Document:

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                                                                   Exhibit 10.15

                             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 Bermuda company, hereby
grants to Marc Grandisson, an employee of the Company on the date hereof (the
"Option Holder"), the option to purchase common shares, $0.01 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 an employee and as compensation for services to
be rendered; and the following terms reflect the Company's Long Term Incentive
Plan for New Employees (the "Plan");

            (a) GRANT. The Option Holder is hereby granted an option (the
"Option") to purchase 37,500 Shares (the "Option Shares") pursuant to the Plan,
the terms of which are incorporated herein by reference. The Option is granted
as of October 23, 2001 (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 shall not be treated as an incentive stock
option as defined in Section 422 of the Internal Revenue Code of 1986, as
amended. In the event of any conflict between this Agreement and the Plan, the
Plan shall control.

            (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, $20.00 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") set forth in paragraph (f) below and shall remain
exercisable until the tenth anniversary of the Date of Grant. Thereafter, the
Option Holder shall cease to have any rights in respect thereof. The right to
exercise the Option shall 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.

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                                      -2-

            (f) EXERCISABILITY. Except as otherwise set forth in paragraph (j)
below, the Option shall become exercisable as to one third of the Option Shares
beginning on the earlier of (A) the date on which the closing occurs under the
Subscription Agreement with new investors entered into substantially
simultaneously with the execution of this agreement or (B) the first anniversary
of the Date of Grant, and as to an additional one-third of the Option Shares on
the first anniversary of the Date of Grant, and as to the final one-third of the
Option Shares on the second anniversary of the Date of Grant, in each case
subject to paragraph (j) below. Subject to paragraph (j) 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 which is then exercisable, as may be
adjusted pursuant to paragraph (g) below.

            (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 (including cash) 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, or any interest therein, 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 by the Option Holder to members of
his or her "immediate family " or to a trust or other entity 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 brother and sisters), in laws, and relationships
arising because of legal adoption.

            (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 whole 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 or has purchased such Shares on the open

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                                      -3-

market) 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 for purposes hereof. 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 for any reason, except due to his death or
Permanent Disability (as defined in the Employment Agreement between the Option
Holder, the Company and Arch Reinsurance Ltd. dated as of October 23, 2001 (the
"Employment Agreement")) or due to a termination of the Option Holder's
employment by the Company for Cause (as defined in the Employment Agreement),
the Option, to the extent then exercisable, may be exercised for 90 days
following termination of employment (but not beyond the Option Period). To the
extent the Option is not exercisable at the time of termination of employment,
the Option shall be immediately forfeited. For purposes of this Option, service
with any of the Company's wholly owned subsidiaries shall be considered to be
service with the Company. In the event of a termination of the Option Holder's
employment for Cause, the Option shall immediately cease to be exercisable and
shall be immediately forfeited. In the event the Option Holder ceases to be an
Employee of the Company due to his death or Permanent Disability, the Option
shall become immediately exercisable in full and shall continue to be
exercisable by the Option Holder (or his Beneficiary or estate in the event of
his death) for the remainder of the Option Period.

            (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

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                                      -4-

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.

            (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. No later than the date of exercise of the Option
granted hereunder, the Option Holder shall pay to the Company or make
arrangements satisfactory to the Committee regarding payment of any federal,
state or local taxes of any kind required by law to be withheld upon the
exercise of such Option and the Company shall, to the extent permitted or
required by law, have the right to deduct from any payment of any kind otherwise
due to the Option Holder, federal, state and local taxes of any kind required by
law to be withheld upon the exercise of such 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) 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.
            EXECUTIVE OFFICES:
            20 Horseneck Lane
            Greenwich, CT  06830
            Attn: Secretary

      If to the Option Holder:

            To the last address delivered to the Company by the Option Holder in
            the manner set forth herein.

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

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            (r) ENTIRE AGREEMENT. This agreement and the Plan constitute 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 and the Plan.

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

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                                      -6-

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

                                        ARCH CAPITAL GROUP LTD.

                                        BY: /s/ Louis T. Petrillo
                                           -------------------------------------

                                        /s/ Marc Grandisson
                                        ----------------------------------------
                                        Marc Grandisson<Page>
                                                                   Exhibit 10.16

                             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 Bermuda company, hereby
grants to Debra M. O'Connor, an employee of the Company on the date hereof (the
"Option Holder"), the option to purchase common shares, $.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 her retention as an employee 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 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 January
30, 2001 (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, $15.00 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 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:

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                  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.

                        (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

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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
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 with any of the Company's wholly owned
subsidiaries shall be considered to be service with the Company.

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      (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 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

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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:

            Debra M. O'Connor
            14 Revere Road
            Riverside, CT  06878

      (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.

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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/ Peter A. Appel
                                           -------------------------------------
                                           Peter A. Appel
                                           President & Chief Executive Officer

                                        /s/ Debra M. O'Connor
                                        ----------------------------------------
                                        Debra M. O'Connor

<Page>

                             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 Bermuda company, hereby
grants to Debra O'Connor, an employee of the Company on the date hereof (the
"Option Holder"), the option to purchase common shares, $0.01 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 service 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
October 23, 2001 (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 shall not be treated as an incentive stock option as
defined in Section 422 of the Internal Revenue Code of 1986, as amended. In the
event of any conflict between this Agreement and the Plan, the Plan shall
control.

       (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, $20.00 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") set forth in paragraph (f) below and shall remain
exercisable until the tenth anniversary of the Date of Grant. Thereafter, the
Option Holder shall cease to have any rights in respect thereof. The right to
exercise the Option shall 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. Except as otherwise set forth in paragraph (j) below,
the Option shall become exercisable as to one third of the Option Shares
beginning on the earlier of (A) the date on which the closing occurs under the
Subscription Agreement with new investors entered into substantially
simultaneously with the execution of this agreement

<Page>
                                      -2-

or (B) the first anniversary of the Date of Grant, and as to an additional
one-third of the Option Shares on the first anniversary of the Date of Grant,
and as to the final one-third of the Option Shares on the second anniversary of
the Date of Grant, in each case subject to paragraph (j) below. Subject to
paragraph (j) 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
which is then exercisable, as may be adjusted pursuant to paragraph (g) below.

       (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 (including cash) 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, or any interest therein, 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 by the Option Holder to members of
his or her "immediate family " or to a trust or other entity 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 brother and sisters), in laws, and relationships
arising because of legal adoption.

       (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 whole 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 or has purchased such Shares on the open market) 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

<Page>
                                      -3-

for purposes hereof. 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 for any reason, except due to his death or Permanent
Disability or due to a termination of the Option Holder's employment by the
Company for Cause, the Option, to the extent then exercisable, may be exercised
for 90 days following termination of employment (but not beyond the Option
Period). To the extent the Option is not exercisable at the time of termination
of employment, the Option shall be immediately forfeited. For purposes of this
Option, service with any of the Company's wholly owned subsidiaries shall be
considered to be service with the Company. In the event of a termination of the
Option Holder's employment for Cause, the Option shall immediately cease to be
exercisable and shall be immediately forfeited. In the event the Option Holder
ceases to be an Employee of the Company due to his death or Permanent
Disability, the Option shall become immediately exercisable in full and shall
continue to be exercisable by the Option Holder (or his Beneficiary or estate in
the event of his death) for the remainder of the Option Period. For purposes
hereof, "Cause" means (a) theft or embezzlement by the Option Holder with
respect to the Company or its subsidiaries; (b) malfeasance or gross negligence
in the performance of the Option Holder's duties; (c) the commission by the
Option Holder of any felony or any crime involving moral turpitude; (d) willful
or prolonged absence from work by the Option Holder (other than by reason of
disability due to physical or mental illness) or failure, neglect or refusal by
the Option Holder to perform his duties and responsibilities without the same
being corrected within ten (10) days after being given written notice thereof;
(e) continued and habitual use of alcohol by the Option Holder to an extent
which materially impairs the Option Holder's performance of his duties without
the same being corrected within ten (10) days after being given written notice
thereof; or (f) the Option Holder's use of illegal drugs without the same being
corrected within ten (10) days after being given written notice thereof. For
purposes hereof, "Permanent Disability" means those circumstances where the
Option Holder is unable to continue to perform the usual customary duties of his
assigned job for a period of six (6) months in any twelve (12) month period
because of physical, mental or emotional incapacity resulting from injury,
sickness or disease. Any

<Page>
                                      -4-

questions as to the existence of a Permanent Disability shall be determined by a
qualified, independent physician selected by the Company and approved by the
Option Holder (which approval shall not be unreasonably withheld). The
determination of any such physician shall be final and conclusive for all
purposes of this Agreement.

       (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.

       (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. No later than the date of exercise of the Option granted
hereunder, the Option Holder shall pay to the Company or make arrangements
satisfactory to the Committee regarding payment of any federal, state or local
taxes of any kind required by law to be withheld upon the exercise of such
Option and the Company shall, to the extent permitted or required by law, have
the right to deduct from any payment of any kind otherwise due to the Option
Holder, federal, state and local taxes of any kind required by law to be
withheld upon the exercise of such 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) 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:

<Page>
                                      -5-

   If to the Company:

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

   If to the Option Holder:

       To the last address delivered to the Company by the Option Holder in the
       manner set forth herein.

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

       (r) ENTIRE AGREEMENT. This agreement and the Plan constitute 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 and the Plan.

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

<Page>
                                      -6-

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

                                     ARCH CAPITAL GROUP LTD.

                                      By: /s/ Peter A. Appel
                                         ------------------------------------

                                     /s/ Debra O'Connor
                                     ----------------------------------------
                                     Debra O'Connor

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