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Exhibit 10.4

SERVICE AGREEMENT

        AGREEMENT, made and entered into as of December 15, 2003 by and between
Axis Specialty Limited, a Bermuda corporation (together with its successors and
assigns, the "Company"), and Michael A. Butt (the "Executive").

        WHEREAS, the Company and the Executive entered into an employment
agreement as of September 19, 2002 (the "Original Agreement");

        WHEREAS, the Company and the Executive desire to continue the
Executive's service as Chairman of the Company's Board of Directors (the
"Board") and the Executive is willing to serve in such position;

        WHEREAS, the Company and the Executive desire to amend and restate the
Original Employment Agreement as set forth herein and the Executive is willing
to continue to serve in his current position under the terms and conditions of
this amended and restated agreement (the "Agreement");

        NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein and for other good and valuable consideration, the Company and
the Executive (the "Parties") agree as follows:

        1.    Term of Service.    The Executive's term of service under this
Agreement (the "Term") commenced on September 19, 2002 and shall continue
through the close of business on December 31, 2008, subject to earlier
termination as provided in Section 8 below. The "Initial Term" shall mean
September 19, 2002 through December 31, 2003 and the "New Term" shall mean
January 1, 2004 through the close of business on December 31, 2008.

        2.    Positions, Duties and Responsibilities.    

        (a)    General.    The Executive shall serve throughout the Term as
Chairman of the Board with all responsibilities and authorities normally
associated with such position. The Executive's services under this Agreement
shall be performed outside the United States. The amount of time the Executive
spends in Bermuda and Europe shall be such time as is reasonably appropriate to
perform his responsibilities and services hereunder, except for the amount of
time necessary for him to attend meetings of the Board and of committees of the
Board of which he is a member. It is understood that the Executive will be
domiciled in Bermuda. The Executive shall devote such time as he reasonably
deems appropriate to performing his responsibilities and services hereunder.

        (b)    Permitted Activities.    Anything herein to the contrary
notwithstanding, nothing shall preclude the Executive from (i) serving on the
boards of directors of a reasonable number of other corporations or the boards
of a reasonable number of trade associations and/or charitable organizations,
(ii) engaging in charitable, community and other business affairs and (iii)
managing his personal investments and affairs, provided such activities do not,
in his reasonable judgment, materially interfere with the proper performance of
his responsibilities and services hereunder.

        3.    Base Fee.    The Executive shall be paid a Base Fee by the Company
at an annual rate of US$500,000 during the Initial Term and at an annual rate of
US$750,000 during the New Term. The Base Fee shall be payable in accordance with
the regular payroll practices applicable to senior executives of the Company,
but no less frequently than monthly; provided, that, only for purposes of
calculating the Base Fee payable hereunder, the Initial Term shall be deemed to
have commenced as of October 1, 2002. Such Base Fee shall be subject to review
for increase at the discretion of the Board (or a committee thereof). The Base
Fee may not be decreased, at any time or for any purpose, during the Term.

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        4.    Annual Bonus.    In addition to the Base Fee provided for in
Section 3 above, the Executive shall be entitled to participate in the incentive
plans or programs of the Company established for senior executives ("Incentive
Plan") and shall have a target bonus opportunity each year during the New Term
of no less than 100% of Base Salary ("Target Bonus"), payable in that amount if
the performance goals established for the relevant year are met. If such
performance goals are exceeded, the Executive shall receive a larger amount of
up to 200% of the Target Bonus or more at the discretion of the Compensation
Committee. The performance goals for each year shall be established by the Board
(or a committee thereof) unless such goals are set forth in the applicable
Incentive Plan. For fiscal year 2003, the Executive may be awarded such annual
bonuses as may be determined by the Board (or a committee thereof), based on any
Incentive Plan; provided, however, in no event shall the aggregate annual
bonuses for the 15-month period commencing October 1, 2002 be less than
$312,500, representing 50% of the Base Fee payable hereunder for such 15-month
period. Any such annual bonus shall, unless otherwise required under the
applicable Incentive Plan, be paid in cash in a lump sum promptly following
determination thereof.

        5.    Equity Awards.    

        (a)    Initial Awards.    The Company and the Executive have previously
entered into a Share Purchase Option Agreement, covering 10,000 voting common
shares of the Company, par value US$0.10 (the "Common Stock"), in the form
attached hereto as Exhibit A (the "Option Agreement"), and a Restricted Share
Grant Agreement, covering 10,000 shares of Common Stock, in the form attached
hereto as Exhibit B (the "Share Agreement").

        (b)    Subsequent Awards.    Beginning in calendar year 2003, the
Executive shall be eligible during the Term to participate in the Company's
long-incentive plans, including, but not limited to, the Company's 2003
Long-Term Equity Compensation Plan, as amended from time to time (including any
successor thereto) and to receive additional equity grants and awards as
determined by the Board (or a committee thereof) in its discretion, with all
such grants and awards to be made on the same terms and conditions as the
initial awards in Section 5(a) above (except that the exercise price for any
options shall be at the market price on the date of grant or such lesser price
as determined by the Board (or a committee thereof).

        6.    Employee Benefit Programs.    During the Term, the Executive shall
be entitled to participate in all employee benefit plans and programs (the
"Benefit Programs") that may from time to time be made available to other senior
executives of the Company generally. To the extent that the Executive is not
eligible to participate in any such Benefit Program, he shall be provided with
the after-tax economic equivalent of the coverages and benefits provided under
such program in which he is unable to participate. In addition, if necessary,
the Executive shall be provided interim coverage until such time as the Company
has adopted a program of employee benefit coverages. Interim coverage may be
provided through purchase of separate insurance contracts, through
self-insurance or, to the extent the Executive is permitted to continue to
maintain on a contributory basis the benefits he presently receives from other
sources, by reimbursing the Executive for the cost thereof on a basis that keeps
the Executive whole after taxes. The Executive shall be entitled to a
supplemental executive retirement benefit upon terms and conditions determined
by the Board, and the Company shall provide this benefit pursuant to a separate
agreement (the "SERP Agreement").

        7.    Expense Reimbursement, Fringe Benefits and Survivor Benefits.    

        (a)    Expense Reimbursement.    The Company shall promptly reimburse
the Executive for all reasonable out-of-pocket travel expenses, entertainment
expenses and other expenses incurred by him in connection with performing
services under this Agreement, such reimbursement to be paid promptly after he
submits reasonable documentation with respect to such expenses. This shall
include, without limitation, reimbursement of any such expenses for air fare
(which the Executive shall be entitled to on a first-class basis (including
flights on the Concorde, if available)), hotel accommodations and meals.

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The Company shall also promptly reimburse the Executive for all costs and
expenses (including, without limitation, attorneys' fees and other charges of
counsel) reasonably incurred by him in connection with negotiating and
documenting this Agreement and related arrangements.

        (b)    Fringe Benefits.    In addition to compensation and benefits as
set forth elsewhere in this Agreement, the Executive shall be entitled to
participate during the Term in any and all of the fringe benefits made available
to senior executives of the Company in accordance with the terms and conditions
then applicable to participating senior executives generally. In all events, the
Executive shall be entitled during the Term to the following:

          (i)  reimbursement or payment of the cost (including initiation fees
and annual dues) of membership in two clubs in Bermuda,

         (ii)  reimbursement or payment of air fare for up to four round-trip
first-class non-business trips per year by the Executive or members of his
family between Bermuda and Europe (the benefit under this Section 7(b)(ii) being
in addition to any reimbursement of airfare described in Section 7(a) above),
and

       (iii)  reimbursement or payment of the cost of financial and tax
planning, and of tax return preparation, such reimbursement not to exceed
US$10,000 per year.

        8.    Termination of Service.    

        (a)    Termination Due to Death.    

          (i)  In the event that the Executive dies during the Term, the Term
shall expire as of the date of his death and the Executive's spouse, if she
survives him, shall be entitled to receive the Executive's Base Fee, at the rate
in effect immediately prior to his death, through the end of the month in which
the Executive dies. In the event that the Executive's spouse does not survive
him, the beneficiary designated by the Executive (or, in the absence of such a
designation, the estate or other legal representative of the Executive) shall be
entitled to receive the Base Fee at the rate in effect immediately prior to his
death, through the end of the month in which the Executive dies. In addition to
the above, the beneficiary designated by the Executive (or, in the absence of
such a designation, the estate or other legal representative of the Executive)
shall be entitled to:

        (A)  a Separation Bonus for the year of death (with the term "Separation
Bonus" meaning an amount no less than the greater of (x) US$500,000 if
termination is during the Initial Term or US$750,000 if termination is during
the New Term and (y) the highest amount awarded to the Executive as an annual
bonus for any of the three years (or such lesser number of years he has then
been employed) immediately preceding the year in which termination occurs);

        (B)  to the extent the awards referred to in Section 5(a) (the "Initial
Awards") are not already vested and exercisable, immediate vesting and
exercisability, as the case may be, as of the date of death, for all outstanding
Initial Awards scheduled to vest on or before the first anniversary of the date
of death, with the Option (as defined in the Option Agreement) to remain
exercisable as to all shares for which it is then vested for the lesser of
(x) one year following the date of death and (y) the remainder of its maximum
stated term, after which the Option shall expire;

        (C)  vesting and exercisability, as the case may be, for other equity
awards, including any restricted shares or stock options, in accordance with
their terms; and

        (D)  any other benefits described in Section 8(f) below.

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        (b)    Termination Due to Disability.    

          (i)  Either Party may terminate the Executive's service under this
Agreement prior to the then-scheduled expiration of the Term due to his
Disability by providing 15 days' prior written notice to the other Party, in
which event the Term shall expire and the Executive shall be entitled to:

        (A)  the Base Fee, at the rate in effect immediately prior to the date
of termination, through the end of the month in which the Executive's service
terminates due to Disability;

        (B)  a lump sum amount equal to one year's Base Fee at the rate in
effect immediately prior to such termination;

        (C)  a Separation Bonus for the year of termination;

        (D)  to the extent the Initial Awards are not already vested and
exercisable, immediate vesting and exercisability, as the case may be, as of the
date of termination, for all outstanding Initial Awards scheduled to vest on or
before the first anniversary of the date of termination, with the Option (as
defined in the Option Agreement) to remain exercisable as to all shares for
which it is then vested for the lesser of (x) one year following the date of
termination and (y) the remainder of its maximum stated term, after which the
Option shall expire;

        (E)  vesting and exercisability, as the case may be, for other equity
awards, including any restricted shares or stock options, in accordance with
their terms;

        (F)   disability benefits in accordance with any applicable Company
plans, programs, policies or agreements;

        (G)  continued coverage for 12 months under all Benefit Programs (or
their equivalent as provided in Section 6 above) in which the Executive was
participating immediately prior to the date of termination; provided, however,
that to the extent the Company is unable to continue such coverage, the Company
shall provide the Executive with economically equivalent benefits determined on
an after-tax basis and, provided further that any such continued coverage shall
be offset by comparable coverage provided to the Executive in connection with
subsequent employment or other service; and

        (H)  any other benefits described in Section 8(f) below.

For purposes of this Agreement, "Disability" shall mean that the Executive has
been unable to substantially perform his duties hereunder, due to physical or
mental incapacity, for 180 consecutive days.

        (c)    Termination for Cause.    

          (i)  The service of the Executive under this Agreement, and the Term,
may be terminated by the Board for Cause prior to the then-scheduled expiration
of the Term. For this purpose, "Cause" shall mean:

        (A)  conviction of the Executive of a felony involving moral turpitude,
or

        (B)  the Executive, in carrying out his duties for the Company under
this Agreement, has been guilty of gross neglect or gross misconduct resulting,
in either case, in material economic harm to the Company; provided, however,
that no act, or failure to act, by the Executive shall constitute Cause if the
Executive believed in good faith that such act, or failure to act, was in, or
not opposed to, the interests of the Company.

Anything herein to the contrary notwithstanding, the Executive shall not be
terminated for "Cause," within the meaning of clause (B) of this
Section 8(c)(i), unless written notice stating the basis for the termination is
provided to the Executive and he is given 15 days to cure the neglect or conduct
that is

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the basis of such claim and, if he fails to cure such neglect or conduct, the
Executive has an opportunity to be heard before the full Board within 15 days
following the end of such cure period and, within five (5) days after such
hearing, there is a unanimous vote of all disinterested members of the Board to
terminate him for Cause.

         (ii)  In the event of a termination for Cause in accordance with
Section 8(c)(i) above, the Executive shall be entitled only to (A) the Base Fee,
at the rate in effect immediately prior to the date of termination, through the
date on which termination for Cause occurs and (B) any other benefits described
in Section 8(f) below.

        (d)    Termination Without Cause or With Good Reason.    

          (i)  Anything in this Agreement to the contrary notwithstanding, the
Executive's service under this Agreement may be terminated, by prior written
notice by the terminating Party to the other Party, prior to the then-scheduled
expiration of the Term by the Company without Cause, or by the Executive with
"Good Reason" (as defined in Exhibit C), as provided in this Section 8(d), in
which event the Term shall expire. A termination due to Disability in accordance
with Section 8(b) above, or for Cause in accordance with Section 8(c) above,
shall not be deemed a termination without Cause or with Good Reason to which
this Section 8(d) applies.

         (ii)  Except in certain circumstances in connection with a Change in
Control as provided in Section 8(d)(iii) below, in the event that the
Executive's service is terminated prior to the then-scheduled expiration of the
Term (x) by the Company without Cause or (y) by the Executive with Good Reason,
the Term shall expire and the Executive shall be entitled to:

        (A)  the Base Fee through the date of termination at the rate in effect
immediately prior to the date of termination;

        (B)  a lump sum amount equal to two years' Base Fee at the rate in
effect immediately prior to such termination;

        (C)  a Separation Bonus for the year of termination;

        (D)  to the extent the Initial Awards are not already vested and
exercisable, immediate vesting and exercisability, as the case may be, as of the
date of termination, for all outstanding Initial Awards scheduled to vest on or
before the first anniversary of the date of termination, with the Option (as
defined in the Option Agreement) to remain exercisable as to all shares for
which it is then vested for the lesser of (x) one year following the date of
termination and (y) the remainder of its maximum stated term, after which the
Option shall expire;

        (E)  vesting and exercisability, as the case may be, for other equity
awards, including any restricted shares or stock options, in accordance with
their terms;

        (F)   continued coverage for 12 months under all Benefit Programs (or
their equivalent as provided in Section 6 above) in which the Executive was
participating immediately prior to the date of termination; provided, however,
that to the extent the Company is unable to continue such coverage, the Company
shall provide the Executive with economically equivalent benefits determined on
an after-tax basis and, provided further that any such continued coverage shall
be offset by comparable coverage provided to the Executive in connection with
subsequent employment or other service; and

        (G)  any other benefits described in Section 8(f) below.

        (iii) In the event that the Executive's service herein is terminated by
the Company without Cause, or by the Executive for Good Reason, in either case
in anticipation of, or within the 12-month period

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following, a Change in Control (as defined in Exhibit D), the Term shall expire
and the Executive shall be entitled to:

        (A)  the benefits described in Section 8(d)(ii)(A), (B), (E), and
(G) above;

        (B)  a lump sum amount equal to two (2) times a Separation Bonus for the
year of termination;

        (C)  to the extent the Initial Awards are not already vested and
exercisable, immediate vesting and exercisability, as the case may be, as of the
date of termination, for all outstanding Initial Awards scheduled to vest on or
before the third anniversary of such date, with the Option (as defined in the
Option Agreement) to remain exercisable as to all shares for which it is then
vested for the lesser of (x) one year following the date of termination and
(y) the remainder of its maximum stated term, after which the Option shall
expire; and

        (D)  continued coverage for 24 months under all Benefit Programs (or
their equivalent as provided in Section 6 above) in which the Executive was
participating immediately prior to the date of termination; provided, however,
that to the extent the Company is unable to continue such coverage, the Company
shall provide the Executive with economically equivalent benefits determined on
an after-tax basis and, provided further that any such continued coverage shall
be offset by comparable coverage provided to the Executive in connection with
subsequent employment or other service.

        (e)    Voluntary Termination by the Executive.    The Executive may
voluntarily terminate his service under this Agreement, by prior written notice
to the Company, before the then-scheduled expiration of the Term, in which event
(x) the Term shall expire as of the date specified by the Executive in writing
and (y) the Executive shall receive the same rights and benefits as applicable
to a termination by the Board for Cause in accordance with Section 8(c) above. A
voluntary termination under this Section 8(e) shall not be deemed a breach of
this Agreement. Neither a termination of the Executive's service due to
Disability in accordance with Section 8(b) above, nor a termination of the
Executive's service by the Executive for "Good Reason" in accordance with
Section 8(d) above, shall be deemed to be a voluntary termination within the
meaning of this Section 8(e).

        (f)    Miscellaneous.    

          (i)  On any termination of the Term, the Executive shall be entitled
to:

        (A)  the balance of any annual, long-term or other incentive award
earned (but not yet paid) prior to such termination;

        (B)  reimbursement of any business or other expenses pursuant to
Section 7 above; and

        (C)  any other rights, compensation and/or benefits as may be due the
Executive in accordance with the terms and provisions of any agreements, plans
or programs of the Company, including this Agreement and the SERP Agreement (but
in no event shall the Executive be entitled to duplicative rights, compensation
and/or benefits).

        (ii) All amounts due under this Section 8 shall be paid in a lump sum
promptly following the date of termination.

        (iii) For purposes of this Agreement, in the event there is a reduction
in Base Fee that would constitute the basis for a termination for Good Reason
pursuant to Section 8(d) above, then "Base Fee" shall mean the Base Fee in
effect immediately prior to any such reduction.

        (g)    No Mitigation; No Offset.    In the event of any termination of
his service under this Agreement, the Executive shall be under no obligation to
seek other employment, and there shall be no offset against amounts due the
Executive under this Agreement or otherwise on account of any

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remuneration attributable to any subsequent employment that he may obtain or any
claim that the Company or any Affiliates (an "Affiliate" of any person means any
person that controls, is controlled by, or is under common control with, such
person) may have against him. Any amounts due under this Section 8 are
considered to be reasonable by the Company and not in the nature of a penalty.

        (h)    Notice Provisions.    In the event written notice of termination
has been given under this Section 8, no subsequent notice of termination,
whether written or otherwise, shall become effective until and unless the prior
notice ceases to be effective, provided, however, that (i) in the case of a
notice of termination for Cause, such notice shall be deemed to cease to be
effective upon cure or a failure to terminate upon a unanimous vote of all
disinterested members of the Board as provided in Section 8(c) above and (ii) in
the case of a notice of a voluntary termination by the Executive, such notice
shall be deemed to cease to be effective 30 days following notice of such
termination.

        9.    Noncompetition, Nonsolicitation, Confidentiality and
Non-Disparagement.    

        (a)    Noncompetition.    For a period of 12 months after termination of
his service hereunder, the Executive shall not, directly or indirectly, whether
as an employee, consultant, partner, principal, agent, distributor,
representative or stockholder (except as a less than one percent stockholder or
other equity holder of a publicly traded entity or a less than five percent
stockholder or other equity holder of a privately held entity), engage in any
activities within the United States, the United Kingdom or Bermuda if such
activities involve, to a material extent, insurance or reinsurance of entities
or exposures that are materially competitive with the businesses that (i) are
then being conducted by the Company or any subsidiary and (ii) were during the
Term either being conducted by, or being actively developed by, the Company or
any subsidiary. Notwithstanding the foregoing, none of the following activities
shall be deemed to violate the prohibition in the immediately preceding
sentence: (x) the Executive's service as a director (or equivalent) of any
entity in the insurance, reinsurance or related businesses and (y) any other
activity that is approved by the Board (which approval shall not be unreasonably
withheld or delayed).

        (b)    Nonsolicitation.    For a period of 12 months after termination
of his service hereunder, the Executive shall not, except in connection with
carrying out his duties for the Company or any subsidiary or otherwise at the
written request of the Company, (i) encourage any employee of the Company or any
subsidiary to leave the employ of the Company or any subsidiary, (ii) hire or
use the services of any employee of the Company or any subsidiary, or (iii)
solicit or cause another person or entity to solicit any customers or brokers of
the Company or any subsidiary to terminate or otherwise adversely modify their
relationship with the Company or any such subsidiary; provided that clause (i)
and clause (ii) of this Section 9(b) shall only apply to individuals employed by
the Company or any subsidiary at any point during the one-year period
immediately preceding the date of termination of Executive's employment. Nothing
in this Section 9(b) shall prevent the Executive from providing employment
references for such employees.

        (c)    Confidentiality.    The Executive covenants that he shall not,
without the prior written consent of the Board or of a person authorized by the
Board, disclose to any person, other than in connection with performing his
duties for the Company, any confidential proprietary information about the
Company or its business, unless and until such information has become known to
the public generally or within any industry in which the Company conducts
business (other than as a result of unauthorized disclosure by the Executive) or
unless (i) such disclosure is in confidence to an attorney for the purpose of
obtaining legal advice, (ii) such disclosure is in connection with any
litigation, arbitration or mediation involving this Agreement or other
agreements or arrangements involving the Parties, including, but not limited to,
the enforcement of this Agreement or such other agreements or arrangements or
(iii) the Executive is required to disclose such information (whether or not in
connection with a disclosure required in clause (ii)) by law or by any court,
arbitrator, mediator or

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administrative or legislative body (including any committee thereof) with
apparent jurisdiction to order the Executive to disclose or make accessible any
information.

        (d)    Non-Disparagement.    The Executive shall not willfully or
knowingly make any public statement that would disparage or defame the Company.
The Company shall not, and shall cause each of the executives and directors of
the Company not to, willfully or knowingly make any public statement that would
disparage or defame the Executive. Notwithstanding the foregoing, nothing in
this Section 9(d) shall prevent any person from (i) responding publicly to any
incorrect, disparaging or defamatory public statement to the extent reasonably
necessary to correct or refute such public statement or (ii) making any truthful
statement to the extent (x) such disclosure is in confidence to an attorney for
the purpose of obtaining legal advice, (y) such disclosure is in connection with
any litigation, arbitration or mediation involving this Agreement or other
agreements or arrangements involving the Parties, including, but not limited to,
the enforcement of this Agreement or such other agreements or arrangements or
(z) the Executive is required to disclose such information (whether or not in
connection with a disclosure required in clause (y)) by law or by any court,
arbitrator, mediator or administrative or legislative body (including any
committee thereof) with apparent jurisdiction.

        (e)    Scope.    For purposes of this Section 9, the Company shall be
deemed to include any entity that (i) is an Affiliate both during the Term and
at the time in question and (ii) is an Affiliate organized after the Term for
the purpose of holding the assets owned by the Company during the Term and/or
operating the business of the Company conducted during the Term. The covenants
set forth in this Section 9, except as provided in Section 9(a) and (b) above,
shall be without limitation as to time and geographic application.

        10.    Indemnification.    

        (a)   During the Term and at all times thereafter, if the Executive is
made a party, is threatened to be made a party, or reasonably anticipates being
made a party, to any Proceeding by reason of the fact that he is or was a
director, officer, member, employee, agent, manager, trustee, consultant or
representative of the Company or any Affiliate or is or was serving at the
request of the Company or any Affiliate, or in connection with his service as a
director, officer, member, employee, agent, manager, trustee, consultant or
representative of another Person, or if any Claim is made, is threatened to be
made, or is reasonably anticipated to be made, that arises out of or relates to
the Executive's service in any of the foregoing capacities, then the Executive
shall promptly be indemnified and held harmless to the fullest extent permitted
or authorized by the Bye-laws of the Company, or if greater, by applicable law,
against any and all costs, expenses, liabilities and losses (including, without
limitation, attorneys' fees, judgments, interest, expenses of investigation,
penalties, fines, ERISA excise taxes or penalties and amounts paid or to be paid
in settlement) incurred or suffered by the Executive in connection therewith or
in connection with seeking to enforce his rights under this Section 10(a), and
such indemnification shall continue as to the Executive even if he has ceased to
be a director, officer, member, employee, agent, manager, trustee, consultant or
representative of the Company or other Person, without limitation in time, and
shall inure to the benefit of the Executive's heirs, executors and
administrators. The Executive shall be entitled to prompt advancement of any and
all costs and expenses (including, without limitation, attorneys' fees and other
charges of counsel) incurred by him in connection with any such Proceeding or
Claim, or in connection with seeking to enforce his rights under this
Section 10(a), any such advancement to be made within 15 days after he gives
written notice, supported by reasonable documentation, requesting such
advancement. Such notice shall include, to the extent required by applicable
law, an undertaking by the Executive to repay the amount advanced, on an
after-tax basis (that is, net of any applicable taxes), if he is ultimately
determined not to be entitled to indemnification against such costs and
expenses. Nothing in this Agreement shall operate to limit or extinguish any
right to indemnification, advancement of expenses, or contribution that the
Executive would otherwise have (including, without limitation, by agreement or
under applicable law). For purposes of this Agreement, "Claim" shall mean any
claim, demand, request, investigation, dispute,

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controversy, threat, discovery request, or request for testimony or information,
"Person" shall mean any individual, corporation, partnership, limited liability
company, joint venture, trust, estate, board, committee, agency, body, employee
benefit plan or other person or entity and "Proceeding" shall mean any actual,
threatened, or reasonably anticipated, action, suit or proceeding, whether
civil, criminal, administrative, investigative, appellate, formal, informal or
other.

        (b)   Neither the failure of the Company (including its Board,
independent legal counsel or stockholders) to have made a determination prior to
the commencement of any Proceeding concerning payment of amounts claimed by the
Executive under Section 10(a) that indemnification of the Executive is proper
because he has met the applicable standard of conduct, nor a determination by
the Company (including its Board, independent legal counsel or stockholders)
that the Executive has not met such applicable standard of conduct, shall create
a presumption that the Executive has not met the applicable standard of conduct.

        (c)   The Executive shall, during his service for the Company, including
as a director, and for at least six years thereafter, be covered by a directors'
and officers' liability insurance policy (or policies) on terms and conditions
no less favorable to him in any respect than those then applying to any other
present or former director or officer of the Company, but in all events, the
minimum aggregate coverage obtained by the Company, under which the Executive is
a covered person, shall be in an amount no less than US$50,000,000.

        11.    Excise Tax Adjustment Payments.    

        (a)    Payments.    In the event that any payment or benefit provided to
or for the benefit of the Executive in connection with this Agreement, any other
agreement or arrangement to which he and the Company are parties, his services
for the Company, or the termination of such services, other than any payment
pursuant to this Section 11(a) (a "Payment"), would be subject to (x) the excise
tax imposed by Section 4999 of the Internal Revenue Code of 1986, as amended
(the "Code"), or any successor to such Section or (y) any interest or penalties
with respect to such excise tax (such excise tax, together with any such
interest and penalties, being hereinafter collectively referred to as the
"Excise Tax"), then the Executive shall be entitled to receive from the Company,
within 15 days following the determination described in Section 11(b) below and
no later than such Excise Tax is due to be paid, through withholding or
otherwise, an additional payment ("Excise Tax Adjustment Payment") in an amount
such that after payment by the Executive of all applicable U.S. Federal, state,
local and other taxes and all applicable non-U.S. taxes (each computed at the
maximum marginal rates and including any interest or penalties imposed with
respect to such taxes), including any Excise Tax, imposed upon the Excise Tax
Adjustment Payment, the Executive retains an amount of the Excise Tax Adjustment
Payment equal to the Excise Tax imposed upon the Payment.

        (b)    Determinations.    All determinations required to be made under
this Section 11, including whether an Excise Tax Adjustment Payment is required
and the amount of such Excise Tax Adjustment Payment, shall be promptly made by
a "big five" accounting firm (the "Accounting Firm"), selected by the Company
with the Executive's approval (which approval shall not be unreasonably withheld
or delayed). The Accounting Firm shall provide detailed supporting calculations
to the Company and the Executive within 15 business days of the date of the
Payment to which the Excise Tax Adjustment Payment relates. As a result of the
uncertainty in the application of Section 4999 of the Code (or any successor to
such Section) at the time of any initial determination hereunder, it is possible
that (x) certain Excise Tax Adjustment Payments will not have been made that
should have been made (an "Underpayment"), or (y) certain Excise Tax Adjustment
Payments will have been made that should not have been made (an "Overpayment"),
consistent with the calculations required to be made hereunder. In the event of
an Underpayment, such Underpayment shall be promptly paid by the Company to or
for the benefit of the Executive. In the event of an Overpayment, such
Overpayment shall be promptly repaid to the Company on an after-tax basis.

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        12.    Resolution of Disputes.    Any dispute between the Parties,
including, without limitation, any dispute arising out of or relating to this
Agreement or any other agreement or arrangement to which the Executive and the
Company are parties, the Executive's service with the Company, or the
termination of such service, shall be resolved by confidential arbitration in
New York City in accordance with the Commercial Arbitration Rules (and not the
National Rules for Resolution of Employment Disputes) of the American
Arbitration Association. Judgment upon the award rendered by the arbitrator(s)
may be entered in any court having jurisdiction thereof. All costs associated
with any such arbitration, including all attorneys' fees and other legal
expenses, shall be paid by the Company.

        13.    Withholding.    Anything in this Agreement to the contrary
notwithstanding, all payments required to be made by the Company hereunder to
the Executive shall be subject to tax withholding to the extent required by
applicable law, treaty or regulation. In lieu of withholding such amounts, in
whole or in part, the Company may accept, in its sole discretion, such other
provision for payment of required tax withholding as the Executive may
reasonably request.

        14.    Representations.    

        (a)   The Company represents and warrants that (i) it is fully
authorized by action of its Board (and of any other person or body whose action
is required) to enter into this Agreement and to perform its obligations under
it, (ii) the Board has approved (A) the transfer of (x) all or any portion of
the Option (as defined in the Option Agreement) as permitted pursuant to
Paragraph (i) of the Option Agreement and (y) all or any of the Shares (as
defined in the Share Agreement) as permitted pursuant to Paragraph (e) of the
Share Agreement and (B) upon exercise of the Option (or any portion thereof) or
the transfer of the Shares, as the case may be, the registration of the shares
in the name of such transferee, (iii) the officer signing this Agreement on its
behalf is duly authorized to do so, (iv) the execution, delivery and performance
of this Agreement by it does not violate any applicable law, regulation, order,
judgment or decree or any agreement, plan, bye-law, charter provision or
corporate governance document to which it is a party or by which it is bound and
(v) upon the execution and delivery of this Agreement by the Parties, this
Agreement shall be a valid and binding obligation of the Company, enforceable
against it in accordance with its terms, except to the extent that
enforceability may be limited by applicable bankruptcy, insolvency or similar
laws affecting the enforcement of creditors' rights generally.

        (b)   The Executive represents and warrants that, to the best of his
knowledge and belief, (i) delivery and performance of this Agreement by him does
not violate any applicable law, regulation, order, judgment or decree or any
agreement to which the Executive is a party or by which he is bound and (ii)
upon the execution and delivery of this Agreement by the Parties, this Agreement
shall be a valid and binding obligation of the Executive, enforceable against
him in accordance with its terms, except to the extent that enforceability may
be limited by applicable bankruptcy, insolvency or similar laws affecting the
enforcement of creditors' rights generally.

        15.    Entire Agreement.    This Agreement, together with its Exhibits
(which form a part of this Agreement for all purposes), amends and restates the
Original Agreement and contains the entire agreement between the Parties
concerning the subject matter hereof and supersedes all prior agreements,
understandings, discussions, negotiations and undertakings, whether written or
oral, between the Parties with respect thereto. In the event of any
inconsistency between any provision of this Agreement and any provision of any
plan, program, policy, arrangement, bye-law, charter document, corporate
governance document, or agreement of the Company or any of its Affiliates, the
provisions of this Agreement shall control to the extent that they are more
favorable to the Executive unless the Executive otherwise agrees in a writing
that expressly refers to the provision of this Agreement whose control he is
waiving.

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        16.    Assignability; Binding Nature.    This Agreement shall be binding
upon and inure to the benefit of the Parties and their respective successors,
heirs and assigns. No rights or obligations of the Executive under this
Agreement may be assigned or transferred by the Executive other than his rights
to compensation and benefits hereunder, which may be transferred by will or
operation of law subject to the limitations of this Agreement. The Parties
recognize that the Executive also may transfer his rights under the Option
Agreement and Share Agreement to the extent therein provided. No rights or
obligations of the Company under this Agreement may be assigned or transferred
by the Company except that such rights or obligations may be assigned or
transferred pursuant to an amalgamation, reconstruction, merger or consolidation
in which Company is not the continuing entity, or a sale or liquidation of all,
or substantially all, of the business and assets of the Company, provided that
the assignee or transferee is the successor to all, or substantially all, of the
business and assets of the Company and such assignee or transferee assumes the
liabilities, obligations and duties of the Company, as contained in this
Agreement, either contractually or as a matter of law.

        17.    Amendment or Waiver.    No provision in this Agreement may be
amended unless such amendment is agreed to in writing, signed by the Executive
and by a duly authorized officer of the Company. No waiver by any person of any
breach of any other person of any condition or provision of this Agreement shall
be deemed a waiver of a similar or dissimilar condition or provision at the same
or any prior or subsequent time. Any waiver must be in writing and signed by, or
on behalf of, the waiving person.

        18.    Notices.    Any notice required or permitted to be given under
this Agreement shall be in writing and shall be deemed to have been given (a)
when delivered personally or (b) on the second business day after the day on
which it is sent by recognized courier with delivery acknowledged by written
receipt or (c) on the fifth business day after it is 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:   AXIS Specialty Limited
106 Pitts Bay Road
Pembroke, HM 08, Bermuda
Attn: Andrew Cook
If to the Executive:
 
Michael A. Butt
Leamington House
50 Harrington Sound Road
Hamilton Parish
Bermuda CR04

        19.    Severability.    In the event that any provision or portion of
this Agreement shall be determined to be invalid or unenforceable for any
reason, in whole or in part, the remaining provisions of this Agreement shall be
unaffected thereby and shall remain in full force and effect to the fullest
extent permitted by law.

        20.    Survivorship.    The respective rights and obligations of the
Parties shall survive any termination of the Executive's service under this
Agreement to the extent necessary to the intended preservation of such rights
and obligations.

        21.    Beneficiaries/References.    The Executive shall be entitled, to
the extent permitted under applicable law, to select and change a beneficiary or
beneficiaries to receive any compensation or benefit hereunder following the
Executive's death by giving the Company written notice thereof. In the event of
the Executive's death or a judicial determination of his incompetence,
references in this Agreement to the Executive shall be deemed, where
appropriate, to refer to his beneficiaries, estate or other legal
representative.

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        22.    Governing Law.    This Agreement shall be governed, construed and
enforced in accordance with its express terms, and otherwise in accordance with
the laws of the State of New York without reference to the principles of
conflict of laws.

        23.    Headings.    The headings of the Sections and subsections of this
Agreement are for convenience only and shall not be deemed to control or affect
the meaning or construction of any provision of this Agreement.

        24.    Counterparts and Fascimile.    This Agreement may be executed in
one or more counterparts. Signatures delivered by facsimile shall be deemed
effective for all purposes to the extent permitted under applicable law.

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        IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
the date first written above.

    Axis Specialty Limited
 
 
By:
/s/  FRANK J. TASCO      

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Frank J. Tasco
Chairman, Compensation Committee
 
 
The Executive        
 
 
/s/  MICHAEL A. BUTT      

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Michael A. Butt

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EXHIBIT A

SHARE PURCHASE OPTION AGREEMENT

        AGREEMENT, made and entered into as of October 1, 2002 (the "Grant
Date") by and between Axis Specialty Limited, a Bermuda corporation (together
with its successors and assigns, the "Company") and Michael A. Butt (the "Option
Holder").

        WHEREAS, the Company and the Option Holder (the "Parties") have as of
September 19, 2002 entered into an agreement (the "Service Agreement") pursuant
to which the Option Holder is to serve the Company as Chairman of its Board of
Directors; and

        WHEREAS, the Company has decided to grant the option described below to
the Option Holder as an inducement to accept such position and as a performance
incentive;

        NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, and for other good and valuable consideration, the Parties
agree as follows:

        (a)    Grant.    The Company hereby unconditionally grants to the Option
Holder, effective as of the Grant Date, the right and option to purchase 10,000
shares (the "Option Shares") of the voting common shares of the Company, par
value US $0.10 (the "Common Stock"), on the terms and conditions hereinafter set
forth (the "Option").

        (b)    Purchase Price.    Except as otherwise provided in Paragraph (h)
below, the purchase price of the Option Shares subject to the Option (the
"Option Price") shall be: US $100.00 per Share.

        (c)    Term of the Option.    The Option shall have a term commencing on
the Grant Date and continuing through the tenth anniversary of such date (the
"Option Period") and shall be exercisable during the Option Period as provided
in Paragraph (d) below.

        (d)    Vesting and Exercisability.    The Option shall vest, and become
exercisable, as to one-third of the Option Shares on each of the first, second
and third anniversaries of the Grant Date, provided that the Option shall vest,
and become exercisable, on certain terminations of the Optionee's service with
the Company under the Service Agreement to the extent set forth in Section 8 of
the Service Agreement. Except to the extent otherwise provided in Section 8 of
the Service Agreement, the Option shall expire on any termination of the Option
Holder's service with the Company. The Option shall be exercisable by the Option
Holder, or in the event of his death or his judicially determined incompetence,
by his estate or other legal representative, or, to the extent the Option is
transferred, in whole or in part, in accordance with the provisions of
Paragraph (i) below, by a transferee of the Option (a "Transferee"). As
hereinafter used, the term "Option Holder" shall include the Option Holder's
estate, other legal representative or Transferee, as appropriate.

        (e)    Exercise of the Option.    In order to exercise the Option, the
Option Holder shall submit to the Company an instrument in writing specifying
the number of Option Shares in respect of which the Option is being exercised,
accompanied by payment, in a manner reasonably acceptable to the Company, of the
aggregate Option Price for the Option Shares in respect of which the Option is
being exercised. A share certificate, or certificates, representing the
purchased Option Shares shall then promptly be delivered to the Option Holder;
provided, however, that the Company shall not be obligated to deliver any Option
Shares hereunder if the delivery of such Option Shares would violate the
provisions 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 delivered without resulting in such violation of law.

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        (f)    Status of Option Shares.    Option Shares purchased pursuant to
any exercise of the Option shall, upon delivery to the Option Holder, rank
equally in all respects with the other shares of the voting Common Stock, but
shall not carry any option or other right to subscribe for additional shares of
Common Stock.

        (g)    Rights as Shareholder.    The Option Holder shall not, by virtue
of the Option, be entitled to any rights of a shareholder of the Company, either
at law or equity, and the grant of the Option shall not confer on the Option
Holder any right with respect to continuance of his service with the Company nor
shall such grant interfere in any way with the right of the Company to terminate
the Option Holder's service at any time. Notwithstanding the foregoing, in the
event that the Option Holder purchases Option Shares pursuant to an exercise of
the Option, the Option Holder shall enjoy, with respect to such Option Shares,
"tag-along" rights, "put" rights, exchange rights, registration rights, rights
with respect to securities of any "Designated Subsidiary" (as defined in the
Company's Bye-Laws) and other comparable rights on the most favorable basis
provided for each such right to any other holder of Common Stock.

        (h)    Recapitalizations and Adjustments.    In the event of any merger,
consolidation, reorganization, recapitalization, spin-off, split-up,
combination, reconstruction, amalgamation, share exchange, liquidation,
dissolution, share split, share dividend, other distribution of securities or
other property in respect of shares or other securities, or other change in
corporate structure or capitalization affecting the rights or value of the
securities then subject to this Option Agreement, the Company shall promptly
make appropriate adjustment(s) in the number and/or kind of securities subject
to this Option Agreement and/or in the Option Price and/or in other terms and
conditions of this Option Agreement, and/or the Company shall promptly make
appropriate provision(s) for supplemental payments of cash, securities and/or
other property, in each case so as to avoid dilution or enlargement of the
rights of the Option Holder and of the after-tax economic opportunity and value
represented by this Option Agreement. If an event occurs that may require an
adjustment (or other action) pursuant to the preceding sentence, the Company
shall promptly deliver to the Option Holder a certificate that specifies (x) the
event in question and (y) either the action(s) being taken or the reasons why
the Company believes no action is needed.

        (i)    Nonassignability and Transferability.    The Option may not be
assigned or otherwise transferred, disposed of or encumbered by the Option
Holder, in whole or in part, except: (i) by will or the laws of descent and
distribution or (ii) by the Option Holder to members of "the Option Holder's
immediate family", to a trust established for the exclusive benefit of one or
more members of "the Option Holder's immediate family" and/or the Option Holder,
or to a partnership pursuant to which the only partners are one or more members
of "the Option Holder's immediate family" and/or the Option Holder. For purposes
of this Agreement, "the Option Holder's immediate family" shall mean the initial
Option Holder's children, stepchildren, grandchildren, parents, spouse, siblings
(including half brothers and sisters), and in-laws, and includes relationships
arising because of legal adoption. The Company represents and warrants that its
Board has approved the transfer of all or any portion of the Option to and the
exercise thereof by the Option Holder's immediate family or trust or partnership
as permitted by this Paragraph (i) and the registration of any Option Shares to
be delivered upon exercise of the Option in the name of any Option Holder to
whom the Option may be transferred pursuant to this Paragraph (i).

        (j)    Obligations as to Share Capital.    The Company agrees that it
shall at all times maintain authorized and unissued share capital sufficient to
fulfill all of its obligations under this Agreement.

        (k)    Restrictions on Transfer of Option Shares.    Neither the Option
Shares nor any interest in them may be sold, assigned, pledged, hypothecated,
encumbered or in any other manner transferred or disposed of, in whole or in
part, except in compliance with the terms, conditions and

15

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restrictions as set forth in the Bye-Laws of the Company, applicable United
States federal and state securities laws or any other applicable laws or
regulations and the terms and conditions of this Agreement. Each certificate for
Option Shares delivered upon exercise of the Option, unless at the time of
exercise such Option Shares are registered under the Securities Act of 1933,
shall bear the following legend or such other legend as the Company reasonably
deems appropriate:

        "These securities have not been registered under the United States
Securities Act of 1933, as amended. These securities cannot be offered,
transferred or sold unless (i) a registration statement under such Act is in
effect with respect to such securities or a written opinion from counsel
reasonably acceptable to Axis Specialty Limited (the "Company") is obtained to
the effect that no such registration is required, and (ii) the transferee is
approved by applicable regulatory authorities, if such approval is required and
(iii) simultaneously the appropriate number of shares of any Designated
Subsidiary (as such term is defined in the Bye-Laws of the Company and only if
the Board of Directors of the Company has constituted any entity a Designated
Subsidiary) is offered, transferred or sold together with each share represented
hereby that is proposed to be offered, transferred or sold. The Company reserves
the right to refuse the transfer of such securities until such conditions have
been fulfilled. Sections 68 through 70 of the Company's Bye-Laws contain other
significant restrictions on transfers of shares of the Company."

Any certificate delivered at any time in exchange or substitution for any
certificate bearing such legend or such other legend reasonably 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 restriction contained herein. The provisions of this
Paragraph (k) shall be binding upon all subsequent holders of certificates
bearing the above legend.

        (l)    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 this Agreement.

        (m)    Incorporation of Provisions.    Sections 11, 12, 14, 15, 16
(first and third sentences only), 17, 18, 19, 21 (second sentence only), 22, 23
and 24 of the Service Agreement (relating, respectively, to excise tax
adjustment payments, resolution of disputes, representations, integration and
inconsistencies, assignability, amendments or waivers, notices, severability,
beneficiaries/references, governing law, headings and counterparts) shall be
deemed incorporated into this Agreement as if fully set forth herein, with all
references to the Executive in such Sections being deemed to be references to
the Option Holder. All capitalized terms not defined in this Share Purchase
Option Agreement shall have the meanings set forth in the Service Agreement.

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        IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
the date first written above.

    Axis Specialty Limited
 
 
By:
       

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

Name:
Title:
 
 
The Option Holder        
 
 

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Michael A. Butt

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EXHIBIT B

RESTRICTED SHARE GRANT AGREEMENT

        AGREEMENT, made and entered into as of October 1, 2002 (the "Grant
Date") by and between Axis Specialty Limited, a Bermuda corporation (together
with its successors and assigns, the "Company") and Michael A. Butt (the
"Grantee").

        WHEREAS, the Company and the Grantee (the "Parties") have concurrently
entered into an agreement (the "Service Agreement") pursuant to which the
Grantee is to serve the Company as Chairman of its Board of Directors (the
"Board"); and

        WHEREAS, the Company has decided to grant the shares described below to
the Grantee as an inducement to accept such position and as a performance
incentive;

        NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, and for other good and valuable consideration, the Parties
agree as follows:

        (a)    Grant.    Subject to the terms and conditions hereof, the Company
hereby grants to the Grantee, effective as of the Grant Date, a restricted stock
award (this "Award") in the aggregate amount of 10,000 shares (the "Shares") of
voting common shares of the Company, par value US$0.10 (the "Common Stock").

        (b)    Vesting of Shares.    At the opening of business on the third
anniversary of the Grant Date, the Shares under this Award shall become fully
vested and nonforfeitable if the Grantee is then continuing to serve the Company
under the Service Agreement, provided that the Shares shall become fully vested
and nonforfeitable on certain terminations of the Grantee's service under the
Service Agreement, under certain circumstances, as set forth in Section 8 of the
Service Agreement. Except as otherwise provided in Section 8 of the Service
Agreement, the Shares shall be forfeited on any termination of the Grantee's
service under the Service Agreement that occurs prior to the third anniversary
of the Grant Date.

        (c)    Holding and Delivery of Share Certificates.    Certificates
representing the Shares shall be held by the Company, along with one or more
stock powers executed by the Grantee in blank (which stock powers shall be used
by the Company solely to effect the forfeiture provisions of Paragraph (b)),
until such Shares have become vested as set forth above. Upon such Shares
becoming vested, one or more certificates representing the securities that then
constitute such Shares, together with any cash or property (other than
securities) received in respect of such Shares as provided in Paragraph (d), and
any associated stock powers, shall promptly be delivered to the Grantee (or
permitted transferee under Paragraph (e), if applicable). The Shares granted
pursuant to this Agreement shall, upon delivery to the Grantee, rank equally in
all respects with the other shares of the voting Common Stock. The Shares, when
delivered, shall be fully paid and non-assessable and shall be free and clear of
any and all liens, encumbrances, charges and other third party rights except to
the extent otherwise provided in Paragraph (e) below, or in the Bye-Laws of the
Company.

        (d)    Rights as Stockholder.    Subject to the terms of this Agreement
and beginning as of the Grant Date, the Grantee shall have all the rights of a
stockholder of the Company with respect to all of the Shares under this Award,
including, without limitation, the right to vote all such Shares and to receive
dividends and other distributions thereon (including, without limitation, any
securities, cash or other property issued or delivered in respect of, in
exchange for, or on conversion of, any such Shares in connection with any
merger, consolidation, combination, reorganization, recapitalization, spin-off,
split-up, exchange of securities, liquidation, dissolution, share split, share
dividend, cash dividend, or other transaction or event), provided, however, that
any dividend or other distribution made in respect of such Shares (x) shall be
deemed to be Shares

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received in substitution for, or in addition to and as part of, the Shares in
respect of which such dividend or other distribution is made and (y) shall
accordingly be subject to the same restrictions hereunder with respect to
vesting, transfer, forfeiture, and delivery upon vesting as to which such Shares
are subject.

        (e)    Restrictions on Transfer of Shares.    Neither the Shares granted
pursuant to this Agreement, nor any interest in them, may be sold, assigned,
pledged, hypothecated, encumbered or in any other manner transferred or disposed
of, in whole or in part, except in compliance with the terms, conditions and
restrictions as set forth in the Bye-Laws of the Company, applicable United
States federal and state securities laws or any other applicable laws or
regulations and the terms and conditions of this Agreement, except: (i) by will
or the laws of descent and distribution or (ii) by the Grantee to members of
"the Grantee's immediate family", to a trust established for the exclusive
benefit of one or more members of "the Grantee's immediate family" and/or the
Grantee, or to a partnership pursuant to which the only partners are one or more
members of "the Grantee's immediate family" and/or the Grantee. For purposes of
this Agreement, "the Grantee's immediate family" shall mean the initial
Grantee's children, stepchildren, grandchildren, parents, spouse, siblings
(including half brothers and sisters), and in-laws, and includes relationships
arising because of legal adoption. The Company represents and warrants that its
Board has approved the transfer of all or any portion of the Shares to the
Grantee's immediate family or trust or partnership as permitted by this
Paragraph (e) and the registration of any Shares in the name of any person to
whom the Shares may be transferred pursuant to this Paragraph (e). Each
certificate for such Shares shall bear the following legend or such other legend
as the Company reasonably deems appropriate:

        "These securities have not been registered under the United States
Securities Act of 1933, as amended. These securities cannot be offered,
transferred or sold unless (i) a registration statement under such Act is in
effect with respect to such securities or a written opinion from counsel
reasonably acceptable to Axis Specialty Insurance Limited (the "Company") is
obtained to the effect that no such registration is required, and (ii) the
transferee is approved by applicable regulatory authorities, if such approval is
required and (iii) simultaneously the appropriate number of shares of any
Designated Subsidiary (as such term is defined in the Bye-Laws of the Company
and only if the Board of Directors of the Company has constituted any entity a
Designated Subsidiary) is offered, transferred or sold together with each share
represented hereby that is proposed to be offered, transferred or sold. The
Company reserves the right to refuse the transfer of such securities until such
conditions have been fulfilled. Sections 68 through 70 of the Company's Bye-Laws
contain other significant restrictions on transfers of shares of the Company."

Any certificate delivered at any time in exchange or substitution for any
certificate bearing such legend or such other legend reasonably deemed
appropriate by the Company shall also bear such legend unless, in the reasonable
opinion of counsel for the Company, the securities represented thereby need no
longer be subject to the restriction contained herein. The provisions of this
Paragraph (e) shall be binding upon all subsequent holders of certificates
bearing the above legend.

        (f)    Shareholder Rights.    Subject to the limitations set forth in
Paragraph  (d), the Grantee shall enjoy with respect to the Shares that are the
subject of this Agreement, "tag along" rights, "put" rights, exchange rights,
registration rights and other comparable rights on the most favorable basis
provided for each such right to any other holder of Common Stock, except that
registration rights shall be provided on the same basis as provided other
minority investors.

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        (g)    Withholding.    The Grantee agrees to make appropriate
arrangements with the Company for satisfaction of any applicable tax withholding
requirements, or similar requirements, arising out of this Agreement.

        (h)    Incorporation of Provisions.    Sections 11, 12, 14, 15, 16
(first and third sentences only), 17, 18, 19, 20, 21 (second sentence only), 22,
23 and 24 of the Service Agreement (relating, respectively to excise tax
adjustment payments, resolution of disputes, representations, integration and
inconsistencies, assignability, amendments or waivers, notices, severability,
beneficiaries/references, governing law, headings and counterparts) shall be
deemed incorporated into this Agreement as if fully set forth herein, with all
references to the Executive in such Sections being deemed to be references to
the Grantee. All capitalized terms not defined in this Restricted Share Grant
Agreement shall have the meanings set forth in the Service Agreement.

20

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        IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
the date first written above.

    Axis Specialty Limited
 
 
By:
       

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Name:
Title:
 
 
The Grantee        
 
 

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Michael A. Butt

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EXHIBIT C

GOOD REASON

        For purposes of this Agreement, "Good Reason" shall mean the occurrence
of any of the following (without the Executive's express prior written consent
and without full cure within ten days of the Executive giving written notice to
the Company or the Board, as the case may be, requesting cure):

(i)(A) The assignment to the Executive of duties materially inconsistent with
the Executive's position and responsibilities as set forth in Section 2 of this
Agreement; (B) any material reduction in the Executive's authorities or
responsibilities; or (C) any removal of the Executive from, or any failure to
elect or reelect the Executive to, the position of Chairman of the Board, except
in connection with a termination of the Executive's service (w) by the Company
(whether for Cause or without Cause), (x) by either Party for Disability, (y) by
the Executive voluntarily or (z) as a result of the Executive's death;

(ii)(A) Any reduction in the Executive's Base Fee or target bonus opportunity as
a percentage of Base Fee or (B) following any Change in Control, failure to pay
the Executive an annual bonus in an amount no less than the greater of
(x) US$750,000 and (y) the largest amount awarded to the Executive as an annual
bonus for any of the three years (or such lesser number of years he has then
been employed) immediately preceding the year in which a Change in Control
occurs and, if applicable, failure to calculate such bonus in a manner as
favorable to the Executive as that used to calculate the most recent annual
bonus paid to the Executive prior to the Change in Control;

(iii)The failure by the Company to obtain the specific assumption of this
Agreement by any successor to, or assign of, the Company or any person acquiring
all or substantially all of the Company's business or assets;

(iv)Any material breach by the Company or any of its Affiliates of any of its
material obligations to the Executive or members of his family, under this
Agreement or otherwise; or

(v)Requiring the Executive to be based at any office or location in violation of
Section 2(a) of the Service Agreement, except for travel reasonably required in
the performance of the Executive's duties.

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EXHIBIT D

CHANGE IN CONTROL

        "Change in Control" shall mean the occurrence of any of the following
events:

(i)any "person," as such term is used as of September 19, 2002 in Sections
3(a)(9) and 13(d) of the United States Securities Exchange Act of 1934, becomes
a "beneficial owner," as such term is used in Rule 13d-3 promulgated under that
Act, of 30% or more of the Voting Stock of the Company, measured either by
number of shares or by voting power;

(ii)the majority of the Board consists of individuals other than "Incumbent
Directors," which term means the members of the Board on September 19, 2002;
provided that any person becoming a director subsequent to such date whose
election or nomination for election was supported by two-thirds of the directors
who then comprised the Incumbent Directors shall be considered to be an
Incumbent Director;

(iii)the Company adopts any plan of liquidation providing for the distribution
of all or substantially all of its assets;

(iv)all or substantially all of the assets or business of the Company is
disposed of pursuant to an amalgamation, merger, consolidation or other
transaction (unless the shareholders of the Company immediately prior to such
merger, consolidation or other transaction beneficially own, directly or
indirectly, in substantially the same proportion as they owned the Voting Stock
of the Company, all of the Voting Stock or other ownership interests of the
entity or entities, if any, that succeed to the business of the Company); or

(v)the Company combines with another entity and is the surviving entity but,
immediately after the combination, the shareholders of the Company immediately
prior to the combination hold, directly or indirectly, 50% or less of the Voting
Stock of the combined entity, measured either by number of shares or by voting
power (there being excluded from the Voting Stock held by such shareholders, but
not from the Voting Stock of the combined entity, any shares received by
Affiliates of such other entity in exchange for Voting Stock of such other
entity).

For purposes of the foregoing, "Voting Stock" shall mean capital stock of any
class or classes having general voting power under ordinary circumstances, in
the absence of contingencies, to elect members of a board of directors (or
equivalent governing person or body).

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QuickLinks

Exhibit 10.4

SERVICE AGREEMENT

EXHIBIT A

SHARE PURCHASE OPTION AGREEMENT

EXHIBIT B

RESTRICTED SHARE GRANT AGREEMENT

EXHIBIT C

GOOD REASON

EXHIBIT D

CHANGE IN CONTROL