<PAGE>

                                                                     EXHIBIT 4.5

                             THIRD AMENDMENT TO THE
                             SHARE PURCHASE WARRANT

     WHEREAS, Montpelier Re Holdings Ltd., a company organized under the laws of
Bermuda (the "Company") and White Mountains Insurance Group, Ltd. ("White
Mountains") are parties to that Warrant Issuance Agreement dated as of December
6, 2001, pursuant to which the Company issued to White Mountains a warrant dated
as of January 3, 2002, as amended by Amendment, dated as of February 11, 2002,
and Amendment to the Share Purchase Warrant, dated as of July 1, 2002 (the
"White Mountains Warrant"), attached hereto as Exhibit A;

     WHEREAS, the Company and Benfield Group plc, which has subsequently changes
its name to Benfield Holdings Limited ("Benfield") are parties to that Warrant
Issuance Agreement dated as of December 6, 2001, pursuant to which the Company
issued to Benfield a warrant dated as of January 3, 2002, as amended by
Amendment, dated as of February 11, 2002, and Amendment to the Share Purchase
Warrant, dated as of July 1, 2002 (the "Benfield Warrant"), attached hereto as
Exhibit B;

     WHEREAS, the Company and Banc of America Securities LLC ("BAS") are parties
to that Warrant Issuance Agreement dated as of December 6, 2001, pursuant to
which the Company issued to BAS a warrant dated as of January 3, 2002, as
amended by Amendment, dated as of February 11, 2002, and Amendment to the Share
Purchase Warrant, dated as of July 1, 2002 (the "BAS Warrant"), attached hereto
as Exhibit C;

     WHEREAS, each of White Mountains, Benfield and BAS (each a "Warrant
Holder"), on the one hand, and the Company, on the other hand, desire to amend
Section 3 of the respective White Mountains Warrant, Benfield Warrant and BAS
Warrant (each referred to individually as a "Warrant") to add a provision
requiring a cash payment in lieu of fractional Common Shares upon exercise of
the Warrants;

     WHEREAS, pursuant to Section 6 of each Warrant, each Warrant may be amended
if the Company has obtained the written consent of the Warrant Holder;

     NOW, THEREFORE, the Company and each Warrant Holder hereby agree as
follows:

          1.  Definitions.  Unless otherwise defined in this Amendment, each
     term used herein that is defined in each Warrant shall have the meaning
     assigned to it in such Warrant.

          2.  Section 3(g) Added.  Each Warrant is hereby amended, effective
     immediately, by inserting the following provision as Section 3(g):

             "(g) Notwithstanding any other provision hereof, no fractional
        amounts of Common Shares will be issued in connection with any exercise
        hereunder, but in lieu of such fractional amounts, the Company shall
        make a cash payment therefor equal to the product of the applicable
        fraction multiplied by 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)."

          3.  Governing Law.  This Amendment shall be governed by and construed
     and enforced in accordance with the internal laws of the State of New York
     except to the extent where the laws of any other jurisdiction are referred
     to herein. Each party hereby irrevocably submits to the nonexclusive
     jurisdiction of the courts of New York 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 (i) it is not
     personally subject to the jurisdiction of any such court, and/or (ii) that
     such suit, action or proceeding is not brought in the proper forum. 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 each
     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.
<PAGE>

          4.  Effect of Agreement.  Except as amended and supplemented by this
     Amendment, all of the terms, conditions, provisions and covenants of each
     Warrant shall remain and continue in full force and effect and are hereby
     ratified, repeated and confirmed in all respects.

          5.  Entire Agreement.  Each Warrant, as amended and supplemented by
     this Amendment, constitutes the entire agreement and understanding among
     the Company, on the one hand, and the respective Warrant Holder, on the
     other hand and supersedes any and all prior agreements and understandings
     relating to the subject matter hereof.

          6.  Counterparts.  This Amendment may be executed in any number of
     counterparts, each of which shall be deemed to be an original and all of
     which together shall be deemed to be one and the same instrument.

                                        2
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have duly executed this Amendment as
of March 31st 2003.

                                          MONTPELIER RE HOLDINGS LTD.

                                          By:      /s/ ANTHONY TAYLOR
                                            ------------------------------------
                                            Name: Anthony Taylor
                                            Title:   President and Chief
                                              Executive Officer

                                          WHITE MOUNTAINS INSURANCE GROUP, LTD.

                                          By:     /s/ RAYMOND BARRETTE
                                            ------------------------------------
                                            Name: Raymond Barrette
                                            Title:   President and Chief
                                              Executive Officer

                                          BENFIELD HOLDINGS LIMITED

                                          By:        /s/ JOHN WHITER
                                            ------------------------------------
                                            Name: John Whiter
                                            Title:   Director

                                          BANC OF AMERICA SECURITIES LLC

                                          By:    /s/ ANTONIO URSANO, JR.
                                            ------------------------------------
                                            Name: Antonio Ursano, Jr.
                                            Title:   Managing Director

                                        3