<PAGE>

                                                                     EXHIBIT 4.4


THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE
UNITED STATES OF AMERICA SECURITIES ACT OF 1933, AS AMENDED (the "Securities
Act"), AND MAY NOT BE SOLD, TRANSFERRED, ASSIGNED OR HYPOTHECATED UNLESS THERE
IS AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT COVERING SUCH SECURITIES,
THE SALE IS MADE IN ACCORDANCE WITH RULE 144 UNDER THE SECURITIES ACT OR THE
COMPANY RECEIVES AN OPINION OF COUNSEL TO THE HOLDER OF THESE SECURITIES
REASONABLY SATISFACTORY TO THE COMPANY, STATING THAT SUCH SALE, TRANSFER,
ASSIGNMENT OR HYPOTHECATION IS EXEMPT FROM THE REGISTRATION AND PROSPECTUS
DELIVERY REQUIREMENTS OF SUCH ACT, AND THERE IS APPLICABLE APPROVAL OR
PERMISSION FROM THE BERMUDA MONETARY AUTHORITY.

IN ADDITION, THE SECURITIES EVIDENCED BY THIS CERTIFICATE ARE SUBJECT TO CERTAIN
TRANSFER RESTRICTIONS IN THE COMPANY'S BYE-LAWS AND PURSUANT TO A SHAREHOLDERS'
AGREEMENT DATED AS OF DECEMBER 22, 1999 AMONG THE COMPANY, MAX RE LTD. AND THE
COMPANY'S SHAREHOLDERS. A COPY OF SUCH BYE-LAWS AND SHAREHOLDERS' AGREEMENT WILL
BE FURNISHED WITHOUT CHARGE BY THE COMPANY TO THE HOLDER HEREOF UPON WRITTEN
REQUEST.


                               MAX RE CAPITAL LTD.

                             SHARE PURCHASE WARRANT


Certificate No.: [         ]                                      Date: [      ]

                  FOR VALUE RECEIVED,  MAX RE CAPITAL LTD., a company  organized
under the laws of Bermuda with limited liability (the "Company"),  hereby grants
                                                       -------
to  Western  General  Insurance,   Ltd.  (the  "Warrant  Holder")  this  warrant
                                                ---------------
certificate (this "Warrant") to purchase, in accordance with the terms set forth
                   -------
herein, [ ] ( ) shares of the Company's Common Shares, initially having a par
value of US$1.00 per share (the "Common Shares"), at a price per share equal to
                                 -------------
US$[ ] as adjusted from time to time pursuant to Section 2 hereof (the "Exercise
                                                                        --------
Price") but at no time shall the  Exercise  Price be less than the then  current
-----
par value of any share to be issued pursuant hereto.

                  This Warrant is issued pursuant to that certain Subscription
Agreement, dated as of March 31, 2000 (the "Subscription Agreement"), between
                                             -----------------------
<PAGE>

the Company and the Warrant Holder. Each capitalized term used in this Warrant
but not otherwise defined herein has the meaning given to such term in the
Subscription Agreement.

                  This warrant is subject to the following provisions:

                  Section 1. Warrant Terms.
                             -------------

                  (a) This Warrant is for the purchase of [ ] ( ) Common Shares
at the Exercise Price, as such price may be adjusted from time to time under the
terms hereof.

                  (b) This  Warrant  shall  expire at 5:00 p.m.  New York  City,
N.Y., U.S.A.  time, on the tenth anniversary of the date hereof (the "Expiration
Date").                                                               ----------
----

                  Section  2.  Anti-dilution  Provisions.  In order  to  prevent
                               -------------------------
dilution of the purchase rights granted under Section 1 hereof, the Exercise
Price shall be subject to adjustment from time to time pursuant to this Section
2.

                  (a) Effect on Exercise Price of Certain  Events.  For purposes
                      -------------------------------------------
of determining the adjusted Exercise Price, the following shall be applicable:

                        (1) Subdivision or Combination of Common Shares.  If the
                            -------------------------------------------
Company, at any time while this Warrant is outstanding, (a) shall pay a stock or
bonus share dividend on its Common Shares, (b) subdivide the class of Common
Shares into a larger number of shares or (c) combine the class of Common Shares
into a smaller number of shares then (i) the Exercise Price thereafter shall be
determined by multiplying the Exercise Price by a fraction the numerator of
which shall be the number of Common Shares (excluding treasury shares, if any)
issued and outstanding before such event and the denominator of which shall be
the number of Common Shares issued and outstanding after such event and (ii) the
number of Common Shares issuable upon exercise of the Warrant shall be
multiplied by a fraction, the numerator of which shall be the number of Common
Shares (excluding treasury shares, if any) issued and outstanding after such
event and the denominator of which shall be the number of Common Shares
(excluding treasury shares, if any) issued and outstanding before such event.
Any adjustment made pursuant to this Section 2(a)(1) shall become effective
immediately after the record date for the determination of shareholders entitled
to receive such dividend or distribution and shall become effective immediately
after the effective date in the case of a subdivision or combination.

                        (2) Amalgamation,    Reorganization,   Reclassification,
                            ----------------------------------------------------
Consolidation,    Merger   or   Sale.   Any   amalgamation,    recapitalization,
------------------------------------
reorganization, reclassification, consolidation, merger of the Company or sale
of all or substantially all of the Company's assets or other transaction, in
each case which is effected in such a manner that the holders of Common Shares
are entitled to receive (either directly or upon subsequent liquidation) shares,
securities or assets with respect to or in exchange for Common Shares is
referred to herein as an "Organic Change." Prior to the consummation of any
                           ---------------

                                        2
<PAGE>

Organic Change, the Company shall make appropriate provisions (in form and
substance satisfactory to the Warrant Holder) to insure that the Warrant Holder
shall thereafter have the right to acquire and receive, in lieu of or in
addition to (as the case may be) Common Shares immediately theretofore
acquirable and receivable upon the exercise of this Warrant, such shares,
securities or assets as such Warrant Holder would have received in connection
with such Organic Change if such Warrant Holder had exercised this Warrant
immediately prior to such Organic Change. In each such Organic Change, the
Company shall also make appropriate provisions (in form and substance
satisfactory to the Warrant Holder) to insure that the provisions of this
Section 2 shall thereafter be applicable to this Warrant (including, in the case
of any such amalgamation, consolidation, merger or sale in which the successor
entity or purchasing entity is other than the Company) and that there is an
immediate adjustment of the Exercise Price to the value for the Common Shares
reflected by the terms of such amalgamation, consolidation, merger or sale, and
a corresponding immediate adjustment in the number of Common Shares acquirable
and receivable upon exercise of this Warrant, if the value so reflected is less
than the Exercise Price in effect immediately prior to such amalgamation,
consolidation, merger or sale). Prior to the consummation of any such
amalgamation, consolidation, merger or sale, the Company shall use its
reasonable efforts to cause the successor entity (if other than the Company
resulting from amalgamation, consolidation or merger) or the entity purchasing
such assets to assume by written instrument (in form and substance satisfactory
to the Warrant Holder), the obligation to deliver to each such Warrant Holder
such shares, securities or assets as, in accordance with the foregoing
provisions, the Warrant Holder may be entitled to acquire; provided, however,
                                                             ------------------
that any such  assumption  shall not  relieve  the  Company  of its  obligations
hereunder.

        (b) Notices.  Immediately upon any adjustment of the Exercise Price, the
            -------
Company shall give, or cause to be given, written notice thereof to the Warrant
Holder, setting forth in reasonable detail and certifying the calculation of
such adjustment. The Company shall give, or cause to be given, written notice to
the Warrant Holder at least twenty (20) days prior to the date on which the
Company closes its books or takes a record (i) with respect to any dividend or
distribution upon Common Shares, (ii) with respect to any pro rata subscription
offer to holders of Common Shares or (iii) for determining rights to vote with
respect to any Organic Change, dissolution or liquidation. The Company shall
also give, or cause to be given, written notice to the Warrant Holder at least
twenty (20) days prior to the date on which any Organic Change shall take place.


        Section 3.      Exercise of Warrant.
                        -------------------

        (a) Exercise Procedure: The Warrant Holder may exercise all or a portion
            ------------------
of this Warrant at any time and from time to time commencing after the date
hereof until 5:00 p.m. New York City time, on the Expiration Date by
surrendering at the registered office of the Company this Warrant and a
completed Exercise Agreement (substantially in the form of Exhibit A attached
                                                              ---------
                                        3
<PAGE>

hereto) and by paying the Exercise Price in one of the following manners:

                  (i)   Cash   Exercise.   The  Warrant   Holder  shall  deliver
                        ---------------
        immediately  available funds or a cashiers check payable to the Company;
        or

                  (ii)  Cashless  Exercise.  After the date of  issuance of this
                        ------------------
        Warrant, if the Common Shares are listed on a national securities
        exchange, automated quotation system or are available for sale in the
        over-the-counter market and the provisions of Section 42A of the Bermuda
        Companies Act 1981, as amended, may be satisfied by the Company, the
        Warrant Holder shall have the right to surrender this Warrant to the
        Company together with a notice of cashless exercise, in which event the
        Company shall issue to the Warrant Holder the number Common Shares
        underlying this Warrant (the "Warrant Shares") determined as follows:
                                      --------------
                                  X = Y (A-B)/A

                                  where:

                                  X = the number of Warrant  Shares to be issued
                                  to the Warrant Holder

                                  Y = the number of Warrant Shares with respect
                                  to which this Warrant is being exercised

                                  A = the average of the per share Market Price
                                  of the Common Shares for the five (5) trading
                                  days immediately prior to (but not including)
                                  the date of exercise (but not less than the
                                  then par value of the Common Shares)

                                  B = the Exercise Price

For purposes of Rule 144 promulgated under the Securities Act, it is intended,
understood and acknowledged that the Warrant Shares issued in a cashless
exercise transaction shall be deemed to have been acquired and paid the full
purchase price therefor by the Warrant Holder, and the holding period for the
Warrant Shares shall be deemed to have been commenced on the issue date to the
extent permitted by Rule 144.

For purposes hereof, "Market Price" means on any particular date (i) the closing
                      ------------
bid price per Common Share on such date on the national securities exchange or
automated quotation system on which the Common Shares are then listed or if
there is no such price on such date, then the closing bid price on such exchange
or quotation system on the date nearest preceding such date, or (ii) if the

                                        4
<PAGE>

Common Shares are not listed then on a national securities exchange or automated
quotation system, the closing bid price for each Common Share in the
over-the-counter market, as reported by the National Quotation Bureau
Incorporated (or similar organization or agency succeeding to its functions of
reporting prices) at the close of business on such date.

        (b) Certificates for the Common Shares acquired through exercise of this
Warrant shall be delivered by the Company to the Warrant Holder within five (5)
business days after (i) receipt by the Company of the items required by Section
3(a) for the respective method or methods of exercise, and (ii) where
applicable, compliance with Section 42A of the Bermuda Companies Act 1981 (and
the Company shall use reasonable efforts to complete the requirements of the
said Section 42A as quickly as possible). Unless this Warrant has expired or all
of the purchase rights represented hereby have been exercised, the Company shall
prepare a new Warrant, substantially identical hereto, representing the rights
formerly represented by this Warrant which have not expired or been exercised
and shall, within such five-day period, deliver such new Warrant to such Warrant
Holder.

        (c) The Common Shares issuable upon exercise of this Warrant shall be
deemed to have been issued to the Warrant Holder on the date by which the
Company receives the completed Exercise Agreement and payment of the Exercise
Price, if any, and, where applicable, has complied with the requirements of the
said Section 42A of the Companies Act 1981, and the Warrant Holder shall be
deemed for all purposes to have become the record holder of such Common Shares
on such date.

        (d) The issuance of certificates for the Common Shares issuable upon
exercise of this Warrant shall be made without charge to the Warrant Holder for
any issuance tax in respect thereof or other cost incurred by the Company in
connection with such exercise and the related issuance of the Common Shares.

        (e) The Company shall at all times reserve and keep available authorized
but unissued Common Shares, solely for the purpose of issuance upon exercise of
this Warrant, such number of Common Shares as are issuable upon exercise of this
Warrant. All Common Shares shall, when issued, be duly and validly issued, fully
paid and nonassessable (meaning that no further sums are required to be paid by
the holders thereof in connection with the issue thereof) and free from all
taxes, liens and charges. The Company shall take such actions as may be
necessary to assure that the Common Shares may be so issued without violation of
any applicable law or governmental regulation or any requirements of any
domestic securities exchange upon which their shares may be listed (except for
official notice of issuance which shall be immediately delivered by the Company
upon each such issuance).

        Section 4.  Warrant  Transferable.  Subject to the  transfer  conditions
                    ---------------------
referred to in the legend endorsed hereon, this Warrant and all rights hereunder
are transferable, in whole or in part, without charge to the Warrant Holder;
upon surrender of this Warrant with a properly executed Assignment
(substantially in the form of Exhibit B hereto) at the registered office of the
                               ---------
Company.  Notwithstanding the foregoing, this Warrant may be transferred only to

                                        5
<PAGE>

the extent that, upon exercise of this Warrant, the transferee would own no more
than 9.9% of the total Common Shares issued and outstanding (after application
of the U.S. tax attribution and constructive ownership rules under the United
States Internal Revenue Code of 1986, as amended, and the rules and regulations
promulgated thereunder), unless such restriction is waived by the unanimous
consent of the Board of Directors of the Company.

        Section 5. Amendment and Waiver.  Except as otherwise  provided  herein,
                   --------------------
the provisions of this Warrant may be amended only if the Company has obtained
the written consent of the Warrant Holder. Notwithstanding the foregoing, the
Company hereby covenants that any time the warrants issued to Moore Holdings,
L.L.C. ("Moore") and Capital Z Investments, L.P. ("Capital Z" and together with
         -----                                      ---------
Moore, the "Founders") by Max Re Ltd.  pursuant to agreements dated December 22,
            --------
1999 are amended, modified, supplemented or restated to grant rights to the
Founders which are more favorable than the rights currently granted to the
Founders under such warrants, (i) the Company shall, within 2 business days of
such amendment, modification, supplement or restatement, provide written notice
of such event to the Warrant Holder and (ii) upon surrender of this Warrant at
the registered office of the Company, this Warrant shall immediately be amended,
supplemented, modified or restated to grant the same rights to the Warrant
Holder so that this Warrant remains pari passu with the warrants issued to the
                                     ----------
Founders.

        Section  6.  Descriptive  Headings.  The  descriptive  headings  of this
                     ---------------------
Warrant are inserted for convenience only and do not constitute a part of this
Warrant.

        Section  7.  Governing  Law.  This  Warrant  shall  be  governed  by and
                     --------------
construed and enforced in accordance with the internal laws of Bermuda without
regard to the principles of conflicts of law thereof. Each party hereby
irrevocably submits to the nonexclusive jurisdiction of the courts of Bermuda
for the adjudication of any dispute hereunder or in connection herewith or with
any transaction contemplated hereby or discussed herein, and hereby irrevocably
waives, and agrees not to assert in any suit, action or proceeding, any claim
that it is not personally subject to the jurisdiction of any such court, that
such suit, action or proceeding is improper. Each party hereby irrevocably
waives personal service of process and consents to process being served in any
such suit, action or proceeding by mailing a copy thereof to such party at the
address for such notices to it under this Warrant and agrees that such service
shall constitute good and sufficient service of process and notice thereof.
Nothing contained herein shall be deemed to limit in any way any right to serve
process in any manner permitted by law. TO THE EXTENT APPLICABLE AND PERMITTED,
EACH PARTY HEREBY IRREVOCABLY WAIVES ANY RIGHT IT MAY HAVE, AND AGREES NOT TO
REQUEST, A JURY TRIAL FOR THE ADJUDICATION OF ANY DISPUTE HEREUNDER OR IN
CONNECTION HEREWITH OR ARISING OUT OF THIS WARRANT OR ANY TRANSACTION
CONTEMPLATED HEREBY.

                                        6
<PAGE>

        Section  8.  Complete  Agreement;   Severability.  Except  as  otherwise
                     -----------------------------------
expressly set forth herein, this Warrant embodies the complete agreement and
understanding among the parties hereto with respect to the subject matter hereof
and supersede and preempt any prior understandings, agreements or
representations by or among the parties, written or oral, which may have related
to the subject matter hereof in any way. In case any provision of this Warrant
shall be invalid, illegal or unenforceable, such invalidity, illegality, or
unenforceability shall not in any way affect or impair any other provision of
this Warrant.

        Section 9. Notices. All notices and other communications provided for or
                   -------
permitted hereunder shall be made in writing by hand-delivery, first-class mail,
facsimile, or air courier guaranteeing overnight delivery.

         If to the Company:                  Max Re Capital Ltd.
                                             Ascot House
                                             28 Queen Street
                                             Hamilton, HM 11
                                             Attention:  Chief Financial Officer

         With a copy to:                     Akin, Gump, Strauss, Hauer & Feld,
                                             L.L.P.
                                             590 Madison Avenue
                                             New York, New York, 10022
                                             Attention:  Kerry E. Berchem, Esq.

         If to the Warrant Holder:           Western General Insurance, Ltd.
                                             2nd Floor
                                             Swan Building
                                             26 Victoria Street
                                             Hamilton HM 12
                                             Bermuda
                                             Attention: Peter Rackley

All such notices and communications shall be deemed to have been duly given when
delivered by hand, if personally delivered; five business days after the date of
deposit in the Bermuda or United States of America mail, if mailed by
first-class air mail; when receipt is acknowledged by the recipient facsimile
machine, if sent by facsimile; and three business days after being delivered to
a next-day air courier.

                                        7
<PAGE>

                IN WITNESS WHEREOF, the Company has caused this Warrant to be
signed and attested by its duly authorized officer and to be dated the date of
issuance hereof.

                                            MAX RE CAPITAL  LTD.




                                            By:
                                               ---------------------------------
                                               Name:  Keith S. Hynes
                                               Title: EVP & CFO



Accepted and Agreed to:
As of [       ]

WESTERN GENERAL INSURANCE, LTD.




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




                                        8
<PAGE>

                                                                       EXHIBIT A

                               EXERCISE AGREEMENT
                               ------------------

To:      MAX RE CAPITAL LTD.


1.      [_]  The undersigned hereby: (1) irrevocably elects to subscribe for
and offers to purchase _______ Common Shares of Max Re Capital, Ltd., pursuant
to Warrant No. ___ heretofore issued to ___________________ on ____________,
[ ]; (2) encloses a payment of $__________ for these shares at a price of
$____ per share (as adjusted pursuant to the provisions of the Warrant); and (3)
requests that a certificate for the shares be issued in the name of the
undersigned and delivered to the undersigned at the address specified below.


2.      [_]   The undersigned hereby: (1) irrevocably elects to exchange
Warrant(s) to purchase _______ Common Shares of Max Re Capital Ltd., pursuant to
Warrant No. ___ heretofore issued to ___________________ on ____________, [ ];
(2) encloses Warrant(s) as a payment of $__________ for these shares at a price
of $____ per share (as adjusted pursuant to the provisions of the Warrant); and
(3) requests that a certificate for the shares be issued in the name of the
undersigned and delivered to the undersigned at the address specified below.




Dated:                           Signature
                                            ------------------------------------


                                 Address
                                            ------------------------------------



                                        9
<PAGE>

                                                                       EXHIBIT B

                                   ASSIGNMENT


                  FOR VALUE RECEIVED, ________________________________ hereby
sells, assigns and transfers all of the rights of the undersigned under the
attached Warrant (Certificate No.:_____) with respect to the number of Common
Shares and covered thereby set forth below, unto:

Names of Assignee                   Address                   No. of Shares




Dated:                               Signature
                                                  ------------------------------


                                     Address
                                                  ------------------------------


                                     Witness
                                                  ------------------------------


                                       10