Document:

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                                                                   Exhibit 10.17

                             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 Louis T. Petrillo, 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 his 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:

            Louis T. Petrillo
            124 West 60th Street, Apt. 43F
            New York, NY 10023

      (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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      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/ Louis T. Petrillo
                                        ----------------------------------------
                                        Louis T. Petrillo

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                             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 Louis Petrillo, 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 40,000 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

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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.
For the avoidance of doubt, exercisability of the Option shall not be
accelerated upon a Change in Control, as defined in the Employment and Change in
Control Agreement between the Company and the Option Holder dated May 5, 2000.

            (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

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                                      -3-

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 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

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                                      -4-

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 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/ Louis T. Petrillo
                                            ------------------------------------
                                            Louis Petrillo<Page>

                                                               EXHIBIT 10.31(j)

                               TENTH AMENDMENT
                 TO THE MASTER LOAN AND SECURITY AGREEMENT

     Tenth Amendment, dated as of November 9, 2001 (this "AMENDMENT"), to the
Master Loan and Security Agreement, dated as of October 29, 1999 (as
previously amended, supplemented or otherwise modified, the "EXISTING LOAN
AGREEMENT", and as amended hereby, the "LOAN AGREEMENT"), between AAMES
CAPITAL CORPORATION (the "BORROWER"), and MORGAN STANLEY DEAN WITTER MORTGAGE
CAPITAL INC., formerly MORGAN STANLEY MORTGAGE CAPITAL INC., (the "LENDER").

                                     RECITALS

     The Borrower and the Lender are parties to the Existing Loan Agreement.
Capitalized terms used but not otherwise defined herein shall have the
meanings given to them in the Existing Loan Agreement.

     The Borrower and the Lender have agreed, subject to the terms and
conditions of this Amendment, that the Existing Loan Agreement be amended to
extend the Termination Date as set forth herein.

     Accordingly, the Borrower and the Lender hereby agree, in consideration
of the mutual premises and mutual obligations set forth herein, that the
Existing Loan Agreement is hereby amended as follows:

     SECTION 1. AMENDMENT.  Section 1.01 of the Existing Loan Agreement
is hereby amended by deleting the definition of "TERMINATION DATE" in its
entirety and substituting in lieu thereof the following new definition:

     "'TERMINATION DATE' shall mean November 16, 2001 or such earlier date on
which this Loan Agreement shall terminate in accordance with the provisions
hereof or by operation of law."

     SECTION 2. CONDITIONS PRECEDENT.  This Amendment shall become effective
on the date (the "AMENDMENT EFFECTIVE DATE") on which the following
conditions precedent shall have been satisfied:

     2.1  DELIVERED DOCUMENTS.  On the Amendment Effective Date, the Lender
shall have received the following documents, each of which shall be
satisfactory to the Lender in form and substance:

          (a) AMENDMENT.  This Amendment, executed and delivered by a duly
     authorized officer of the Borrower and the Lender; and

          (b) OTHER DOCUMENTS.  Such other documents as the Lender or counsel
     to the Lender may reasonably request.

                                    1

<Page>

     2.2 NO DEFAULT.  On the Amendment Effective Date, (i) the Borrower and
the Guarantor shall be in compliance with all the terms and provisions set
forth in the Existing Loan Agreement on its part to be observed or performed,
(ii) the representations and warranties made and restated by the Borrower
pursuant to Section 3 of this Amendment shall be true and complete on and as
of such date with the same force and effect as if made on and as of such date
and (iii) no Default shall have occurred and be continuing on such date.

     SECTION 3. REPRESENTATIONS AND WARRANTIES.  The Borrower and the
Guarantor hereby represents and warrants to the Lender that it is in
compliance with all the terms and provisions set forth in the Loan Documents
on its part to be observed or performed, and that no Default has occurred or
is continuing, and hereby confirms and reaffirms the representations and
warranties contained in Section 6 of the Loan Agreement.

     SECTION 4. LIMITED EFFECT.  Except as expressly amended and modified by
this Amendment, the Existing Loan Agreement shall continue to be, and shall
remain, in full force and effect in accordance with its terms; PROVIDED,
HOWEVER, that reference therein and herein to the "Loan Documents" shall be
deemed to include, in any event, (i) the Existing Loan Agreement, (ii) this
Amendment, (iii) the Note and (iv) the Custodial Agreement.  Each reference
to the Loan Agreement in any of the Loan Documents shall be deemed to be a
reference to the Loan Agreement as amended hereby.

     SECTION 5. COUNTERPARTS.  This Amendment may be executed by each of the
parties hereto on any number of separate counterparts, each of which shall be
an original and all of which taken together shall constitute one and the same
instrument.

     SECTION 6. GOVERNING LAW.  THIS AMENDMENT SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK WITHOUT
REFERENCE TO THE CHOICE OF LAW PROVISIONS THEREOF.

                   (REMAINDER OF PAGE INTENTIONALLY LEFT BLANK)

                                       2

<Page>

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and delivered as of the day and year first above written.

                                       BORROWER

                                       AAMES CAPITAL CORPORATION

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

                                       GUARANTOR

                                       AAMES FINANCIAL CORPORATION

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

                                       LENDER

                                       MORGAN STANLEY DEAN WITTER
                                       MORTGAGE CAPITAL INC. (formerly
                                       MORGAN STANLEY MORTGAGE
                                       CAPITAL INC.)

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

                                          3

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