Exhibit 10.11

                             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 is the President and Chief Executive Officer of
the Company; and

     WHEREAS, the Option Holder has been granted the following award as
compensation for services to be rendered and in consideration for the Option
Holder's noncompetition and nonsolicitation agreements set forth herein; and

     WHEREAS, this Option has also been granted to the Option Holder in lieu of
payment of an annual cash bonus or receipt of other incentive compensation for
calendar year 2001; and

     WHEREAS, this Option is granted pursuant to 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 422,407 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. 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, $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

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until the tenth anniversary of the Date of Grant. Thereafter, the Option Holder
shall cease to have any rights in respect thereof. Subject to paragraphs (f) and
(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, as may be
adjusted pursuant to paragraph (g) 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) Vesting and Exercisability.

     (i) This Option, to the extent of 50,000 Shares, shall be vested and
exercisable on the Date of Grant.

     (ii) This Option, to the extent of an additional 172,407 Shares, shall
become vested and exercisable on the Vesting Date (as defined below.)

     (iii) This Option, to the extent of an additional 200,000 Shares (the "B
Shares"), shall become vested on the Vesting Date and shall become exercisable
on the later of (x) the Vesting Date and (y) the Market Price Date (as defined
below).

     The "Market Price Date" shall be the date on which the Market Price (as
defined in paragraph 4 of the Company's Class B Warrants (the "Class B
Warrants")) of the common stock of the Company has traded at or above $30.00 per
share (the "Hurdle Price") for 20 out of 30 consecutive trading days at any time
following the Date of Grant. The Hurdle Price shall be subject to adjustment
from time to time for any event which would subject the Purchase Price (as
defined in the Class B Warrants) to an adjustment by the same percentage as the
percentage adjustment of the Purchase Price in accordance with paragraph 4 of
the Class B Warrants. Notwithstanding the foregoing, in the event that, prior to
the occurrence of the Market Price Date, either a Change of Control (as defined
in the Class B Warrants) of the Company occurs or none of the Class B Warrants
remain outstanding, the date of such Change of Control or the date none of the
Class B Warrants remain outstanding, as the case may be, shall be the Market
Price Date.

     The "Vesting Date" shall be the earlier of (i) the date the Company has
consummated the sale or other disposition (or, in the case of the escrowed
assets referred to below, termination or settlement of the escrow) of at least
50%, by book value on the date hereof , of its Non-Core Assets or (ii) the first
anniversary of the Date of Grant.

     "Non-Core Assets" shall mean the following: (A) unless it has been
designated a Core Asset by the Company, American Independent Insurance Holding
Company, a Penn-


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sylvania corporation; (B) Hales & Co. Inc., a Delaware corporation; (C) escrow
assets under the Folkamerica disposition agreement, net of the contingent
reserve recorded as of June 30, 2001, as adjusted for 18.5% tax benefits and
minus all liabilities, contingent or otherwise, not transferred to the purchaser
under such disposition agreement, including "Excluded Liabilities" under such
disposition agreement; and (D) all non-public securities held by the Company,
Arch Capital Group (U.S.) Inc., a Delaware corporation, and Arch Reinsurance
Company, a Nebraska corporation.

     (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. 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.

     (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
(which shall


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include a broker assisted exercise arrangement), 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 (a) due to his death or disability (as determined under
the Company's long-term disability plan), or (b) due to termination (x) by the
Company for any reason or (y) by the Option Holder for Good Reason, the Option,
to the extent not already vested and exercisable in full, shall become
immediately vested and 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 full Option Period. In the event the Option Holder ceases to be an
employee of the Company due to termination by the Option Holder not for Good
Reason, the Option, to the extent then vested and exercisable, may be exercised
for the full term of the Option Period, and, with respect to the option to
purchase B Shares, to the extent then vested, the Option shall become
exercisable on the Market Price Date and shall remain exercisable through the
remainder of the Option. To the extent the Option is not vested immediately
following the time of termination of employment, the Option shall be immediately
forfeited.


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     Termination of employment by the Option Holder for "Good Reason" 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; (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 on
the Date of Grant; 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 for Good Reason by giving the Company
a written notice of termination specifying in reasonable detail the
circumstances constituting such Good Reason. 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 for Good Reason 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.

     (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.


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     (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) Noncompetition. The Option Holder acknowledges that during his
employment with the Company, he has become familiar with trade secrets and other
confidential information concerning the Company, its subsidiaries and their
respective predecessors, and that his services are of special, unique and
extraordinary value to the Company. In addition, the Option Holder hereby agrees
that at any time during his employment by the Company, and for a period ending
two (2) years after the date of termination of his employment with the Company
for any reason, he will not, without the Company's written consent, be employed
by, manage or consult with the insurance or reinsurance businesses of any
business in competition with the insurance and reinsurance businesses of the
Company or its subsidiaries as such insurance or reinsurance businesses of the
Company and its subsidiaries exist or are in process as of the date of
termination, within any geographical area in which the Company or its
subsidiaries engage in such businesses.

     (p) Nonsolicitation. The Option Holder hereby agrees that during his
employment with the Company and for a period of two (2) years after the date of
termination of his employment with the Company for any reason the Option Holder
will not, without the consent of the Company, induce or attempt to induce any
employee of the Company or its subsidiaries to leave the employ of the Company
or its subsidiaries.

     (q) Enforcement. If, at the enforcement of paragraphs (o) or (p) above, a
court holds that the duration, scope or area restrictions stated herein are
unreasonable under circumstances then existing, the parties agree that the
maximum duration, scope or area reasonable under such circumstances will be
substituted for the stated duration, scope or area and that the court will be
permitted to revise the restrictions contained therein to cover the maximum
duration, scope and area permitted by law. Paragraphs (o), (p) and (q) hereof
shall survive, in accordance with their terms, and continue in full force and
effect following exercise of this Option.

     (r) 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.

     (s) 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 Associa-


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tion. All costs associated with any arbitration, including all legal expenses,
for both parties shall be borne by the Company.

     (t) 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:

                           Peter A. Appel
                           2 Lounsbery Road
                           Bedford Corners, NY  10549


     (u) 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.

     (v) 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.

     (w) 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/ Robert Clements
                                 --------------------------------
                                       Robert Clements
                                       Chairman


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