Document:

Exhibit 10.9

                             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 John M. Pasquesi, Vice Chairman 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 agreeing to be employed by the Company as its Vice Chairman
and as compensation for services to be rendered;

     WHEREAS, this option has been granted under 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 375,473 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 service 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 in full on the second anniversary of the
Date of Grant. Subject to paragraph (j) below, the Option may be exercised at
any time or from time to time

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                                      -2-

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. 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 (which shall include by broker assisted exercise arrangements), 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 for purposes
hereof. Option Shares will be issued accordingly by the Company on the date of
exercise.

     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

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                                      -3-

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 Employment. In the event the Option Holder's employment
with the Company terminates (i) due to his death or Permanent Disability (as
defined in the Employment Agreement between the Option Holder and the Company
dated as of October 23, 2001 (the "Employment Agreement")) or (ii) due to
termination of his employment by the Company not for Cause (as defined in the
Employment Agreement) or termination of his employment by the Option Holder for
Good Reason (as defined in the Employment Agreement), 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. In the event the Option Holder's employment is
terminated by the Option Holder not for Good Reason (and not due to his death or
Permanent Disability) or by the Company for Cause, the Option, to the extent
then exercisable, may be exercised for the remainder of the Option Period, and,
to the extent the Option is not then exercisable, the Option shall be
immediately forfeited.

     (k) Obligations as to Capital and Registration. 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. The Company also agrees to use
reasonable best efforts to maintain an effective Registration Statement on Form
S-8 (or any similar successor form) covering the issuance to the Option Holder
of the Option Shares.

     (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.

<PAGE>
                                      -4-

     (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:

                  John M. Pasquesi
                  Otter Capital LLC
                  One Maritime Plaza
                  San Francisco, CA  94111

     Copies (which shall not constitute notice) of notices to the Option Holder
     shall also be sent to:

                  Greene Radovsky Maloney & Share LLP
                  Four Embarcadero Center, Suite 4000
                  San Francisco, California  94111

                  Attn:  Richard L. Greene, Esq.

     (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.

<PAGE>
                                      -5-

     (r) Entire Agreement. This Agreement constitutes the entire agreement among
the parties relating to the subject matter hereof, and any previous agreement or
understanding among the parties with respect thereto is superseded by this
Agreement 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/ Louis T. Petrillo
                                  ----------------------------------------------
                               Name:   Louis T. Petrillo
                               Title:  Senior Vice President, General Counsel
                                       and Secretary

                               /s/ John M. Pasquesi
                               --------------------------
                               John M. PasquesiExhibit 10.10

                             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 John M. Pasquesi (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
consideration for his having provided structuring and advisory services to the
Company in connection with various financing alternatives;

     (a) Grant. The Option Holder is hereby granted an option (the "Option") to
purchase 750,946 Shares (the "Option Shares"). The Option is granted as of
October 23, 2001 (the "Date of Grant") and such grant is subject to the terms
and conditions herein. 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. This Option shall be rescinded if it is not approved by shareholders of
the Company prior to the first anniversary hereof.

     (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 during the period beginning
on the Date of Grant and ending on the tenth anniversary of the Date of Grant
(the "Option Period"). Thereafter, the Option Holder shall cease to have any
rights in respect thereof.

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

     (f) Adjustments. 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
in-

<PAGE>
                                      -2-

creased 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.

     (g) 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.

     (h) Exercise of Option. In order to exercise the Option, the Option Holder
shall submit to the Company an instrument in writing signed by the Option
Holder, specifying the whole 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 include by broker assisted exercise arrangements), 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 for purposes
hereof. Option Shares will be issued accordingly by the Company on the date of
exercise.

     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.

<PAGE>
                                      -3-

     (i) Obligations as to Capital and Registration. 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. The Company also agrees to use
reasonable best efforts to maintain an effective Registration Statement on Form
S-8 (or any similar successor form) covering the issuance to the Option Holder
of the Option Shares.

     (j) 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.

     (k) 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.

     (l) 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.

     (m) 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.

     (n) 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

<PAGE>
                                      -4-

         If to the Option Holder:

                  John M. Pasquesi
                  Otter Capital LLC
                  One Maritime Plaza
                  San Francisco, CA  94111

          Copies (which shall not constitute notice) of notices to the Option
          Holder shall also be sent to:

                  Greene Radovsky Maloney & Share LLP
                  Four Embarcadero Center, Suite 4000
                  San Francisco, California  94111

                  Attn:  Richard L. Greene, Esq.

     (o) 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.

     (p) 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.

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

<PAGE>
                                      -5-

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

                              ARCH CAPITAL GROUP LTD.

                              By:/s/ Louis T. Petrillo
                                 ----------------------------------------------
                              Name:    Louis T. Petrillo
                              Title:   Senior Vice President, General Counsel
                                       and Secretary

                              /s/ John M. Pasquesi
                              --------------------------
                              John M. Pasquesi

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