Document:

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                                                                  EXHIBIT 10.2.1

                             ARCH CAPITAL GROUP LTD.

                      NON-QUALIFIED STOCK OPTION AGREEMENT

        FOR GOOD AND VALUABLE CONSIDERATION, receipt of which is hereby
acknowledged, Arch Capital Group Ltd. (the "Company"), a Delaware corporation,
hereby grants to Peter A. Appel, an officer of the Company on the date hereof
(the "Option Holder"), the option to purchase common stock, $.01 par value per
share, of the Company ("Shares"), upon the following terms:

        WHEREAS, the Option Holder has been granted the following award in
connection with his retention as President and Chief Executive Officer and as
compensation for services to be rendered; and the following terms reflect the
Company's 1995 Long Term Incentive and Share Award Plan (as amended, the
"Plan");

        (a) GRANT. The Option Holder is hereby granted an option (the "Option")
to purchase 100,000 Shares (the "Option Shares") pursuant to the Plan, the terms
of which are incorporated herein by reference. The Option is granted as of April
24, 2000 (the "Date of Grant") and such grant is subject to the terms and
conditions herein and the terms and conditions of the applicable provisions of
the Plan. Such Option shall not be treated as an incentive stock option under
Section 422 of the Internal Revenue Code of 1986, as amended.

        (b) STATUS OF OPTION SHARES. The Option Shares shall upon issue rank
equally in all respects with the other Shares.

        (c) OPTION PRICE. The purchase price for the Option Shares shall be,
except as herein provided, $15.125 per Option Share, hereinafter sometimes
referred to as the "Option Price," payable immediately in full upon the exercise
of the Option.

        (d) TERM OF OPTION. The Option may be exercised only during the period
(the "Option Period") commencing on the Date of Grant and shall continue for ten
years from such Date of Grant; thereafter the Option Holder shall cease to have
any rights in respect thereof. Subject to paragraph (i) below, the Option may be
exercised at any time or from time to time during the Option Period in regard to
all or any portion of the Option, as may be adjusted pursuant to paragraph (f)
below. The right to exercise the Option may be subject to sooner termination in
the event employment with the Company is terminated, as provided in paragraph
(i) below.

        (e) NO RIGHTS OF SHAREHOLDER. The Option Holder shall not, by virtue
hereof, be entitled to any rights of a shareholder in the Company, either at law
or in equity.

        (f) ADJUSTMENTS FOR RECAPITALIZATION AND DIVIDENDS. In the event that,
prior to the expiration of the Option, any dividend in Shares, recapitalization,
Share split, reverse split, reorganization, merger, consolidation, spin-off,
combination, repurchase, or share exchange, or other such change affects the
Shares such that they are increased or decreased or changed into or exchanged
for a different number or kind of shares, other securities of the Company or of
another corporation or other consideration, then in order to maintain the
proportionate interest of the Option Holder and preserve the value of the
Option, (i) there shall automatically be substituted for each Share subject to
the unexercised Option the number and kind of shares, other securities or other
consideration into which each outstanding Share shall be changed or for which
each such Share shall be exchanged, and (ii) the exercise price shall be
increased or

<PAGE>

decreased proportionately so that the aggregate purchase price for the Shares
subject to the unexercised Option shall remain the same as immediately prior to
such event.

        (g) NONTRANSFERABILITY. The Option may not be assigned or otherwise
transferred, disposed of or encumbered by the Option Holder, other than by will
or by the laws of descent and distribution. During the lifetime of the Option
Holder, the Option shall be exercisable only by the Option Holder or by his or
her guardian or legal representative. Notwithstanding the foregoing, the Option
may be transferred for no consideration by the Option Holder to members of his
or her "immediate family" or to a trust established for the exclusive benefit of
solely one or more members of the Option Holder's "immediate family." Any Option
held by the transferee will continue to be subject to the same terms and
conditions that were applicable to the Option immediately prior to the transfer,
except that the Option will be transferable by the transferee only by will or
the laws of descent and distribution. For purposes hereof, "immediate family"
means the Option Holder's children, stepchildren, grandchildren, parents,
stepparents, grandparents, spouse, siblings (including half brothers and
sisters), in-laws, and relationships arising because of legal adoption.

        (h) EXERCISE OF OPTION. In order to exercise the Option, the Option
Holder shall submit to the Company an instrument in writing signed by the Option
Holder, specifying the number of Option Shares in respect of which the Option is
being exercised, accompanied by payment, in a manner acceptable to the Company,
of the Option Price for the Option Shares for which the Option is being
exercised. Payment to the Company in cash or Shares already owned by the Option
Holder (provided that the Option Holder has owned such Shares for a minimum
period of six months) and having a total Fair Market Value (as defined below)
equal to the exercise price, or in a combination of cash and such Shares, shall
be deemed acceptable. Option Shares will be issued accordingly by the Company
within 15 business days, and a share certificate dispatched to the Option Holder
within 30 days.

        The Company shall not be required to issue fractional Shares upon the
exercise of the Option. If any fractional interest in a Share would be
deliverable upon the exercise of the Option in whole or in part but for the
provisions of this paragraph, the Company, in lieu of delivering any such
fractional share therefor, shall pay a cash adjustment therefor in an amount
equal to their Fair Market Value (or if any Shares are not publicly traded, an
amount equal to the book value per share at the end of the most recent fiscal
quarter) multiplied by the fraction of the fractional share which would
otherwise have been issued hereunder. Anything to the contrary herein
notwithstanding, the Company shall not be obligated to issue any Option Shares
hereunder if the issuance of such Option Shares would violate the provision of
any applicable law, in which event the Company shall, as soon as practicable,
take whatever action it reasonably can so that such Option Shares may be issued
without resulting in such violations of law. For purposes hereof, Fair Market
Value shall mean the mean between the high and low selling prices per Share on
the immediately preceding date (or, if the Shares were not traded on that day,
the next preceding day that the Shares were traded) on the principal exchange on
which the Shares are traded, as such prices are officially quoted on such
exchange.

        (i) TERMINATION OF SERVICE. In the event the Option Holder ceases to be
an employee of the Company (i) due to retirement after attainment of age 65,
(ii) due to death or disability, as determined under the Company's long-term
disability plan, or (iii) due to (A) termination by the Company without Cause
(as defined below) or (B) Constructive Termination (as defined below), the
Option may be exercised at any time during the Option Period. If the Option
Holder ceases to be an employee of the Company for any other reason, the Option
may be exercised at any time within 30 days after the date of such termination,
but not later than termination of the Option Period. For purposes of this
Option, service with any of the Company's wholly owned subsidiaries shall be
considered to be service with the Company. Termination of the Option Holder's
employment by the Company or any of its subsidiaries for

                                       2
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"Cause" shall mean termination by reason of the Option Holder's willful
engagement in conduct which involves dishonesty or moral turpitude in connection
with his employment and which is demonstrably and materially injurious to the
financial condition or reputation of the Company. An act or omission shall be
deemed "willful" only if done, or omitted to be done, in bad faith and without
reasonable belief that it was in the best interest of the Company.
Notwithstanding the foregoing, the Option Holder shall not be deemed to have
been terminated for Cause unless and until there shall have been delivered to
the Option Holder a written notice of termination from the compensation
committee of the Board after reasonable notice to the Option Holder and an
opportunity for him, together with his counsel, to be heard before such
committee. Termination of employment by the Option Holder due to "Constructive
Termination" shall mean termination by the Option Holder subsequent to any of
the following: (a) the assignment of duties and responsibilities inconsistent in
any material and adverse respect with the Option Holder's position or a
significant diminution in his duties or responsibilities; provided, however,
that Constructive Termination shall not be deemed to occur upon a change in
duties or responsibilities that is solely and directly a result of the Company
no longer being a publicly traded entity, and does not involve any other event
set forth in this definition; (b) reduction in the Option Holder's base salary
or bonus opportunity; (c) the requirement that the Option Holder work at a
location outside of Fairfield County, Connecticut, or Westchester County, New
York; (d) the failure to provide the Option Holder with benefits and incentive
compensation opportunities at least as favorable, in the aggregate, as the
benefits and incentive compensation opportunities available to the Employee
immediately prior to a Change in Control (as defined in Restricted Share
Agreement, dated as of April 24, 2000, between the Company and the Option
Holder); or (e) the failure to secure the agreement of any successor corporation
or other entity to the Company to fully assume the Company's obligations under
the arrangements described herein. The Option Holder shall exercise his right to
terminate employment due to Constructive Termination by giving the Company a
written notice of termination specifying in reasonable detail the circumstances
constituting such Constructive Termination. In that event, the Option Holder's
employment shall terminate on the last day of the month in which such notice is
given unless an earlier date is specified in writing by the Executive. A
termination of employment by the Option Holder shall be due to Constructive
Termination if one of the occurrences specified in clauses (a) through (e) of
this subsection shall have occurred, notwithstanding that the Option Holder may
have other reasons for terminating employment, including employment by another
employer which the Option Holder desires to accept.

        (j) OBLIGATIONS AS TO CAPITAL. The Company agrees that it will at all
times maintain authorized and unissued share capital sufficient to fulfill all
of its obligations under the Option.

        (k) TRANSFER OF SHARES. The Option, the Option Shares, or any interest
in either, may be sold, assigned, pledged, hypothecated, encumbered, or
transferred or disposed of in any other manner, in whole or in part, only in
compliance with the terms, conditions and restrictions as set forth in the
governing instruments of the Company, applicable United States federal and state
securities laws and the terms and conditions hereof. Each certificate for Option
Shares issued upon exercise of the Option, unless at the time of exercise such
Option Shares are registered under the Securities Act of 1933, as amended, shall
bear the following legend or such other legend as the Company deems appropriate:

      "The securities evidenced hereby have not been registered under the
      Securities Act of 1933, as amended (the 'Act'), and may not be offered,
      sold or otherwise transferred except (i) in compliance with the provisions
      of any applicable state securities or 'Blue Sky' laws and (ii) (A)
      pursuant to an effective registration under the Act, (B) in compliance
      with Rule 144 under the Act, (C) inside the United States to a Qualified
      Institutional Buyer in compliance with Rule 144A under the Act, (D)
      outside the United States in compliance with Rule 904 of Regulation S
      under

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      the Act or (E) inside the United States to an institutional 'accredited
      investor' as defined in Rule 501(a)(1), (2), (3) or (7) under the Act in a
      transaction which, in the opinion of counsel reasonably satisfactory to
      the Company, qualifies as an exempt transaction under the Act and the
      rules and regulations promulgated thereunder."

Any certificate issued at any time in exchange or substitution for any
certificate bearing such legend or such other legend deemed appropriate by the
Company shall also bear such legend unless, in the opinion of counsel for the
Company, the securities represented thereby need no longer be subject to the
restrictions set forth therein. The provisions of this paragraph (l) shall be
binding upon all subsequent holders of certificates bearing the above legend and
all subsequent holders of the Option, if any.

        (l) EXPENSES OF ISSUANCE OF OPTION SHARES. The issuance of stock
certificates upon the exercise of the Option in whole or in part, shall be
without charge to the Option Holder. The Company shall pay, and indemnify the
Option Holder from and against any issuance, stamp or documentary taxes (other
than transfer taxes) or charges imposed by any governmental body, agency or
official (other than income taxes) by reason of the exercise of the Option in
whole or in part or the resulting issuance of the Option Shares.

        (m) WITHHOLDING. The Option Holder agrees to make appropriate
arrangements with the Company for satisfaction of any applicable tax withholding
requirements, or similar requirements, arising out of the Option.

        (n) REFERENCES. References herein to rights and obligations of the
Option Holder shall apply, where appropriate, to the Option Holder's legal
representative or estate without regard to whether specific reference to such
legal representative or estate is contained in a particular provision of this
Option.

        (o) SETTLEMENT OF DISPUTES. Any dispute between the parties arising from
or relating to the terms of this Option shall be resolved by arbitration held in
the State of Connecticut in accordance with the rules of the American
Arbitration Association. All costs associated with any arbitration, including
all legal expenses, for both parties shall be borne by the Company.

        (p) NOTICES. Any notice required or permitted to be given under this
agreement shall be in writing and shall be deemed to have been given when
delivered personally or by courier, or sent by certified or registered mail,
postage prepaid, return receipt requested, duly addressed to the party concerned
at the address indicated below or to such changed address as such party may
subsequently by similar process give notice of:

        If to the Company:

        Arch Capital Group Ltd.
        20 Horseneck Lane
        Greenwich, CT  06830
        Attn:  Secretary

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<PAGE>

        If to the Option Holder:

        Peter A. Appel
        [address of Option Holder]

        (q) GOVERNING LAW. This agreement shall be governed by and construed in
accordance with the laws of the State of New York, without giving effect to
principles of conflict of laws.

        (r) ENTIRE AGREEMENT. This agreement constitutes the entire agreement
among the parties relating to the subject matter hereof, and any previous
agreement or understanding among the parties with respect thereto is superseded
by this agreement.

        (s) COUNTERPARTS.  This agreement may be executed in two counterparts,
each of which shall constitute one and the same instrument.

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<PAGE>

        IN WITNESS WHEREOF, the undersigned have executed this agreement as of
the Date of Grant.

                                    ARCH CAPITAL GROUP LTD.

                                    By:   /s/ Robert Clements
                                       -----------------------------------------
                                       Robert Clements
                                          Chairman

                                          /s/ Peter A. Appel
                                       -----------------------------------------
                                       Peter A. Appel

                                       6<PAGE>

                                                                  EXHIBIT 10.2.2

      Each of Debra M. O'Connor and Louis T. Petrillo has entered into the
following Incentive Stock Option Agreement with Arch Capital Group Ltd., dated
as of May 5, 2000:

                             ARCH CAPITAL GROUP LTD.

                        INCENTIVE STOCK OPTION AGREEMENT

        FOR GOOD AND VALUABLE CONSIDERATION, receipt of which is hereby
acknowledged, Arch Capital Group Ltd. (the "Company"), a Delaware corporation,
hereby grants to _______________, an employee of the Company on the date hereof
(the "Option Holder"), the option to purchase common stock, $.01 par value per
share, of the Company ("Shares"), upon the
following terms:

        WHEREAS, the Employee has been granted the following award in connection
with his retention as an employee and as compensation for services to be
rendered; and the following terms reflect the Company's 1999 Long Term Incentive
and Share Award Plan (the "Plan");

        (a) GRANT. The Option Holder is hereby granted an option (the "Option")
to purchase 10,000 Shares (the "Option Shares") pursuant to the Plan, the terms
of which are incorporated herein by reference. The Option is granted as of May
5, 2000 (the "Date of Grant") and such grant is subject to the terms and
conditions herein and the terms and conditions of the applicable provisions of
the Plan. This Option is intended to be an incentive stock option as defined in
Section 422 of the Internal Revenue Code of 1986, as amended. However, the
Option will qualify as an incentive stock option only to the extent that the
aggregate fair market value (determined on the Date of Grant) of the Shares
(together with Shares under other incentive stock options granted by the Company
or any subsidiary to the Option Holder) for which the incentive stock options
first become exercisable in any calendar year does not exceed $100,000. Should
the fair market value exceed $100,000, the Option to the extent of such excess
shall be regarded as a non-qualified stock option.

        (b) STATUS OF OPTION SHARES. The Option Shares shall upon issue rank
equally in all respects with the other Shares.

        (c) OPTION PRICE. The purchase price for the Option Shares shall be,
except as herein provided, $16.00 per Option Share, hereinafter sometimes
referred to as the "Option Price," payable immediately in full upon the exercise
of the Option.

        (d) TERM OF OPTION. The Option may be exercised only during the period
(the "Option Period") commencing in accordance with paragraph (f) below and
shall continue for ten years from the Date of Grant; thereafter the Option
Holder shall cease to have any rights in respect thereof. The right to exercise
the Option may be subject to sooner termination in the event employment with the
Company is terminated, as provided in paragraph (j) below.

        (e) NO RIGHTS OF SHAREHOLDER. The Option Holder shall not, by virtue
hereof, be entitled to any rights of a shareholder in the Company, either at law
or in equity.

        (f) EXERCISABILITY. One-fourth of the Option shall become exercisable on
each of the first, second, third and fourth anniversary of the Date of Grant,
subject to paragraph (j) below; provided that such Option, to the extent not
already exercisable in full, shall become immediately and fully exercisable (1)
to the extent provided in paragraph (j) below and (2) upon a Change in Control.
Subject to paragraph (j) below, the Option may be exercised at any time or from
time to time during the Option Period in

<PAGE>

regard to all or any portion of the Option which is then exercisable, as may be
adjusted pursuant to paragraph (g) below.

               "Change in Control" means any of the following occurring
      after the date hereof:

               a. any person (within the meaning of the Securities Exchange Act
            of 1934, as amended (the "Exchange Act")), other than a Permitted
            Person or an Initial Investor, is or becomes the "beneficial owner"
            (as defined in Rule 13d-3 under the Exchange Act), directly or
            indirectly, of Voting Securities representing 35% or more of the
            total voting power of all the then outstanding Voting Securities; or

               b. any Initial Investor is or becomes the "beneficial owner" (as
            defined in Rule 13d-3 under the Exchange Act), directly or
            indirectly, of Voting Securities representing 50% or more of the
            total voting power of all the then outstanding Voting Securities; or

               c. the individuals who, as of the Date of Grant, constitute the
            Board of Directors of the Company (the "Board") together with those
            who become directors subsequent to such date and whose
            recommendation, election or nomination for election to the Board was
            approved by a vote of at least a majority of the directors then
            still in office who either were directors as of such date or whose
            recommendation, election or nomination for election was previously
            so approved, cease for any reason to constitute a majority of the
            members of the Board; or

               d. the consummation of a merger, consolidation, recapitalization,
            liquidation, sale or disposition by the Company of all or
            substantially all of the Company's assets, or reorganization of the
            Company, other than any such transaction which would (x) result in
            at least 60% of the total voting power represented by the voting
            securities of the surviving entity or, in the case of an asset sale,
            the successor entity, outstanding immediately after such transaction
            being beneficially owned, directly or indirectly, by the
            stockholders of the Company immediately preceding the transaction
            and (y) not otherwise be deemed a Change in Control under
            subparagraphs a, b, c or e of this paragraph (f); or

               e. the Board adopts a resolution to the effect that, for purposes
            hereof, a Change in Control has occurred.

                  (i) "Initial Investors" means (A) The Trident Partnership,
               L.P.; (B) Marsh & McLennan Risk Capital Holdings, Ltd.; or (C)
               any majority-owned subsidiary or parent (or equivalent in the
               case of a non-corporate entity) of the foregoing.

                  (ii) "Permitted Persons" means (A) the Company; (B) any
               Related Party; or (C) any group (as defined in Rule 13d-3 under
               the Exchange Act) comprised of any or all of the foregoing.

                  (iii) "Related Party" means (A) a majority-owned subsidiary of
               the Company; (B) a trustee or other fiduciary holding securities
               under an employee benefit plan of the Company or any
               majority-owned subsidiary of the Company; or (C) a corporation
               owned directly or indirectly by the stockholders of the Company
               in substantially the same proportion as their ownership of Voting
               Securities.

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<PAGE>

                  (iv) "Voting Security" means any security of the Company which
               carries the right to vote generally in the election of directors.

        (g) ADJUSTMENTS FOR RECAPITALIZATION AND DIVIDENDS. In the event that,
prior to the expiration of the Option, any dividend in Shares, recapitalization,
Share split, reverse split, reorganization, merger, consolidation, spin-off,
combination, repurchase, or share exchange, or other such change affects the
Shares such that they are increased or decreased or changed into or exchanged
for a different number or kind of shares, other securities of the Company or of
another corporation or other consideration, then in order to maintain the
proportionate interest of the Option Holder and preserve the value of the
Option, (i) there shall automatically be substituted for each Share subject to
the unexercised Option the number and kind of shares, other securities or other
consideration into which each outstanding Share shall be changed or for which
each such Share shall be exchanged, and (ii) the exercise price shall be
increased or decreased proportionately so that the aggregate purchase price for
the Shares subject to the unexercised Option shall remain the same as
immediately prior to such event.

        (h) NONTRANSFERABILITY. The Option may not be assigned or otherwise
transferred, disposed of or encumbered by the Option Holder, other than by will
or by the laws of descent and distribution. During the lifetime of the Option
Holder, the Option shall be exercisable only by the Option Holder or by his or
her guardian or legal representative.

        (i) EXERCISE OF OPTION. In order to exercise the Option, the Option
Holder shall submit to the Company an instrument in writing signed by the Option
Holder, specifying the number of Option Shares in respect of which the Option is
being exercised, accompanied by payment, in a manner acceptable to the Company,
of the Option Price for the Option Shares for which the Option is being
exercised. Payment to the Company in cash or Shares already owned by the Option
Holder (provided that the Option Holder has owned such Shares for a minimum
period of six months) and having a total Fair Market Value (as defined below)
equal to the exercise price, or in a combination of cash and such Shares, shall
be deemed acceptable. Option Shares will be issued accordingly by the Company
within 15 business days, and a share certificate dispatched to the Option Holder
within 30 days.

        The Company shall not be required to issue fractional Shares upon the
exercise of the Option. If any fractional interest in a Share would be
deliverable upon the exercise of the Option in whole or in part but for the
provisions of this paragraph, the Company, in lieu of delivering any such
fractional share therefor, shall pay a cash adjustment therefor in an amount
equal to their Fair Market Value (or if any Shares are not publicly traded, an
amount equal to the book value per share at the end of the most recent fiscal
quarter) multiplied by the fraction of the fractional share which would
otherwise have been issued hereunder. Anything to the contrary herein
notwithstanding, the Company shall not be obligated to issue any Option Shares
hereunder if the issuance of such Option Shares would violate the provision of
any applicable law, in which event the Company shall, as soon as practicable,
take whatever action it reasonably can so that such Option Shares may be issued
without resulting in such violations of law. For purposes hereof, Fair Market
Value shall mean the mean between the high and low selling prices per Share on
the immediately preceding date (or, if the Shares were not traded on that day,
the next preceding day that the Shares were traded) on the principal exchange on
which the Shares are traded, as such prices are officially quoted on such
exchange.

        (j) TERMINATION OF SERVICE. In the event the Option Holder ceases to be
an employee of the Company (i) due to retirement after attainment of age 65 or
(ii) due to death or disability, as determined under the Company's long-term
disability plan, the Option, to the extent not already exercisable in full,
shall become immediately and fully exercisable at the time of such termination
of service, and the Option may be exercised at any time during the Option
Period. If the Option Holder ceases to be an employee of the Company for any
other reason, the portion of the Option which is not then exercisable shall be

                                       3
<PAGE>

cancelled on the date service terminates, and the portion of the Option which is
then exercisable may be exercised at any time within 30 days after the date of
such termination, but not later than termination of the Option Period. For
purposes of this Option, service any of the Company's wholly owned subsidiaries
shall be considered to be service with the Company.

        (k) OBLIGATIONS AS TO CAPITAL. The Company agrees that it will at all
times maintain authorized and unissued share capital sufficient to fulfill all
of its obligations under the Option.

        (l) TRANSFER OF SHARES. The Option, the Option Shares, or any interest
in either, may be sold, assigned, pledged, hypothecated, encumbered, or
transferred or disposed of in any other manner, in whole or in part, only in
compliance with the terms, conditions and restrictions as set forth in the
governing instruments of the Company, applicable United States federal and state
securities laws and the terms and conditions hereof. Each certificate for Option
Shares issued upon exercise of the Option, unless at the time of exercise such
Option Shares are registered under the Securities Act of 1933, as amended, shall
bear the following legend or such other legend as the Company deems appropriate:

      "The securities evidenced hereby have not been registered under the
      Securities Act of 1933, as amended (the 'Act'), and may not be offered,
      sold or otherwise transferred except (i) in compliance with the provisions
      of any applicable state securities or 'Blue Sky' laws and (ii) (A)
      pursuant to an effective registration under the Act, (B) in compliance
      with Rule 144 under the Act, (C) inside the United States to a Qualified
      Institutional Buyer in compliance with Rule 144A under the Act, (D)
      outside the United States in compliance with Rule 904 of Regulation S
      under the Act or (E) inside the United States to an institutional
      'accredited investor' as defined in Rule 501(a)(1), (2), (3) or (7) under
      the Act in a transaction which, in the opinion of counsel reasonably
      satisfactory to the Company, qualifies as an exempt transaction under the
      Act and the rules and regulations promulgated thereunder."

Any certificate issued at any time in exchange or substitution for any
certificate bearing such legend or such other legend deemed appropriate by the
Company shall also bear such legend unless, in the opinion of counsel for the
Company, the securities represented thereby need no longer be subject to the
restrictions set forth therein. The provisions of this paragraph (l) shall be
binding upon all subsequent holders of certificates bearing the above legend and
all subsequent holders of the Option, if any.

        (m) EXPENSES OF ISSUANCE OF OPTION SHARES. The issuance of stock
certificates upon the exercise of the Option in whole or in part, shall be
without charge to the Option Holder. The Company shall pay, and indemnify the
Option Holder from and against any issuance, stamp or documentary taxes (other
than transfer taxes) or charges imposed by any governmental body, agency or
official (other than income taxes) by reason of the exercise of the Option in
whole or in part or the resulting issuance of the Option Shares.

        (n) WITHHOLDING. The Option Holder agrees to make appropriate
arrangements with the Company for satisfaction of any applicable tax withholding
requirements, or similar requirements, arising out of the Option.

        (o) REFERENCES. References herein to rights and obligations of the
Option Holder shall apply, where appropriate, to the Option Holder's legal
representative or estate without regard to whether specific reference to such
legal representative or estate is contained in a particular provision of this
Option.

        (p) SETTLEMENT OF DISPUTES. Any dispute between the parties arising from
or relating to the terms of this Option shall be resolved by arbitration held in
the State of Connecticut in accordance with

                                       4
<PAGE>

the rules of the American Arbitration Association. All costs associated with any
arbitration, including all legal expenses, for both parties shall be borne by
the Company.

        (q) NO MITIGATION. To the extent that the vesting of any portion of the
Option is accelerated upon a Change in Control or upon a termination of service
as provided herein, neither the Option, nor any Option Shares nor any interest
in either, shall be reduced by any compensation received by the Option Holder in
connection with any other employment.

        (r) NOTICE OF TRANSFER. The Option Holder agrees that, in the event he
or she disposes (whether by sale, exchange, gift or any other transfer) of any
Shares acquired by the Option Holder on exercise of this Option within two years
from the Date of Grant or within one year after the acquisition of such Shares
pursuant to this agreement, the Option Holder will notify the Company no later
than 15 days after the date of such disposition of the date and number of Shares
so disposed of by the Option Holder and any consideration received.

        (s) NOTICES. Any notice required or permitted to be given under this
agreement shall be in writing and shall be deemed to have been given when
delivered personally or by courier, or sent by certified or registered mail,
postage prepaid, return receipt requested, duly addressed to the party concerned
at the address indicated below or to such changed address as such party may
subsequently by similar process give notice of:

    If to the Company:

        Arch Capital Group Ltd.
        20 Horseneck Lane
        Greenwich, CT  06830
        Attn:  Secretary

    If to the Option Holder:

        [name and address of Option Holder]

        (t) GOVERNING LAW. This agreement shall be governed by and construed in
accordance with the laws of the State of New York, without giving effect to
principles of conflict of laws.

        (u) ENTIRE AGREEMENT. This agreement constitutes the entire agreement
among the parties relating to the subject matter hereof, and any previous
agreement or understanding among the parties with respect thereto is superseded
by this agreement.

        (v) COUNTERPARTS.  This agreement may be executed in two
counterparts, each of which shall constitute one and the same instrument.

                                       5
<PAGE>

        IN WITNESS WHEREOF, the undersigned have executed this agreement as of
the Date of Grant.

                                    ARCH CAPITAL GROUP LTD.

                                    By: /s/ Peter A. Appel
                                       -------------------------------------
                                       Peter A. Appel
                                       President and Chief Executive Officer

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

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