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                                                                     Exhibit 4.5















                        ENDURANCE SPECIALTY HOLDINGS LTD.



                           WARRANT FOR CLASS A SHARES



                            DATED AS OF JULY __, 2002



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THIS WARRANT HAS NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF
1933, AS AMENDED (THE "SECURITIES ACT"), OR ANY UNITED STATES STATE OR FOREIGN
SECURITIES LAWS AND MAY NOT BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS
(I) (A) A REGISTRATION STATEMENT IS IN EFFECT UNDER THE SECURITIES ACT WITH
RESPECT TO THIS WARRANT, OR (B) A WRITTEN OPINION OF COUNSEL OR OTHER EVIDENCE
REASONABLY ACCEPTABLE TO ENDURANCE SPECIALTY HOLDINGS LTD. ("ENDURANCE") HAS
BEEN OBTAINED TO THE EFFECT THAT NO SUCH REGISTRATION IS REQUIRED, (II) THE
TRANSFEREE, IF REQUIRED BY LAW, IS APPROVED BY THE APPLICABLE BERMUDA REGULATORY
AUTHORITIES, AND (III) THE TRANSFER IS PERMITTED UNDER THE TERMS OF THIS
WARRANT.

ANY SALE, ASSIGNMENT, TRANSFER, PLEDGE OR OTHER DISPOSITION OF THE RIGHTS
REPRESENTED HEREBY IS RESTRICTED BY, AND THE RIGHTS OF THE HOLDER HEREOF ARE
SUBJECT TO, THE TERMS AND CONDITIONS CONTAINED IN THE BYE-LAWS OF ENDURANCE AND
THE SHAREHOLDERS AGREEMENT DATED AS OF JULY __, 2002, AS THEY MAY BE AMENDED
FROM TIME TO TIME.


                         THIS WARRANT IS SUBJECT TO THE
                   RESTRICTIONS ON TRANSFER SET FORTH HEREIN.

No. of Class A Shares: [o]                                      Warrant No. [o]
Date of Issuance: July __, 2002


                                     WARRANT

                 To Purchase Class A Shares, US$1.00 par value,
                      of Endurance Specialty Holdings Ltd.

         THIS WARRANT CERTIFIES THAT, for value received, the registered holder
hereof, [o], a company incorporated under the laws of [o] (together with its
successors and permitted assigns, the "Warrant Holder"), is entitled to purchase
from ENDURANCE SPECIALTY HOLDINGS LTD., an exempt company organized under the
laws of Bermuda (together with its successors and permitted assigns,
"Endurance"), [o] Class A Shares ("Class A Shares"), US$1.00 par value each, of
Endurance (the "Warrant Shares"), at the price of US$100.00 per Warrant Share,
as adjusted in accordance with the terms hereof, but in no event less than par
value (as adjusted, the "Exercise Price"), subject to the limitations contained
in Article IV, at any time from and after the date hereof until December 14,
2011 (the "Warrant Exercise Period").

                     ARTICLE I. OWNERSHIP OF THIS WARRANT.

         Endurance may deem and treat the Warrant Holder as the holder and owner
hereof, notwithstanding any notations of ownership or writing hereon made by
anyone other than Endurance, for all purposes and shall not be affected by any
notice to the contrary, until


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presentation of this Warrant for registration of transfer as provided in Article
III. Endurance shall provide from and after the Original Issue Date for a
transfer agent and registrar (collectively, the "Agent") for this Warrant. The
Agent shall keep a register in which it shall record the registration and
transfer of this Warrant and the name and address of the Warrant Holder.

                            ARTICLE II. REPLACEMENT.

         Upon receipt by Endurance of evidence reasonably satisfactory to it of
the loss, theft, destruction or mutilation of this Warrant, and, in the case of
loss, theft or destruction, of indemnity or security reasonably satisfactory to
it, and upon surrender of this Warrant at the office of the Agent, if mutilated,
Endurance will make and deliver at its own expense a new Warrant of like tenor,
in replacement of this Warrant. At the request of the Warrant Holder to exchange
this Warrant for Warrants of different denominations, and upon surrender of this
Warrant at the office of the Agent, Endurance will deliver at its own expense
new Warrants in exchange therefor, in those denominations requested by the
Warrant Holder. This Warrant shall be promptly canceled by Endurance upon the
surrender hereof in connection with any replacement.

                      ARTICLE III. EXERCISE AND TRANSFER.

         Section 3.1 Procedure for Exercise. In order to exercise this Warrant,
the Warrant Holder shall complete the Subscription Form attached hereto, and
deliver to the Agent this Warrant, together with the aggregate Exercise Price of
the Warrant Shares then being purchased (the "Warrant Price"). Payment of the
Warrant Price shall be made at the option of the Warrant Holder by one or more
of the following methods: (i) by delivery of a certified or bank check in the
amount of the Warrant Price, (ii) by instructing Endurance to withhold a number
of Warrant Shares then issuable upon exercise of this Warrant with an aggregate
Fair Value equal to the Warrant Price or (iii) by surrendering to Endurance
Ordinary Shares or Class A Shares previously acquired by the Warrant Holder with
an aggregate Fair Value equal to the Warrant Price. In the event of any
withholding of Warrant Shares or surrender of Ordinary Shares or Class A Shares
pursuant to clause (ii) or (iii) above where the number of shares whose Fair
Value is equal to the Warrant Price is not a whole number, the number of shares
withheld by or surrendered to Endurance shall be rounded up to the nearest whole
share and Endurance shall make a cash payment to the Warrant Holder based on the
incremental fraction of a share being so withheld by or surrendered to
Endurance. The exercise of this Warrant shall be deemed to be effected, and the
Exercise Price and the number of Warrant Shares issuable in connection with such
exercise shall be determined, as of the close of business on the Business Day on
which delivery of the completed Subscription Form and all other items required
to be delivered in connection with such exercise by the Warrant Holder pursuant
to this Section 3.1 or otherwise shall have been delivered to the Agent (the
"Exercise Date"). Upon receipt of such Subscription Form and other items,
Endurance shall, subject to this Section 3.1, as promptly as practicable, and in
any event other than where it shall be necessary for the Board to determine the
Fair Value of any securities, within five Business Days thereafter, execute or
cause to be executed and deliver or cause to be delivered to the Warrant Holder
a certificate or certificates representing the aggregate number of Warrant
Shares specified in such Subscription Form, and, if applicable, cash in lieu of
a fractional share of a Warrant Share as provided herein. Each certificate so


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delivered shall be in such authorized denomination as may be requested by the
Warrant Holder and shall be registered in the name of the Warrant Holder or, to
the extent permitted by law, the Bye-Laws, Shareholders Agreement and the
provisions of this Warrant, in the name of the Person designated by the Warrant
Holder. The Person (whether the Warrant Holder or Warrant Holder's transferee)
in whose name any such certificate shall be issuable upon such exercise shall be
deemed to have become the holder of record of the Warrant Shares represented
thereby as of the time when the exercise of this Warrant, with respect to such
Warrant Shares, shall be deemed to have been effected. If this Warrant shall
have been exercised only in part, Endurance shall, at its expense at the time of
delivery of said certificate or certificates, deliver to said registered holder
a new Warrant evidencing the rights of said holder to purchase the remaining
Warrant Shares covered by this Warrant. The Warrant Holder understands that this
Warrant shall expire immediately to the extent that it is not exercised before
the end of the Warrant Exercise Period.

         Section 3.2 Expenses; Taxes. Without limiting Section 7.3, Endurance
shall pay all expenses and all Bermuda stamp, transfer or similar duties or
taxes payable in connection with the preparation, execution and delivery of the
certificates pursuant to this Article III. Endurance may make such provision as
it deems appropriate for the withholding of any other taxes or payment of any
other taxes which it determines it may be required to withhold or pay in
connection with the issuance of this Warrant or the Warrant Shares issuable upon
exercise of this Warrant.

                            ARTICLE IV. [RESERVED].

                      ARTICLE V. RESTRICTIONS ON TRANSFER.

         Section 5.1 Limitations on Transfer; Not Registered Under the
Securities Act. This Warrant shall be transferable to the same extent as the
underlying Warrant Shares are transferable in accordance with the procedures
specified in the Bye-Laws and the Shareholders Agreement, subject to Bermuda
Monetary Authority consent, if required. The Warrant Holder, by acceptance
hereof, acknowledges that neither this Warrant nor the Warrant Shares issuable
upon the exercise of this Warrant have been registered under the Securities Act
or the applicable securities laws of any other jurisdiction and that this
Warrant (and the Warrant Shares issuable upon exercise of this Warrant) are
subject to the restrictions on transferability set forth in the legend which
appears on the face of this Warrant and which are referred to in Section 5.2,
respectively.

         Section 5.2 Restrictive Legends on Certificates Representing Warrant
Shares. Each certificate representing Warrant Shares shall contain such legends
as shall be required by the Shareholders Agreement and the Bye-Laws.

         Section 5.3 Reservation of Warrant Shares; Character of Warrant Shares.
From and after the Original Issue Date, Endurance shall at all times reserve and
keep available for issuance upon the exercise of this Warrant such number of its
authorized but unissued Class A Shares as will be sufficient to permit the
exercise in full of this Warrant. All Warrant Shares issuable upon the exercise
of this Warrant shall be, when issued, duly authorized, validly issued and fully
paid.

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                     ARTICLE VI. ANTI-DILUTION PROVISIONS.

         The number of Warrant Shares for which this Warrant is exercisable and
the Exercise Price shall be subject to adjustment from time to time as set forth
in this Article VI.

         Section 6.1 Share Dividends, Subdivisions and Combinations. If at any
time Endurance shall: (i) take a record of the holders of Ordinary Shares for
the purpose of entitling them to receive a dividend payable in, or other
distribution of, additional Ordinary Shares, (ii) subdivide the outstanding
Ordinary Shares into a larger number of Ordinary Shares, or (iii) combine the
outstanding Ordinary Shares into a smaller number of Ordinary Shares; then the
Exercise Price shall be adjusted to equal the product of the Exercise Price in
effect immediately prior to such event multiplied by a fraction the numerator of
which is equal to the number of Ordinary Shares outstanding immediately prior to
the adjustment and the denominator of which is equal to the number of Ordinary
Shares outstanding immediately after such adjustment.

         Section 6.2 Issuance of Additional Ordinary Shares.

                (a) If at any time Endurance shall issue or sell any Ordinary
Shares in a Subsequent Issuance for a consideration per share that is less than
the Exercise Price in effect immediately prior to such issuance or sale, then,
forthwith upon such issuance or sale, the Exercise Price shall be reduced to an
amount determined by dividing (i) an amount equal to the sum of (x) the total
number of Ordinary Shares and Class A Shares outstanding immediately prior to
such Subsequent Issuance multiplied by the then existing Exercise Price, plus
(y) the aggregate consideration (determined in accordance with the provisions of
Section 6.6 hereof), if any, received by Endurance in connection with such
Subsequent Issuance, by (ii) the total number of Ordinary Shares and Class A
Shares outstanding immediately after such Subsequent Issuance.

                (b) The provisions of this Section 6.2 shall not apply to (i)
any issuance of Ordinary Shares for which an adjustment is provided for under
Section 6.1 or (ii) any issuance or sale of Ordinary Shares pursuant to the
exercise of any Share Purchase Rights or Convertible Securities to the extent
that an adjustment shall have been previously made hereunder in connection with
the issuance of such Share Purchase Rights or Convertible Securities pursuant to
the provisions of Section 6.3 hereof.

         Section 6.3 Issuances of Share Purchase Rights and Convertible
Securities.

                (a) In the event that Endurance shall at any time issue, sell
or grant any Share Purchase Rights in a Subsequent Issuance, then, for the
purpose of Section 6.2 above, Endurance shall be deemed to have issued at that
time a number of Ordinary Shares equal to the maximum number of Ordinary Shares
that are or may become issuable upon exercise of such Share Purchase Rights (or
upon exercise of any Convertible Securities issuable upon exercise of such Share
Purchase Rights) for a consideration per share equal to (i) the aggregate
consideration per share (determined in accordance with the provisions of Section
6.6 hereof) received by Endurance in connection with the issuance, sale or grant
of such Share Purchase Rights plus (ii) the minimum amount of such consideration
per share receivable by Endurance in connection





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with the exercise of such Share Purchase Rights (and the exercise of any
Convertible Securities issuable upon exercise of such Share Purchase Rights).

                (b) In the event that Endurance shall at any time issue or sell
any Convertible Securities in a Subsequent Issuance, then, for the purposes of
Section 6.2 above, Endurance shall be deemed to have issued at that time a
number of Ordinary Shares equal to the maximum number of Ordinary Shares that
are or may become issuable upon the exercise of the conversion or exchange
rights associated with such Convertible Securities for a consideration per share
equal to (i) the aggregate consideration per share (determined in accordance
with the provisions of Section 6.6 hereof) received by Endurance in connection
with the issuance or sale of such Convertible Securities plus (ii) the minimum
amount of such consideration per share receivable by Endurance in connection
with the exercise of such conversion or exchange rights.

                (c) If, at any time after any adjustment of the Exercise Price
shall have been made hereunder as the result of any issuance, sale or grant of
any Share Purchase Rights or Convertible Securities, the maximum number of
shares issuable upon exercise of such Share Purchase Rights or of the rights of
conversion or exchange associated with such Convertible Securities shall
increase, or the minimum amount of consideration per share receivable in
connection with such exercise shall decrease, whether by operation of any
antidilution rights pertaining to such Share Purchase Rights or Convertible
Securities, by agreement of the Parties or otherwise, the Exercise Price then in
effect shall first be readjusted to eliminate the effects of the original
issuance, sale or grant of such Share Purchase Rights or Convertible Securities
on such Exercise Price and then readjusted as if such Share Purchase Rights or
Convertible Securities had been issued on the effective date of such increase in
number of shares or decrease in consideration, but only if the effect of such
two-step readjustment is to reduce the Exercise Price below the Exercise Price
in effect immediately prior to such increase or decrease.

                (d) If, at any time after any adjustment of the Exercise Price
shall have been made hereunder as the result of any issuance, sale or grant of
any Share Purchase Rights or Convertible Securities, any of such Share Purchase
Rights or the rights of conversion or exchange associated with such Convertible
Securities shall expire by their terms or any of such Share Purchase Rights or
Convertible Securities shall be repurchased by Endurance or a subsidiary thereof
for a consideration per underlying Ordinary Share not exceeding the amount of
such consideration received by Endurance in connection with the issuance, sale
or grant of such Share Purchase Rights or Convertible Securities, the Exercise
Price then in effect shall forthwith be increased to the Exercise Price that
would have been in effect if such expiring Share Purchase Rights or rights of
conversion or exchange or such repurchased Share Purchase Rights or Convertible
Securities had never been issued. Similarly, if at any time after any such
adjustment of the Exercise Price shall have been made pursuant to Section 6.2,
(i) any additional consideration is received or becomes receivable by Endurance
in connection with the issuance or exercise of such Share Purchase Rights or
Convertible Securities or (ii) there is a reduction in the conversion ratio
applicable to such Convertible Securities so that fewer Ordinary Shares will be
issuable upon the conversion or exchange thereof or there is a decrease in the
number of Ordinary Shares issuable upon exercise of such Share Purchase Rights,
the Exercise Price then in effect shall be forthwith readjusted to the Exercise
Price that would have been in effect had such changes taken place at the time
that such Share Purchase Rights or Convertible Securities were



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initially issued, granted or sold. In no event shall any readjustment under this
Section 6.3(d) affect the validity of any Warrant Shares issued upon any
exercise of this Warrant prior to such readjustment, nor shall any such
readjustment have the effect of increasing the Exercise Price above the Exercise
Price that would have been in effect if the related Share Purchase Rights or
Convertible Securities had never been issued.

         Section 6.4 Adjustment of Number of Shares Purchasable. Upon any
adjustment of the Exercise Price as provided in Section 6.1, 6.2 or 6.3 hereof,
the Warrant Holder shall thereafter be entitled to purchase upon the exercise of
this Warrant, at the Exercise Price resulting from such adjustment, the number
of Class A Shares (calculated to the nearest 1/100th of a share) obtained by
multiplying the Exercise Price in effect immediately prior to such adjustment by
the number of Class A Shares issuable on the exercise hereof immediately prior
to such adjustment and dividing the product thereof by the Exercise Price
resulting from such adjustment.

         Section 6.5 Reorganization, Reclassification, Merger, Amalgamation
Consolidation or Disposition of Assets. In the event that Endurance shall
reorganize its capital, reclassify its capital stock, merge, amalgamate or
consolidate with or into another corporation (where Endurance is not the
surviving corporation or where there is any change whatsoever in, or
distribution with respect to, the outstanding Ordinary Shares), or sell,
transfer or otherwise dispose of all or substantially all of its property,
assets or business to another corporation and, pursuant to the terms of such
reorganization, reclassification, merger, amalgamation, consolidation or
disposition of assets, (i) shares of common stock of the successor or acquiring
corporation or of Endurance (if it is the surviving corporation) or (ii) any
cash, shares of stock or other securities or property of any nature whatsoever
(including warrants or other subscription or purchase rights) in addition to or
in lieu of common stock of the successor or acquiring corporation ("Other
Property") are to be received by or distributed to the holders of Ordinary
Shares who are holders immediately prior to such transaction, then the Warrant
Holder shall have the right thereafter to receive, upon exercise of this
Warrant, the number of common shares of the successor or acquiring corporation
or Endurance, if it is the surviving corporation, and Other Property receivable
upon or as a result of such reorganization, reclassification, merger,
amalgamation, consolidation or disposition of assets by a holder of the number
of Ordinary Shares for which this Warrant is exercisable immediately prior to
such event. In such event, the aggregate Exercise Price otherwise payable for
the Warrant Shares shall be allocated among the common shares and Other Property
receivable as a result of such reorganization, reclassification, merger,
amalgamation, consolidation or disposition of assets in proportion to the
respective fair market values of such common shares and Other Property as
determined in good faith by the Board. In case of any such reorganization,
reclassification, merger, amalgamation, consolidation or disposition of assets,
Endurance shall require as a condition that the successor or acquiring
corporation (if other than Endurance) expressly assume the due and punctual
observance and performance of each and every covenant and condition of this
Warrant to be performed and observed by Endurance and all the obligations and
liabilities hereunder, subject to such modifications as may be reasonably deemed
appropriate (as determined by resolution of the Board) in order to provide for
adjustments of any common shares of such successor or acquiring corporation for
which this Warrant thus becomes exercisable, which modifications shall be as
equivalent as practicable to the adjustments provided for in this Article VI.
For purposes of this



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Section 6.5, "common shares of the successor or acquiring corporation" shall
include stock of such corporation of any class that is not preferred as to
dividends or assets over any other class of stock of such corporation and that
is not subject to redemption and shall also include any evidences of
indebtedness, shares of stock or other securities that are convertible into or
exchangeable for any such stock, either immediately or upon the arrival of a
specified date or the happening of a specified event, and any warrants or other
rights to subscribe for or purchase any such stock. The foregoing provisions of
this Section 6.5 shall similarly apply to successive reorganizations,
reclassifications, mergers, amalgamations, consolidations or dispositions of
assets.

         Section 6.6 Determination of Consideration. For purposes of Sections
6.2, 6.3 and 6.4 hereof, the consideration received and/or receivable by
Endurance in connection with the issuance, sale, grant or exercise of additional
Ordinary Shares, Share Purchase Rights or Convertible Securities, irrespective
of the accounting treatment of such consideration, shall be valued as follows:

                (a) Cash Payment. In the case of cash, the net amount received
by Endurance after deduction of any accrued interest or dividends, but including
any underwriting commissions or concessions paid or allowed by Endurance.

                (b) Securities or Other Property. In the case of securities or
other property, the fair market value thereof as of the date immediately
preceding such issuance, sale, grant or exercise as determined in good faith by
the Board.

                (c) Allocation Related to Ordinary Shares or Class A Shares.
In the event Ordinary Shares or Class A Shares are issued or sold together with
other securities or other assets of Endurance for a consideration which covers
both, the consideration received (computed as provided in (a) and (b) above)
shall be allocable to such Ordinary Shares or Class A Shares, as the case may
be, as determined in good faith by the Board.

                (d) Allocation Related to Share Purchase Rights and Convertible
Securities. In case any Share Purchase Rights or Convertible Securities shall be
issued or sold together with other securities or other assets of Endurance,
together comprising one integral transaction in which no specific consideration
is allocated to the Share Purchase Rights or Convertible Securities, the
consideration allocable to such Share Purchase Rights or Convertible Securities
shall be determined in good faith by the Board.

                (e) Dividends in Securities. In case Endurance shall declare a
dividend or make any other distribution upon any shares of Endurance payable in
either case in Ordinary Shares or Convertible Securities, such Ordinary Shares
or Convertible Securities, as the case may be, issuable in payment of such
dividend or distribution shall be deemed to have been issued or sold without
consideration.

                (f) Amalgamation, Merger, Consolidation or Sale of Assets. In
case any Ordinary Shares, Share Purchase Rights or Convertible Securities shall
be issued in connection with any amalgamation, merger or consolidation in which
Endurance is the surviving corporation, the amount of consideration therefor
shall be deemed to be the fair value of such



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portion of the assets and business of the non-surviving corporation attributable
to such Ordinary Shares, Share Purchase Rights or Convertible Securities, as is
determined in good faith by the Board.

                (g) Challenge to Good Faith Determination. Whenever the Board
shall be required to make a determination in good faith of the fair value of any
item under this Article VI, such determination may be challenged in good faith
by the Warrant Holder, and any dispute shall be resolved by an investment
banking or appraisal firm of recognized national standing selected by Endurance
and acceptable to the Majority Warrant Holders and whose decision shall be
binding on Endurance and the Warrant Holder. The fees and expenses of such firm
shall be paid by Endurance.

         Section 6.7 Other Dilutive Events. In case any event shall occur as to
which the other provisions of this Article VI are not strictly applicable but as
to which the failure to make any adjustment would not fairly protect the
purchase rights represented by this Warrant in accordance with the essential
intent and principles hereof (including, without limitation, the issuance of
securities other than Ordinary Shares or Class A Shares which have the right to
participate in distributions to the holders of Ordinary Shares or Class A
Shares, the granting of "phantom share" rights or "share appreciation rights" or
the repurchase of outstanding Ordinary Shares, Convertible Securities or Share
Purchase Rights for a purchase price exceeding the fair market value thereof),
then, in each such case, the Majority Warrant Holders may select an independent
investment banking firm of nationally recognized standing and reasonably
acceptable to Endurance to make a determination as to the adjustment, if any,
required to be made on a basis consistent with the essential intent and
principles established herein as a result of such event in order to preserve the
purchase rights represented by this Warrant. If the investment bank selected by
the Majority Warrant Holders is not reasonably acceptable to Endurance, and
Endurance and the Majority Warrant Holders cannot agree on a mutually acceptable
investment bank, then Endurance and the Majority Warrant Holders shall each
choose one such investment bank and the respective chosen firms shall jointly
select a third investment bank, which shall make such determination. Endurance
shall pay the costs and fees of each such investment bank (including any such
investment bank selected by the Majority Warrant Holders), and the decision of
the investment bank making such determination shall be final and binding on
Endurance and the Warrant Holder. Promptly after receipt of the opinion of such
investment bank as to any such required adjustments, Endurance shall take any
actions necessary to implement same.

         Section 6.8 Cash and In-Kind Dividends.

                (a) Cash Dividends. In the event that Endurance at any time
after the Original Issue Date shall pay a dividend or make any other
distribution with respect to the Ordinary Shares (or any other shares of
Endurance for which this Warrant becomes exercisable pursuant to this Article
VI) in the form of cash, the Exercise Price shall be reduced by the amount to be
received in respect of each Ordinary Share. In the event that the adjustment
provided for in the immediately preceding sentence would result in the Exercise
Price being less than the par value of a Warrant Share, no such adjustment shall
be made and in lieu thereof an adjustment shall be made pursuant to Section
6.8(b). In the event of an adjustment pursuant to this Section 6.8(a), no
adjustment shall be made to the number and class of securities subject to this
Warrant.

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                (b) In-Kind Dividends. In the event that Endurance at any time
after the Original Issue Date shall pay a dividend or make any other
distribution with respect to the Ordinary Shares (or any other shares of
Endurance for which this Warrant becomes exercisable pursuant to this Article
VI) whether in the form of evidences of indebtedness, securities or other
property (other then a stock dividend subject to the provisions of Section 6.1
above or a cash dividend or distribution with respect to which an adjustment is
made pursuant to Section 6.8(a) above), then the number and class of securities
subject to this Warrant and the Exercise Price shall be appropriately and
equitably adjusted in good faith by the Board, such adjustments to be made
without an increase in the aggregate Exercise Price and to preserve the purchase
rights represented by this Warrant so that, unless otherwise requested by the
Warrant Holder, the property (including securities) to be received by the
Warrant Holder upon exercise of this Warrant after such dividend or other
distribution shall be as nearly as practicable to those which the Warrant Holder
would have been entitled had the Warrant Holder exercised this Warrant
immediately prior to the record date for such dividend or distribution,
provided, that Endurance shall not be required to retain or acquire any property
(including securities) to be delivered to the Warrant Holder upon exercise of
this Warrant if to do so would cause a dividend or distribution that was not
otherwise taxable to Endurance or its shareholders to become taxable. Such
adjustments may be challenged in good faith by the Warrant Holder, in which
cases the Majority Warrant Holders may select an independent investment banking
firm of nationally recognized standing and reasonably acceptable to Endurance to
make a determination as to the adjustments, if any, required to be made on a
basis consistent with the essential intent and principles established herein as
a result of such event in order to preserve the purchase rights represented by
this Warrant. If the investment bank selected by the Majority Warrant Holders is
not reasonably acceptable to Endurance, and Endurance and the Majority Warrant
Holders cannot agree on a mutually acceptable investment bank, then Endurance
and the Majority Warrant Holders shall each choose one such investment bank and
the respective chosen firms shall jointly select a third investment bank, which
shall make such determination. Endurance shall pay the costs and fees of each
such investment bank (including any such investment bank selected by the
Majority Warrant Holders), and the decision of the investment bank making such
determination shall be final and binding on Endurance and the Warrant Holder.
Promptly after receipt of the opinion of such investment bank as to any such
required adjustments, Endurance shall take any actions necessary to implement
same.

         Section 6.9 Other Provisions Applicable to Adjustments Under this
Section. The following provisions shall be applicable to the adjustments
provided for pursuant to this Article VI:

                (a) When Adjustments To Be Made. Adjustments shall be made
whenever and as often as any specified event requiring such an adjustment shall
occur. For the purpose of any such adjustment, any specified event shall be
deemed to have occurred at the close of business on the date of its occurrence.

                (b) Record Date. If Endurance shall take a record of the
holders of the Ordinary Shares for the purpose of entitling them (i) to receive
a dividend or other distribution payable in Ordinary Shares, Convertible
Securities or Share Purchase Rights or (ii) to subscribe for or purchase
Ordinary Shares, Convertible Securities or Share Purchase Rights, then all


                                     - 9 -
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references to the date of the issuance or sale of such Ordinary Shares,
Convertible Securities or Share Purchase Rights shall be deemed to be references
to such record date.

                (c) Fractional Interests. In computing adjustments, fractional
interests in Ordinary Shares shall be taken into account to the nearest 1/100th
of a share.

                (d) When Adjustment Not Required. If Endurance shall take a
record of the holders of its Ordinary Shares for the purpose of entitling them
to receive a dividend or distribution to which the provisions of Section 6.1
would apply, but shall, thereafter and before the distribution to shareholders
thereof, legally abandon its plan to pay or deliver such dividend or
distribution, then thereafter no adjustment shall be required by reason of the
taking of such record and any such adjustment previously made in respect thereof
shall be rescinded and annulled.

                (e) Certain Limitations. Notwithstanding anything herein to the
contrary, Endurance agrees not to enter into any transaction that, by reason of
any adjustment under Section 6.1, 6.2 or 6.3 above, would cause the Exercise
Price to be less than the par value of the Ordinary Shares and Class A Shares,
unless Endurance first reduces the par value of the Ordinary Shares and Class A
Shares to be less than the Exercise Price that would result from such
transaction.

                (f) Notice of Adjustments. Whenever the number of Class A
Shares for which this Warrant is exercisable or the Exercise Price shall be
adjusted pursuant to this Article VI, Endurance shall forthwith prepare a
certificate to be executed by its chief financial officer setting forth, in
reasonable detail, the event requiring the adjustment and the method by which
such adjustment was calculated, specifying the number of Class A Shares for
which this Warrant is exercisable and (if such adjustment was made pursuant to
Section 6.5) describing the number and kind of any other shares or Other
Property for which this Warrant is exercisable, and any related change in the
Exercise Price, after giving effect to such adjustment or change. Endurance
shall promptly cause a signed copy of such certificate to be delivered to the
Warrant Holder. Endurance shall keep at its principal office copies of all such
certificates and cause the same to be available for inspection at said office
during normal business hours by the Warrant Holder.

                (g) Independent Application. Except as otherwise provided
herein, all sections of this Article VI are intended to operate independently of
one another (but without duplication). If an event occurs that requires the
application of more than one section, all applicable sections shall be given
independent effect without duplication.

                           ARTICLE VII. MISCELLANEOUS

         Section 7.1 Notices of Dividends or Distributions. If Endurance shall
take a record of the holders of Ordinary Shares for the purpose of determining
the holders thereof who are entitled to receive any dividend or distribution, in
whatever form, Endurance shall provide to the Warrant Holder a notice specifying
the date or expected date on which any such record is to be taken for the
purpose of such dividend or distribution, and the amount and character of such
dividend or distribution. Such notice shall be given at least thirty (30), but
not more than ninety


                                     - 10 -
<PAGE>


(90), days prior to the record date therein specified, and shall describe the
material terms of the matter in question. In the event that Endurance at any
time sends any other notice to the holders of Ordinary Shares or Class A Shares,
it shall concurrently send a copy of such notice to the Warrant Holder;
provided, however, in no event shall such notice be sent to the Warrant Holder
less than (a) twenty (20) days prior to the record date or the date on which
Endurance's transfer books are to be closed in respect of the event for which
notice is being given and (b) thirty (30) days prior to the event for which
notice is given.

         Section 7.2 Entire Agreement. This Warrant (including any exhibits and
annexes hereto) constitutes the entire agreement among the Parties and
supersedes all prior agreements and understandings, oral and written, among the
Parties with respect to the subject matter hereof.

         Section 7.3 Taxes Payable Upon Exercise. Endurance shall not be
required to pay any federal, state, local or foreign income taxes, if any,
payable by the recipient of such Ordinary Shares upon exercise of this Warrant,
or any taxes which may be payable in respect of any transfer involved in the
issuance of Ordinary Shares in a name other than that of the Warrant Holder, and
Endurance shall not be required to issue or deliver any such shares unless and
until the person requesting such issuance shall have paid to Endurance the
amount of any such transfer taxes, or shall have established to the satisfaction
of Endurance that such taxes have been paid.

         Section 7.4 Fractional Shares. No fractional Class A Shares shall be
issued upon exercise of this Warrant, but in lieu thereof Endurance shall pay a
cash adjustment in an amount equal to such fraction multiplied by the Fair Value
per Class A Share on the date on which this Warrant was duly exercised.

         Section 7.5 Severability. Wherever possible, each provision hereof
shall be interpreted in such manner as to be effective and valid under
applicable law, but in case any one or more of the provisions contained herein
shall, for any reason, be held to be invalid, illegal or unenforceable in any
respect, such provision shall be ineffective to the extent, but only to the
extent, of such invalidity, illegality or unenforceability without invalidating
the remainder of such invalid, illegal or unenforceable provision or provisions
or any other provisions hereof, unless such a construction would be
unreasonable.

         Section 7.6 Assignability. Except as expressly permitted by Section
5.1, this Warrant and the rights hereunder shall not be assignable by the
Warrant Holder without the prior written consent of Endurance. Endurance may not
assign its obligations hereunder.

         Section 7.7 Amendment; Waiver. No provision of this Warrant may be
amended, waived or otherwise modified except by an instrument in writing
executed by Endurance and the Warrant Holder and consented to in writing by all
other Warrant Holders.

         Section 7.8 Headings. The Article and Section headings contained in
this Warrant are for convenience only and shall not affect the meaning or
interpretation of this Warrant.

                                     - 11 -
<PAGE>

         Section 7.9 Notices. All notices or other communications required or
permitted hereunder shall be in writing and shall be deemed given (a) when
delivered personally, (b) if transmitted by facsimile, when confirmation of
transmission is received, (c) if sent by registered or certified mail, postage
prepaid, return receipt requested, on the third Business Day after mailing or
(d) if sent by reputable overnight courier service, when received; and shall be
addressed as follows:

<TABLE>
<CAPTION>

If to Endurance:                          with a copy to:
---------------                           --------------
<S>                                       <C>
Endurance Specialty Holdings Ltd.         Endurance Specialty Holdings Ltd.
Cedar House                               48 Par-la-Ville Road, Suite 784
41 Cedar Avenue                           Hamilton HM 11, Bermuda
Hamilton HM12, Bermuda                    Attention: Chief Executive Officer/President
Attention: The Secretary                  Facsimile:  441-278-0401
Facsimile:  441-292-8666
</TABLE>


         Section 7.10 Payments. Unless otherwise provided in this Warrant,
payments hereunder shall be made by wire transfer of immediately available funds
in the lawful currency of the United States.

         Section 7.11 Arbitration. (a) Except as otherwise expressly set forth
herein, each Party agrees that all disputes arising out of, related to or in
connection with this Warrant or any of the transactions contemplated hereby,
including any question regarding this Warrant's formation, existence, validity
or termination, and whether arising during or after the period of this Warrant,
shall be referred to, and finally resolved by, arbitration in the manner set out
herein. Each Party hereby irrevocably waives any right to trial in any court
that otherwise would have jurisdiction over any dispute set forth in the
foregoing sentence. The place of the arbitration proceedings shall be Bermuda
and the arbitration tribunal (the "Tribunal") shall apply the laws of Bermuda as
the proper law of this Warrant.

         (b) In the event that any Party shall deliver a written demand for
arbitration (the "Arbitration Demand Notice") to another Party with respect to
any such dispute, such Parties shall attempt in good faith to agree upon one
arbitrator to resolve such dispute. If, within thirty days of delivery of the
Arbitration Demand Notice, such Parties are unable to agree upon a single
arbitrator, each such Party shall, within ten days, appoint an arbitrator. The
arbitrators so appointed (the "Appointed Arbitrators") shall promptly (and in
any event within ten days) appoint a third arbitrator to the Tribunal (the
"Chairman"). If the Appointed Arbitrators are unable to agree upon the Chairman
within such ten-day period, the Appointed Arbitrators may apply to the Appointer
(as defined below) for the appointment of the Chairman. The Appointer shall be
the President of the Chartered Institute of Arbitrators Bermuda Branch.


         (c) Unless the Parties to an arbitration proceeding otherwise agree,
each arbitrator shall be impartial and either (i) an attorney with at least ten
years admission to the bar with specialist knowledge of the insurance and
reinsurance industry or (ii) an insurance and reinsurance industry professional
with at least ten years relevant work experience. Any objection


                                     - 12 -
<PAGE>


to the qualifications of any arbitrator, if any, must be made within ten days of
notice of the nomination or appointment of such arbitrator.

         (d) The Tribunal shall decide by majority. If no majority can be
reached, the verdict of the Chairman shall prevail. The Tribunal shall have
power to fix all procedural rules for the holding of the arbitration, including
discretionary power to make orders as to matters such as pleadings, discovery,
examination of witnesses and any other matter whatsoever relating to the conduct
of the arbitration, and may receive and act on such evidence as it shall in its
sole discretion deem proper. All costs and expenses of the arbitration shall be
at the discretion of the Tribunal, which may direct to and by whom and in what
manner such costs and expenses shall be paid. The award of the Tribunal shall be
in writing, shall state reasons for the award and shall be final and binding
upon the parties to such arbitration. Judgment on the award may be entered by
any court having jurisdiction thereof or having jurisdiction over the parties
thereto or their assets.

         Section 7.12 Governing Law. This Warrant shall be governed by and
construed in accordance with the substantive laws of Bermuda, without regard to
its conflicts of laws doctrine.

         Section 7.13 The Parties agree and acknowledge that money damages are
not an adequate remedy for any breach of the provisions of this Warrant and that
any Party is entitled to specific performance and other injunctive relief in
order to enforce or prevent violation of the provisions of this Warrant. Any
dispute arising out of, relating to or in connection with this Warrant for which
specific performance is sought as a remedy will not be subject to arbitration
pursuant to Section 7.11. The failure or delay of any Party to enforce at any
time any provision of this Warrant shall not be construed to be a waiver of such
provision, nor in any way to affect the validity of this Warrant or any part
hereof or the right of any Party thereafter to enforce each and every such
provision. No waiver of any breach of this Warrant shall be held to constitute a
waiver of any other or subsequent breach.

         Section 7.14 Execution in Counterparts. This Warrant may be executed in
any number of counterparts, each of which shall be deemed an original
instrument, but all of which together shall constitute one and the same
instrument, and shall become binding when one or more counterparts have been
signed by and delivered to each of the Parties.

                           ARTICLE VIII. DEFINITIONS

         Section 8.1 Definitions. The following terms shall be defined as set
forth below:

         "Affiliate" shall mean, with respect to any Person, a Person that
directly or indirectly controls, is controlled by or is under common control
with such Person. For the purpose of this definition, the term "control" means
the power to direct the management of an entity, directly or indirectly, whether
through the ownership of voting securities, by contract or otherwise; and the
terms "controlled" and "controlling" have meanings correlative to the foregoing.

                                     - 13 -
<PAGE>

         "Appraised Value" per Ordinary Share as of a date specified herein
shall mean the value of such a share as of such date as determined by an
investment bank of nationally recognized standing selected by the Majority
Warrant Holders and reasonably acceptable to Endurance. If the investment bank
selected by the Majority Warrant Holders is not reasonably acceptable to
Endurance, and Endurance and the Majority Warrant Holders cannot agree on a
mutually acceptable investment bank, then Endurance and the Majority Warrant
Holders shall each choose one such investment bank and the respective chosen
firms shall jointly select a third investment bank, which shall make the
determination. Endurance shall pay the costs and fees of each such investment
bank (including any such investment bank selected by the Majority Warrant
Holders), and the decision of the investment bank making such determination of
Appraised Value shall be final and binding on Endurance and the Warrant Holder.
Such Appraised Value shall be determined as a pro rata portion of the value of
Endurance taken as a whole, based on the higher of (A) the value derived from a
hypothetical sale of Endurance as a going concern by a willing seller to a
willing buyer (neither acting under any compulsion) and (B) the liquidation
value of Endurance. No discount shall be applied on account of (i) this Warrant
or Warrant Shares representing a minority interest, (ii) any lack of liquidity
of the Ordinary Shares or this Warrant, (iii) the fact that this Warrant or
Warrant Shares may constitute "restricted securities" for securities law
purposes, (iv) the existence of Endurance's right, as set forth in the Bye-Laws
and the Shareholders Agreement, to require shareholders to sell the Shares to
the Shareholders (as defined in the Shareholders Agreement), to Endurance or to
one or more third parties designated by Endurance or (v) the existence of the
possibility of a reduction in voting power pursuant to the Bye-Laws. The
Appraised Value per Class A Share as of any date shall be identical to the
Appraised Value per Ordinary Share on such date.

         "Board" shall mean the Board of Directors of Endurance.

         "Business Day" shall mean any day except a Saturday, Sunday or other
day on which banks in any of Hamilton, Bermuda, or New York, New York are
authorized or obligated by law or executive order to close.

         "Bye-Laws" means the Bye-Laws of Endurance, as they may be amended from
time to time.

         "Code" shall mean the United States Internal Revenue Code of 1986, as
amended, or any United States federal statute then in effect that has replaced
such statute, and a reference to a particular section thereof shall be deemed to
include a reference to the comparable section, if any, of any such replacement
United States federal statute.

         "Controlled Shares" in reference to any Person shall mean all Shares
that such Person is deemed to own directly, indirectly or by attribution (within
the meaning of Section 958 of the Code).

         "Convertible Securities" shall mean evidences of indebtedness, shares
(including, without limitation, the Class A Shares (notwithstanding any
limitations on conversion thereof)), or other securities that are convertible
into or exchangeable for, with or without payment of additional consideration in
cash or property, Ordinary Shares, either immediately or upon the occurrence of
a specified date or a specified event.

                                     - 14 -
<PAGE>

         "Current Market Price" per Ordinary Share as of any specified date
shall mean the average of the daily market prices of the Ordinary Shares for the
shorter of (x) the twenty (20) consecutive Business Days immediately preceding
such date or (y) the period commencing on the Business Day next following the
first public announcement of any event giving rise to an adjustment of the
Exercise Price pursuant to Article VI of this Warrant. The "daily market price"
for each such Business Day shall be: (i) if the Ordinary Shares are then listed
on a national securities exchange or on The Nasdaq National Market, the last
sale price, regular way, on such day on the principal stock exchange or market
system on which the Ordinary Shares are then listed or admitted to trading, or,
if no such sale takes place on such day, the average of the closing bid and
asked prices for the Ordinary Shares on such day as reported on such stock
exchange or market system or (ii) if the Ordinary Shares are not then listed or
admitted to trading on any national securities exchange or on The Nasdaq
National Market but are traded over-the-counter, the average of the closing bid
and asked prices for the Ordinary Shares as reported on Nasdaq or the Electronic
Bulletin Board or in the National Daily Quotation Sheets, as applicable.

         "Fair Value" per Ordinary Share as of any specified date shall mean (A)
if the Ordinary Shares are publicly traded on such date, the Current Market
Price per share or (B) if the Ordinary Shares are not publicly traded on such
date, (i) the fair market value per Ordinary Share as determined in good faith
by the Board and set forth in a written notice to the Warrant Holder or (ii) if
the Warrant Holder objects in writing to such price as determined by the Board
within thirty days after receiving notice of same, the Appraised Value per
Ordinary Share as of such date. The Fair Value per Class A Share as of any date
shall be identical to the Fair Value per Ordinary Share on such date.

         "Majority Warrant Holders" with respect to a given determination, shall
mean the holders of Original Warrants representing more than fifty percent of
the Warrant Shares then issuable upon exercise of the Original Warrants directly
affected by such determination.

         "Ordinary Shares" shall mean the Ordinary Shares, US$1.00 par value
each, of Endurance.

         "Original Issue Date" shall mean the date on which the Original
Warrants were issued, as set forth on the cover page of this Warrant.

         "Original Warrants" shall mean the warrants originally issued by
Endurance on the Original Issue Date, including this Warrant, that are identical
as to terms and conditions (including the warrants to purchase Ordinary Shares
issued by Endurance on the Original Issue Date that are substantially similar to
this Warrant, except that they may be exercised for Ordinary Shares and, in some
circumstances, Class A Shares), except as to the number of Warrant Shares for
which they may be exercised (and all warrants issued upon transfer, division or
combination thereof, or in substitution therefor, in each case that are
identical as to terms and conditions, except as to the number of Warrant Shares
for which they may be exercised).

         "Party" shall mean Endurance or the Warrant Holder, as the case may be.

                                     - 15 -
<PAGE>

         "Person" shall mean any individual, partnership, corporation, limited
liability company, joint venture, joint-stock company, trust, unincorporated
organization, government (including agencies and political subdivisions thereof)
or other entity.

         "Related Person" with respect to any holder of Endurance securities
shall mean any Person to which ownership of shares in the share capital of
Endurance by such holder is attributed under Section 958 of the Code, provided
that such Person does not own (within the meaning of Section 958 of the Code)
any other shares in the share capital of Endurance.

         "Shares" shall mean any shares in the share capital of Endurance.

         "Share Purchase Rights" shall mean any options, warrants or other
securities or rights to subscribe to or exercisable for the purchase of Ordinary
Shares or Convertible Securities, whether or not immediately exercisable.

         "Shareholders Agreement" shall mean the Shareholders Agreement, dated
as of July __, 2002, by and among Endurance and each of the shareholders and
warrant holders listed on Schedule A thereto.

         "Subsequent Issuance" shall mean any sale or issuance by Endurance of
Ordinary Shares, Convertible Securities or Share Purchase Rights after the
original issuance of this Warrant other than:

                (a) any issuance of Warrant Shares upon exercise of this
Warrant and any issuance of Ordinary Shares, Convertible Securities or Share
Purchase Rights (and any issuance of Ordinary Shares pursuant to the conversion,
exchange or exercise of any such Convertible Securities or Share Purchase
Rights) deemed to have been issued as of the Original Issue Date;

                (b) any issuance of Ordinary Shares, Convertible Securities or
Share Purchase Rights (or any issuance of Ordinary Shares upon exercise of such
Convertible Securities or Share Purchase Rights) to directors, officers,
employees or consultants of Endurance or any of its subsidiaries pursuant to a
stock option or stock incentive plan or agreement approved by the Board.

         "US$" shall mean United States Dollars. To the extent any losses,
liabilities or other amounts described or referred to in this Warrant are stated
or denominated in currencies other than United States Dollars, such losses,
liabilities or amounts shall be stated, for purposes of this Warrant, in their
respective United States Dollar equivalents as shown on the books of Endurance.
All references to "dollars" or "$" shall mean United States Dollars unless
otherwise specifically indicated.

                            [SIGNATURE PAGE FOLLOWS]


                                     - 16 -
<PAGE>


                  IN WITNESS WHEREOF, Endurance has caused this Warrant to be
signed and delivered by its duly authorized officer, and to be dated as of the
date first above written.

                                    ENDURANCE SPECIALTY HOLDINGS LTD.



                                    By:  _______________________________
                                          Name:
                                          Title:





<PAGE>


SUBSCRIPTION FORM

To Be Executed by the Registered Holder
Desiring to Exercise the Within Warrant of

ENDURANCE SPECIALTY HOLDINGS LTD.

                  The undersigned registered holder hereby exercises the right
to purchase ___ Class A Shares covered by the within Warrant, according to the
conditions thereof, and herewith makes payment therefor, all at the price and on
the terms and conditions specified in the Warrant, and requests that the
certificate(s) for such shares be issued in the name of, and delivered to,
______________________________, whose address is ______________________

__________________________________________________________________________.

                                 Name of Registered Holder


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


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


                                 -------------------------------------------
                                 Title


                                 -------------------------------------------
                                 Address


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


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

NOTICE:

         The signature on the foregoing Subscription Form must correspond to the
name as written upon the face of the within Warrant in every particular, without
alteration or enlargement or any change whatsoever.