Warrants is received of the amount so deposited to its
account. The Warrant Agent shall promptly confirm such telephone advice to the
Company in writing.

               (b) The Warrant Agent shall, from time to time, as promptly as
practicable, advise the Company of (i) the number of Warrants exercised, (ii)
the instructions of each holder

                                       3
<PAGE>   4

of the Warrant Certificates evidencing such Warrants with respect to delivery of
the Warrant Securities to which such holder is entitled upon such exercise,
(iii) delivery of Warrant Certificates evidencing the balance, if any, of the
Warrants remaining after such exercise, and (iv) such other information as the
Company shall reasonably require.

               (c) As soon as practicable after the exercise of any Warrant, the
Company shall issue to or upon the order of the holder of the Warrant
Certificate evidencing such Warrant the Warrant Securities to which such holder
is entitled, in fully registered form, registered in such name or names as may
be directed by such holder. If fewer than all of the Warrants evidenced by such
Warrant Certificate are exercised, the Company shall execute, and an authorized
officer of the Warrant Agent shall manually countersign and deliver, a new
Warrant Certificate evidencing the number of such Warrants remaining
unexercised.

               (d) The Company shall not be required to pay any stamp or other
tax or other governmental charge required to be paid in connection with any
transfer involved in the issue of the Warrant Securities, and in the event that
any such transfer is involved, the Company shall not be required to issue or
deliver any Warrant Security until such tax or other charge shall have been paid
or it has been established to the Company's satisfaction that no such tax or
other charge is due.

               (e) Prior to the issuance of any Warrants there shall have been
reserved, and the Company shall at all times keep reserved, out of its
authorized but unissued Warrant Securities, a number of shares sufficient to
provide for the exercise of the Warrant Certificates.

                                   ARTICLE III

                       OTHER PROVISIONS RELATING TO RIGHTS
                       OF HOLDERS OF WARRANT CERTIFICATES.

        SECTION 3.01 No Rights as Warrant Securityholder Conferred by Warrants
or Warrant Certificates. No Warrant Certificates or Warrant evidenced thereby
shall entitle the holder thereof to any of the rights of a holder of Warrant
Securities, including, without limitation, the right to receive the payment of
dividends or distributions, if any, on the Warrant Securities or to exercise any
voting rights.

        SECTION 3.02 Lost, Stolen, Mutilated or Destroyed Warrant Certificates.
Upon receipt by the Warrant Agent of evidence reasonably satisfactory to it and
the Company of the ownership of and the loss, theft, destruction or mutilation
of any Warrant Certificate and of indemnity reasonably satisfactory to the
Warrant Agent and the Company and, in the case of mutilation, upon surrender
thereof to the Warrant Agent for cancellation, then, in the absence of notice to
the Company or the Warrant Agent that such Warrant Certificate has been acquired
by a bona fide purchaser, the Company shall execute, and an authorized officer
of the Warrant Agent shall manually countersign and deliver, in exchange for or
in lieu of the lost, stolen, destroyed or mutilated Warrant Certificate, a new
Warrant Certificate of the same tenor and evidencing a like number of Warrants.
Upon the issuance of any new Warrant Certificate under this Section, the Company
may require the payment of a sum sufficient to cover any tax or other
governmental charge that may be imposed in relation thereto and any other
expenses (including

                                       4
<PAGE>   5

the fees and expenses of the Warrant Agent) in connection therewith. Every
substitute Warrant Certificate executed and delivered pursuant to this Section
in lieu of any lost, stolen or destroyed Warrant Certificate shall represent an
additional contractual obligation of the Company, whether or not the lost,
stolen or destroyed Warrant Certificate shall be at any time enforceable by
anyone, and shall be entitled to the benefits of this Agreement equally and
proportionately with any and all other Warrant Certificates duly executed and
delivered hereunder. The provisions of this Section are exclusive and shall
preclude (to the extent lawful) all other rights and remedies with respect to
the replacement of mutilated, lost, stolen or destroyed Warrant Certificates.

        SECTION 3.03 Holder of Warrant Certificate May Enforce Rights.
Notwithstanding any of the provisions of this Agreement, any holder of a Warrant
Certificate, without the consent of the Warrant Agent, the holder of any Warrant
Securities or the holder of any other Warrant Certificate, may, in such holder's
own behalf and for such holder's own benefit, enforce, and may institute and
maintain any suit, action or proceeding against the Company suitable to enforce,
or otherwise in respect of, such holder's right to exercise the Warrants
evidenced by such holder's Warrant Certificate in the manner provided in such
holder's Warrant Certificate and in this Agreement.

        SECTION 3.04 Reclassification, Consolidation, Merger, Sale, Conveyance
or Lease. In case any of the following shall occur while any Warrants are
outstanding: (a) any reclassification or change of the outstanding shares of
Warrant Securities; or (b) any consolidation or merger to which the Company is
party (other than a consolidation or a merger in which the Company is the
continuing corporation and which does not result in any reclassification of, or
change in, the outstanding shares of Warrant Securities issuable upon exercise
of the Warrants); or (c) any sale, conveyance or lease to another corporation of
the property of the Company as an entirety or substantially as an entirety; then
the Company, or such successor or purchasing corporation, as the case may be,
shall make appropriate provision by amendment of this Agreement or otherwise so
that the holders of the Warrants then outstanding shall have the right at any
time thereafter, upon exercise of such Warrants, to purchase the kind and amount
of shares of stock and other securities and property receivable upon such a
reclassification, change, consolidation, merger, sale, conveyance or lease as
would be received by a holder of the number of shares of Warrant Securities
issuable upon exercise of such Warrant immediately prior to such
reclassification, change, consolidation, merger, sale, conveyance or lease, and,
in the case of a consolidation, merger, sale, conveyance or lease, the Company
shall thereupon be relieved of any further obligation hereunder or under the
Warrants, and the Company as the predecessor corporation may thereupon or at any
time thereafter be dissolved, wound up or liquidated. Such successor or assuming
corporation thereupon may cause to be signed, and may issue either in its own
name or in the name of the Company, any or all of the Warrants issuable
hereunder which heretofore shall not have been signed by the Company, and may
execute and deliver Warrant Securities in its own name, in fulfillment of its
obligations to deliver Warrant Securities upon exercise of the Warrants. All the
Warrants so issued shall in all respects have the same legal rank and benefit
under this Agreement as the Warrants theretofore or thereafter issued in
accordance with the terms of this Agreement as though all of such Warrants had
been issued at the date of the execution hereof. In any case of any such
reclassification, change, consolidation, merger, conveyance, transfer or lease,
such changes in phraseology and form (but not in substance) may be made in the
Warrants thereafter to be issued as may be appropriate.

                                       5
<PAGE>   6

        The Warrant Agent may receive a written opinion of legal counsel as
conclusive evidence that any such reclassification, change, consolidation,
merger, conveyance, transfer or lease complies with the provisions of this
Section 3.04.

                                   ARTICLE IV

                              EXCHANGE AND TRANSFER
                            OF WARRANT CERTIFICATES.

        SECTION 4.01 Exchange and Transfer of Warrant Certificates. [If Offered
Securities with Warrants which are immediately detachable -- Upon] [If Offered
Securities with Warrants which are not immediately detachable -- Prior to the
Detachable Date a Warrant Certificate may be exchanged or transferred only
together with the Offered Security to which the Warrant Certificate was
initially attached, and only for the purpose of effecting or in conjunction with
an exchange or transfer of such Offered Security. Prior to any Detachable Date,
each transfer of the Offered Security [on the register of the Offered
Securities] shall operate also to transfer the related Warrant Certificates.
After the Detachable Date upon] surrender at the corporate trust office of the
Warrant Agent [or _____________________], Warrant Certificates evidencing
Warrants may be exchanged for Warrant Certificates in other denominations
evidencing such Warrants or the transfer thereof may be registered in whole or
in part; provided that such other Warrant Certificates evidence the same
aggregate number of Warrants as the Warrant Certificates so surrendered. The
Warrant Agent shall keep, at its corporate trust office [and
at_____________________], books in which, subject to such reasonable regulations
as it may prescribe, it shall register Warrant Certificates and exchanges and
transfers of outstanding Warrant Certificates, upon surrender of the Warrant
Certificates to the Warrant Agent at its corporate trust office [or
_____________________] for exchange or registration of transfer, properly
endorsed or accompanied by appropriate instruments of registration of transfer
and written instructions for transfer, all in form satisfactory to the Company
and the Warrant Agent. No service charge shall be made for any exchange or
registration of transfer of Warrant Certificates, but the Company may require
payment of a sum sufficient to cover any stamp or other tax or other
governmental charge that may be imposed in connection with any such exchange or
registration of transfer. Whenever any Warrant Certificates are so surrendered
for exchange or registration of transfer, an authorized officer of the Warrant
Agent shall manually countersign and deliver to the person or persons entitled
thereto a Warrant Certificate or Warrant Certificates duly authorized and
executed by the Company, as so requested. The Warrant Agent shall not be
required to effect any exchange or registration of transfer which will result in
the issuance of a Warrant Certificate evidencing a fraction of a Warrant or a
number of full Warrants and a fraction of a Warrant. All Warrant Certificates
issued upon any exchange or registration of transfer of Warrant Certificates
shall be the valid obligations of the Company, evidencing the same obligations
and entitled to the same benefits under this Agreement as the Warrant
Certificate surrendered for such exchange or registration of transfer.

        SECTION 4.02 Treatment of Holders of Warrant Certificates. [If Offered
Securities and Warrants are not immediately detachable -- Prior to the
Detachable Date, the Company, the Warrant Agent and all other persons may treat
the owner of the Offered Security as the owner of the Warrant Certificates
initially attached thereto for any purpose and as the person entitled to
exercise the rights represented by the Warrants evidenced by such Warrant
Certificates, any

                                       6
<PAGE>   7

notice to the contrary notwithstanding. After the Detachable Date and prior to
due presentment of a Warrant Certificate for registration of transfer,] [T]he
Company and the Warrant Agent may treat the registered holder of a Warrant
Certificate as the absolute owner thereof for any purpose and as the person
entitled to exercise the rights represented by the Warrants evidenced thereby,
any notice to the contrary notwithstanding.

        SECTION 4.03 Cancellation of Warrant Certificates. Any Warrant
Certificate surrendered for exchange, registration of transfer or exercise of
the Warrants evidenced thereby shall, if surrendered to the Company, be
delivered to the Warrant Agent and all Warrant Certificates surrendered or so
delivered to the Warrant Agent shall be promptly cancelled by the Warrant Agent
and shall not be reissued and, except as expressly permitted by this Agreement,
no Warrant Certificate shall be issued hereunder in exchange therefor or in lieu
thereof. The Warrant Agent shall deliver to the Company from time to time or
otherwise dispose of cancelled Warrant Certificates in a manner satisfactory to
the Company.

                                    ARTICLE V

                          CONCERNING THE WARRANT AGENT.

        SECTION 5.01 Warrant Agent. The Company hereby appoints
__________________ as Warrant Agent of the Company in respect of the Warrants
and the Warrant Certificates upon the terms and subject to the conditions herein
set forth; and _________________________ hereby accepts such appointment. The
Warrant Agent shall have the powers and authority granted to and conferred upon
it in the Warrant Certificates and hereby and such further powers and authority
to act on behalf of the Company as the Company may hereafter grant to or confer
upon it. All of the terms and provisions with respect to such powers and
authority contained in the Warrant Certificates are subject to and governed by
the terms and provisions hereof.

        SECTION 5.02 Conditions of Warrant Agent's Obligations. The Warrant
Agent accepts its obligations herein set forth upon the terms and conditions
hereof, including the following to all of which the Company agrees and to all of
which the rights hereunder of the holders from time to time of the Warrant
Certificates shall be subject:

               (a) Compensation and Indemnification. The Company agrees promptly
to pay the Warrant Agent the compensation to be agreed upon with the Company for
all services rendered by the Warrant Agent and to reimburse the Warrant Agent
for reasonable out-of-pocket expenses (including counsel fees) incurred other
than as a result of the Warrant Agent's negligence, bad faith or willful
misconduct in connection with the services rendered hereunder by the Warrant
Agent. The Company also agrees to indemnify the Warrant Agent for, and to hold
it harmless against, any loss, liability or expense incurred other than as a
result of the Warrant Agent's negligence, bad faith or willful misconduct,
arising out of or in connection with its acting as Warrant Agent hereunder, as
well as the costs and expenses of defending against any claim of such liability.

               (b) Agent for the Company. In acting under this Warrant Agreement
and in connection with the Warrant Certificates, the Warrant Agent is acting
solely as agent of the

                                       7
<PAGE>   8

Company and does not assume any obligations or relationship of agency or trust
for or with any of the holders of Warrant Certificates or beneficial owners of
Warrants.

               (c) Counsel. The Warrant Agent may consult with counsel
satisfactory to it, and the written advice of such counsel shall be full and
complete authorization and protection in respect of any action taken, suffered
or omitted by it hereunder in good faith and in accordance with the advice of
such counsel.

               (d) Documents. The Warrant Agent shall be protected and shall
incur no liability for or in respect of any action taken or thing suffered by it
in reliance upon any Warrant Certificate, notice, direction, consent,
certificate, affidavit, statement or other paper or document reasonably believed
by it to be genuine and to have been presented or signed by the proper parties.

               (e) Certain Transactions. The Warrant Agent, and its
stockholders, officers, directors and employees, may become the owner of, or
acquire any interest in, Warrants, with the same rights that it or they would
have if it were not the Warrant Agent hereunder, and, to the extent permitted by
applicable law, it or they may engage or be interested in any financial or other
transaction with the Company and may act on, or as depositary, trustee or agent
for, any committee or body of holders of Warrant Securities or other obligations
of the Company as freely as if it were not the Warrant Agent hereunder. Nothing
in this Warrant Agreement shall be deemed to prevent the Warrant Agent from
acting in any other capacity for the Company or for any other legal entity.

               (f) No Liability for Interest. Unless otherwise agreed with the
Company, the Warrant Agent shall have no liability for interest on any monies at
any time received by it pursuant to any of the provisions of this Agreement or
of the Warrant Certificates.

               (g) No Liability for Invalidity. The Warrant Agent shall have no
liability with respect to any invalidity of this Agreement or any of the Warrant
Certificates (except as to the Warrant Agent's countersignature thereon).

               (h) No Responsibility for Representations. The Warrant Agent
shall not be responsible for any of the recitals or representations herein or in
the Warrant Certificates (except as to the Warrant Agent's countersignature
thereon), all of which are made solely by the Company.

               (i) No Implied Obligations. The Warrant Agent shall be obligated
to perform only such duties as are herein and in the Warrant Certificates
specifically set forth and no implied duties or obligations shall be read into
this Agreement or the Warrant Certificates against the Warrant Agent. The
Warrant Agent shall not be under any obligation to take any action hereunder
which may tend to involve it in any expense or liability, the payment of which
within a reasonable time is not, in its reasonable opinion, assured to it. The
Warrant Agent shall not be accountable or under any duty or responsibility for
the use by the Company of any of the Warrant Certificates authenticated by the
Warrant Agent and delivered by it to the Company pursuant to this Agreement or
for the application by the Company of the proceeds of the Warrant Certificates.
The Warrant Agent shall have no duty or responsibility in case of any default by
the

                                       8
<PAGE>   9

Company in the performance of its covenants or agreements contained herein or in
the Warrant Certificates or in the case of the receipt of any written demand
from a holder of a Warrant Certificate with respect to such default, including,
without limiting the generality of the foregoing, any duty or responsibility to
initiate or attempt to initiate any proceedings at law or otherwise or, except
as provided in Section 6.02 hereof, to make any demand upon the Company.

        SECTION 5.03 Resignation and Appointment of Successor.

               (a) The Company agrees, for the benefit of the holders from time
to time of the Warrant Certificates, that there shall it all times be a Warrant
Agent hereunder until all the Warrants have been exercised or are no longer
exercisable.

               (b) The Warrant Agent may at any time resign as such agent by
giving written notice to the Company of such intention on its part, specifying
the date on which its desired resignation shall become effective; provided that
such date shall not be less than three months after the date on which such
notice is given unless the Company otherwise agrees. The Warrant Agent hereunder
may be removed at any time by the filing with it of an instrument in writing
signed by or on behalf of the Company and specifying such removal and the
intended date when it shall become effective. Such resignation or removal shall
take effect upon the appointment by the Company, as hereinafter provided, of a
successor Warrant Agent (which shall be a bank or trust company authorized under
the laws of the jurisdiction of its organization to exercise corporate trust
powers) and the acceptance of such appointment by such successor Warrant Agent.
The obligation of the Company under Section 5.02(a) shall continue to the extent
set forth therein notwithstanding the resignation or removal of the Warrant
Agent.

               (c) In case at any time the Warrant Agent shall resign, or shall
be removed, or shall become incapable of acting, or shall be adjudged a bankrupt
or insolvent, or shall commence a voluntary case under the Federal bankruptcy
laws, as now or hereafter constituted, or under any other applicable Federal or
State bankruptcy, insolvency or similar law or shall consent to the appointment
of or taking possession by a receiver, custodian, liquidator, assignee, trustee,
sequestrator (or other similar official) of the Warrant Agent or its property or
affairs, or shall make an assignment for the benefit of creditors, or shall
admit in writing its inability to pay its debts generally as they become due, or
shall take corporate action in furtherance of any such action, or a decree or
order for relief by a court having jurisdiction in the premises shall have been
entered in respect of the Warrant Agent in an involuntary case under the Federal
bankruptcy laws, as now or hereafter constituted, or any other applicable
Federal or State bankruptcy, insolvency or similar law, or a decree or order by
a court having jurisdiction in the premises shall have been entered for the
appointment of a receiver, custodian, liquidator, assignee, trustee,
sequestrator (or similar official) of the Warrant Agent or of its property or
affairs, or any public officer shall take charge or control of the Warrant Agent
or of its property or affairs for the purpose of rehabilitation, conservation,
winding up or liquidation, a successor Warrant Agent, qualified as aforesaid,
shall be appointed by the Company by an instrument in writing, filed with the
successor Warrant Agent. Upon the appointment as aforesaid of a successor
Warrant Agent and acceptance by the successor Warrant Agent of such appointment,
the Warrant Agent shall cease to be Warrant Agent hereunder.

                                       9
<PAGE>   10

               (d) Any successor Warrant Agent appointed hereunder shall
execute, acknowledge and deliver to its predecessor and to the Company an
instrument accepting such appointment hereunder, and thereupon such successor
Warrant Agent, without any further act, deed or conveyance, shall become vested
with all the authority, rights, powers, trusts, immunities, duties and
obligations of such predecessor with like effect as if originally named as
Warrant Agent hereunder, and such predecessor, upon payment of its charges and
disbursements then unpaid, shall thereupon become obligated to transfer, deliver
and pay over, and such successor Warrant Agent shall be entitled to receive, all
monies, securities and other property on deposit with or held by such
predecessor, as Warrant Agent hereunder.

               (e) Any corporation into which the Warrant Agent hereunder may be
merged or converted or any corporation with which the Warrant Agent may be
consolidated, or any corporation resulting from any merger, conversion or
consolidation to which the Warrant Agent shall be a party, or any corporation to
which the Warrant Agent shall sell or otherwise transfer all or substantially
all the assets and business of the Warrant Agent, provided that it shall be
qualified as aforesaid, shall be the successor Warrant Agent under this
Agreement without the execution or filing of any paper or any further act on the
part of any of the parties hereto.

                                   ARTICLE VI

                                 MISCELLANEOUS.

        SECTION 6.01 Amendment. This Agreement may be amended by the parties
hereto, without the consent of the holder of any Warrant Certificate, for the
purpose of curing any ambiguity, or of curing, correcting or supplementing any
defective provision contained herein, or making any other provisions with
respect to matters or questions arising under this Agreement as the Company and
the Warrant Agent may deem necessary or desirable; provided that such action
shall not materially adversely affect the interests of the holders of the
Warrant Certificates.

        The parties hereto may also modify or amend this Agreement and the terms
of the Warrant Certificates with the consent of the holders of not less than a
majority in number of the then outstanding unexercised Warrant Certificates
affected thereby; provided that no such modification or amendment that
accelerates the expiration date, increases the exercise price or reduces the
number of outstanding Warrant Certificates the consent of the holders of which
is required for any such modification or amendment, may be made without the
consent of each holder affected thereby.

        SECTION 6.02 Notices and Demands to the Company and Warrant Agent. If
the Warrant Agent shall receive any notice or demand addressed to the Company by
the holder of a Warrant Certificate pursuant to the provisions of the Warrant
Certificates, the Warrant Agent shall promptly forward such notice or demand to
the Company.

        SECTION 6.03 Addresses. Any communication from the Company to the
Warrant Agent with respect to this Agreement shall be addressed to ____________,
Attention: ______ and any communication from the Warrant Agent to the Company
with respect to this Agreement shall be addressed to IndyMac Bancorp, Inc., 155
North Lake Avenue, Pasadena, California

                                       10
<PAGE>   11

91101, (or such other address as shall be specified in writing by the Warrant
Agent or by the Company).

        SECTION 6.04 Applicable Law. The validity, interpretation and
performance of this Agreement and each Warrant Certificate issued hereunder and
of the respective terms and provisions thereof shall be governed by, and
construed in accordance with, the laws of the State of New York.

        SECTION 6.05 Delivery of Prospectus. The Company shall furnish to the
Warrant Agent sufficient copies of a prospectus relating to the Warrant
Securities deliverable upon exercise of the Warrants (the "Prospectus"), and the
Warrant Agent agrees that upon the exercise of any Warrant, the Warrant Agent
will deliver to the holder of the Warrant Certificate evidencing such Warrant,
prior to or concurrently with the delivery of the Warrant Securities issued upon
such exercise, a Prospectus. The Warrant Agent shall not, by reason of any such
delivery, assume any responsibility for the accuracy or adequacy of such
Prospectus.

        SECTION 6.06 Obtaining of Governmental Approvals. The Company will from
time to time take all action which may be necessary to obtain and keep effective
any and all permits, consents and approvals of governmental agencies and
authorities and securities act filings under United States Federal and State
laws (including without limitation a registration statement in respect of the
Warrants and Warrant Securities under the Securities Act of 1933), which may be
or become requisite in connection with the issuance, sale, transfer, and
delivery of the Warrant Securities issued upon exercise of the Warrant
Certificates, the exercise of the Warrants, the issuance, sale, transfer and
delivery of the Warrants or upon the expiration of the period during which the
Warrants are exercisable.

        SECTION 6.07 Persons Having Rights under Warrant Agreement. Nothing in
this Agreement shall give to any person other than the Company, the Warrant
Agent and the holders of the Warrant Certificates any right, remedy or claim
under or by reason of this Agreement.

        SECTION 6.08 Headings. The descriptive headings of the several Articles
and Sections of this Agreement are inserted for convenience only and shall not
control or affect the meaning or construction of any of the provisions hereof.

        SECTION 6.09 Counterparts. This Agreement may be executed in any number
of counterparts, each of which as so executed shall be deemed to be an original,
but such counterparts shall together constitute but one and the same instrument.

        SECTION 6.010 Inspection of Agreement. A copy of this Agreement shall be
available at all reasonable times at the principal corporate trust office of the
Warrant Agent for inspection by the holder of any Warrant Certificate. The
Warrant Agent may require such holder to submit his Warrant Certificate for
inspection by it.

                                       11
<PAGE>   12

        IN WITNESS WHEREOF, IndyMac Bancorp, Inc. and ______ have caused this
Agreement to be signed by their respective duly authorized officers, and their
respective corporate seals to be affixed hereunto, and the same to be attested
by their respective Secretaries or one of their respective Assistant
Secretaries, all as of the day and year first above written.

                                            INDYMAC BANCORP, INC.

                                            By:
                                               --------------------------------
                                                 Title:

Attest:

---------------------------
Title:

                                            [WARRANT AGENT]

                                            By
                                               --------------------------------
                                                 Title:

Attest:

---------------------------
Title:

                                       12
<PAGE>   13

                                    EXHIBIT A

                           FORM OF WARRANT CERTIFICATE
                          [Face of Warrant Certificate]

<TABLE>
<S>                                                <C>
[Form of Legend if Offered Securities with        Prior to _________ this Warrant  Certificate
Warrants which are not immediately detachable.    cannot be transferred or exchanged unless
                                                  attached to a [Title of Offered Securities].

[Form of Legend if Warrants are not immediately   Prior to ___________, Warrants evidenced by
exercisable.                                      this Warrant Certificate cannot be exercised.]

</TABLE>

                EXERCISABLE ONLY IF COUNTERSIGNED BY THE WARRANT
                            AGENT AS PROVIDED HEREIN

                              INDYMAC BANCORP, INC.
                              WARRANTS TO PURCHASE
                          [Title of Warrant Securities]

          VOID AFTER 5 P.M., NEW YORK CITY TIME, ON __________________

                                         No. ______________  __________ Warrants

        This certifies that _________________ or registered assigns is the
registered owner of the above indicated number of Warrants, each Warrant
entitling such owner [if Offered Securities with Warrants which are not
immediately detachable --, subject to the registered owner qualifying as a
"holder" of this Warrant Certificate, as hereinafter defined) to purchase, at
any time [after 5 P.M., New York City time, on ____ and] on or before 5 P.M.,
New York City time, on _________, __, shares of [Title of Warrant Securities]
(the "Warrant Securities"), of IndyMac Bancorp, Inc. (the "Company") on the
following basis: during the period from ____, through and including ______, the
exercise price of each Warrant will be ___________; during the period from
________________, through and including ___________, the exercise price of each
Warrant will be (the "Warrant Price"). No adjustment shall be made for any
dividends on any Warrant Securities issuable upon exercise of any Warrant. The
holder may exercise the Warrants evidenced hereby by providing certain
information set forth on the back hereof and by paying in full [in lawful money
of the United States of America] [in cash or by certified check or official bank
check or by bank wire transfer, in each case,] [by bank wire transfer] in
immediately available funds, the Warrant Price for each Warrant exercised to the
Warrant Agent (as hereinafter defined) and by surrendering this Warrant
Certificate, with the purchase form on the back hereof duly executed, at the
corporate trust office of [name of Warrant Agent], or its successor as warrant
agent (the "Warrant Agent"), [or ________], which is, on the date hereof, at the
address specified on the reverse hereof, and upon compliance with and subject to
the conditions set forth herein and in the Warrant Agreement (as hereinafter
defined).

        The term "holder" as used herein shall mean [if Offered Securities with
Warrants which are not immediately detachable --, prior to ______ (the
"Detachable Date"), the registered owner of the Company's [title of Offered
Securities] to which this Warrant Certificate is initially

                                      A-1
<PAGE>   14

attached, and after such Detachable Date,] the person in whose name at the time
this Warrant Certificate shall be registered upon the books to be maintained by
the Warrant Agent for that purpose pursuant to Section 4.01 of the Warrant
Agreement.

        Any whole number of Warrants evidenced by this Warrant Certificate may
be exercised to purchase Warrant Securities in registered form. Upon any
exercise of fewer than all of the Warrants evidenced by this Warrant
Certificate, there shall be issued to the holder hereof a new Warrant
Certificate evidencing the number of Warrants remaining unexercised.

        This Warrant Certificate is issued under and in accordance with the
Warrant Agreement dated as of ______ (the "Warrant Agreement") between the
Company and the Warrant Agent and is subject to the terms and provisions
contained in the Warrant Agreement, to all of which terms and provisions the
holder of this Warrant Certificate consents by acceptance hereof. Copies of the
Warrant Agreement are on file at the above-mentioned office of the Warrant Agent
[and at ______].

        [If Offered Securities with registered Warrants which are not
immediately detachable -- Prior to __________, this Warrant Certificate may be
exchanged or transferred only together with the [Title of Offered Securities]
("Offered Securities") to which this Warrant Certificate was initially attached,
and only for the purpose of effecting, or in conjunction with, an exchange or
transfer of such Offered Security. After such date, transfer of this] [if
Offered Securities with registered Warrants which are immediately detachable --
Transfer of this] Warrant Certificate may be registered when this Warrant
Certificate is surrendered at the corporate trust office of the Warrant Agent
[or ______] by the registered owner or such owner's assigns, in person or by an
attorney duly authorized in writing, in the manner and subject to the
limitations provided in the Warrant Agreement.

        [If Offered Securities with Warrants which are not immediately
detachable -- Except as provided in the immediately preceding paragraph, after]
[if Offered Securities with Warrants which are immediately detachable or Warrant
alone -- After] countersignature by the Warrant Agent and prior to the
expiration of this Warrant Certificate, this Warrant Certificate may be
exchanged at the corporate trust office of the Warrant Agent [or ______] for
Warrant Certificates representing the same aggregate number of Warrants.

        This Warrant Certificate shall not entitle the holder hereof to any of
the rights of a holder of the Warrant Securities, including, without limitation,
the right to receive payments of dividends or distributions, if any, on the
Warrant Securities or to exercise any voting rights.

                                      A-2
<PAGE>   15

        This Warrant Certificate shall not be valid or obligatory for any
purpose until countersigned by the Warrant Agent.

        Dated as of ____________

                                            INDYMAC BANCORP, INC.

                                            By
                                               ---------------------------
                                                 Title:

Attest:

---------------------------------

Countersigned:

---------------------------------
                 As Warrant Agent

By
   ------------------------------
       Authorized Signature

                                      A-3
<PAGE>   16

                        [Reverse of Warrant Certificate]
                      Instructions for Exercise of Warrant

        To exercise the Warrants evidenced hereby, the holder must pay [in
United States dollars] [in cash or by certified check or official bank check or
by bank wire transfer, in each case] [by bank wire transfer] in immediately
available funds the Warrant Price in full for Warrants exercised to [insert name
of Warrant Agent] [corporate trust department] [insert address of Warrant
Agent], Attn. ____________ [or ______________________ ], which [payment] [wire
transfer] must specify the name of the holder and the number of Warrants
exercised by such holder. In addition, the holder must complete the information
required below and present this Warrant Certificate in person or by mail
(certified or registered mail is recommended) to the Warrant Agent at the
appropriate address set forth below. This Warrant Certificate, completed and
duly executed, must be received by the Warrant Agent within five business days
of the [payment] [wire transfer].

                     To Be Executed Upon Exercise of Warrant

        The undersigned hereby irrevocably elects to exercise ___ Warrants,
evidenced by this Warrant Certificate, to purchase ___ shares of the [Title of
Warrant Securities] (the "Warrant Securities") of IndyMac Bancorp, Inc. and
represents that he has tendered payment for such Warrant Securities [in Dollars]
[in cash or by certified check or official bank check or by bank wire transfer,
in each case] [by bank wire transfer] in immediately available funds to the
order of IndyMac Bancorp, Inc., c/o [insert name and address of Warrant Agent],
in the amount of ___ in accordance with the terms hereof. The undersigned
requests that said principal amount of Warrant Securities be in fully registered
form in the authorized denominations, registered in such names and delivered all
as specified in accordance with the instructions set forth below.

                                       A-4

<PAGE>   17

        If the number of Warrants exercised is less than all of the Warrants
evidenced hereby, the undersigned requests that a new Warrant Certificate
representing the remaining Warrants evidenced hereby be issued and delivered to
the undersigned unless otherwise specified in the instructions below.

Dated:                                        Name
       -------------------------------------      ------------------------------

                                              Address
--------------------------------------------          --------------------------
(Insert Social Security or Other Identifying
Number of Holder)                             ----------------------------------

Signature Guaranteed

--------------------------------------------
                                             Signature
                                                      -------------------------
                                              (Signature must conform in all
                                              respects to name of  holder as
                                              specified on the face of this
                                              Warrant Certificate and must bear
                                              a signature guarantee by a bank,
                                              trust company or member broker of
                                              the New York Stock Exchange)

        The Warrants evidenced hereby may be exercised at the following
addresses:

By hand at
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By mail at
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        [Instructions as to form and delivery of Warrant Securities and, if
applicable, Warrant Certificates evidencing unexercised Warrants -- complete as
appropriate.]

                                       A-5

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