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                                                                  EXHIBIT 10.38

                         RENAISSANCERE OPTION AGREEMENT

NONE OF THE RENRE OPTION (AS DEFINED BELOW) AND THE COMMON SHARES DELIVERABLE
UPON EXERCISE OF THE RENRE OPTION HAVE BEEN REGISTERED UNDER THE U.S. SECURITIES
ACT OF 1933. NEITHER THE RENRE OPTION, NOR ANY INTEREST THEREIN, NOR ANY COMMON
SHARES DELIVERABLE UPON EXERCISE THEREOF MAY BE ASSIGNED OR OTHERWISE
TRANSFERRED, DISPOSED OF OR ENCUMBERED EXCEPT FOLLOWING RECEIPT BY PLATINUM
UNDERWRITERS HOLDINGS, LTD. (THE "COMPANY") OF EVIDENCE SATISFACTORY TO IT,
WHICH MAY INCLUDE AN OPINION OF UNITED STATES COUNSEL, THAT SUCH TRANSFER DOES
NOT REQUIRE REGISTRATION UNDER THE SECURITIES ACT OR STATE SECURITIES LAWS AND
UPON OBTAINMENT OF ANY REQUIRED GOVERNMENT APPROVALS AND EXCEPT TO THE EXTENT
PERMITTED HEREIN. TRANSFER (AS DEFINED IN THE COMPANY'S BYE-LAWS) OF THE RENRE
OPTION OR ANY INTEREST THEREIN, OR ANY COMMON SHARES DELIVERABLE UPON EXERCISE
THEREOF, MAY BE DISAPPROVED BY THE BOARD OF DIRECTORS OF THE COMPANY IF, IN ITS
REASONABLE JUDGMENT, IT HAS REASON TO BELIEVE THAT SUCH TRANSFER MAY EXPOSE THE
COMPANY, ANY SUBSIDIARY THEREOF, ANY SHAREHOLDER OR ANY PERSON CEDING INSURANCE
TO THE COMPANY OR ANY SUCH SUBSIDIARY TO ADVERSE TAX OR REGULATORY TREATMENT IN
ANY JURISDICTION. COMMON SHARES OBTAINED UPON EXERCISE OF THE RENRE OPTION ARE
SUBJECT TO SUBSTANTIAL RESTRICTIONS ON TRANSFER AS SET FORTH IN SECTION 6 OF
THIS OPTION AGREEMENT.

      This OPTION AGREEMENT is made this 1st day of November 2002 between
PLATINUM UNDERWRITERS HOLDINGS, LTD., a company organized under the laws of the
Islands of Bermuda (the "Company"), and RENAISSANCERE HOLDINGS LTD., a company
organized under the laws of the Islands of Bermuda ("RenRe").

                                   RECITALS:

      WHEREAS, the Company is contemplating an initial public offering (the
"Public Offering") of its common shares of par value U.S. $0.01 per share (the
"Common Shares");

      WHEREAS, RenRe and the Company have entered into an Investment Agreement,
dated as of September 20, 2002 (the "Investment Agreement") in which RenRe and
the Company have set forth certain terms of their continuing relationship
following the Public Offering; and

      WHEREAS, as contemplated by the Investment Agreement, contingent upon the
consummation of the Public Offering, RenRe will purchase from the Company a
number of Common Shares determined as set forth in the Investment Agreement and
the RenRe Option, as defined below, exercisable under the circumstances
specified in this Agreement.

<PAGE>

      NOW, THEREFORE, in furtherance of the transactions contemplated by the
Investment Agreement, and in consideration of the mutual promises, covenants and
agreements set forth therein and herein, the receipt and sufficiency of which
are acknowledged, the parties hereby agree as follows:

1. (a) The Company grants RenRe an option (the "RenRe Option") to purchase for
cash up to 2,500,000 Common Shares (the "RenRe Option Shares") following the
completion of the Public Offering.

      (b) The RenRe Option is exercisable, at an exercise price per Common Share
equal to 120 percent of the initial public offering price per Common Share (the
"RenRe Option Price"), in whole or in part at any time prior to the tenth
anniversary of the completion of the Public Offering (the "Exercise Period").

      (c) An "Exercise Date" is any day during an Exercise Period, other than a
Saturday, Sunday or other day on which banking institutions in New York City or
Bermuda are authorized or obligated by law or executive order to close (a
"Business Day"). A RenRe Option may be exercised as provided herein until 12:01
A.M., New York City time, on the first day after the expiration of the Exercise
Period.

      (d) Notwithstanding anything to the contrary in this Agreement, RenRe's
beneficial ownership interest in the Common Shares may not at any time and under
any circumstances exceed 19.9% of the then outstanding Common Shares or such
higher limit as the Company may approve in writing. It is agreed and understood
that, prior to any exercise of the RenRe Option, RenRe shall, if necessary,
dispose of such number of Common Shares so that, immediately after any exercise
of the RenRe Option, except with the prior written approval of the Company,
RenRe will not beneficially own more than 19.9% of the then outstanding Common
Shares.

      (e) RenRe Option Shares upon issue will rank equally in all respects with
the other Common Shares of the Company, but in no case will any RenRe Option
Shares carry any option or other right to subscribe for further additional
shares.

      (f) RenRe is not, solely by virtue hereof, entitled to any rights of a
shareholder in the Company either at law or in equity.

      (g) Upon any merger, amalgamation, consolidation, scheme of arrangement or
similar transaction involving the Company and any third party that is not a
subsidiary of the Company, or any sale of all or substantially all the assets of
the Company to any third party that is not a subsidiary of the Company (each, a
"Transaction") in which all holders of Common Shares become entitled to receive,
in respect of such shares, any capital stock, rights to acquire capital stock or
other securities of the Company or of any other person, any cash or any other
property, or any combination of the foregoing (collectively, "Transaction
Consideration"), the RenRe Option shall entitle RenRe to receive all Transaction
Consideration that RenRe would have been entitled to if it had exercised the
RenRe Option in full immediately prior to the Transaction (to the extent it
remains unexercised and without regard to the limitations in Section 1(c)
hereof), in each case upon payment by RenRe of the RenRe Option Price as in
effect immediately prior to such time. In determining the kind and amount of
Transaction Consideration that RenRe would


                                       2
<PAGE>

be entitled to receive in respect of any Transaction pursuant to this Section
1(g), RenRe shall be entitled to exercise any rights of election as to the kinds
and amounts of consideration receivable in such Transaction that are provided to
holders of Common Shares in such Transactions. Any adjustment in respect of a
Transaction pursuant to this Section 1(g) shall become effective immediately
after the effective time of such Transaction, retroactive to any record date
therefor. The Company shall take such action as is necessary to ensure that
RenRe shall be entitled to receive Transaction Consideration upon the terms and
conditions provided in this Section 1(g). Notwithstanding the foregoing, if an
adjustment is made pursuant to this Section 1(g) in respect of a Transaction
that involves a Change of Control (as defined below), RenRe shall be entitled to
exercise the RenRe Option pursuant to this Section 1(g) without regard to
Section 1(c) hereof A Transaction is deemed to have involved a "Change of
Control" if the beneficial owners of the outstanding Common Shares immediately
prior to the effective time of such Transaction are not the beneficial owners of
a majority of the total voting power of the surviving or acquiring entity in the
Transaction, as the case may be, immediately after such effective time.

2. (a) To exercise the RenRe Option in accordance with Section 1(b) hereof,
RenRe shall provide written notice to the Company of its intention to exercise
all or a portion of the RenRe Option at least ten (10) Business Days prior to
the intended Exercise Date (such notice must indicate the number of the RenRe
Option Shares RenRe intends to purchase upon exercise of the RenRe Option and
must be in writing signed by or on behalf of RenRe and delivered or sent to the
Company in accordance with Section 8 hereof).

      (b) The Company shall issue and allot RenRe Option Shares upon exercise of
the RenRe Option and payment of the total price payable therefor.

      (c) Concurrently with the issuance of the RenRe Option Shares pursuant to
Section 2(b) above, RenRe shall pay the aggregate RenRe Option Price for any
exercise hereunder by wire transfer of immediately available funds to an account
specified at least five (5) Business Days in advance by the Company such RenRe
Option Price being an amount in U.S. dollars equal to the product of (i) the
number of RenRe Option Shares that RenRe intends to purchase pursuant to any
exercise of the RenRe Option and (ii) the RenRe Option Price.

      (d) Notwithstanding anything to the contrary in this Agreement, the RenRe
Option may not be exercised under this Agreement unless the required regulatory
approvals set forth in Section 5 shall have been obtained.

3. (a) In case the Company at any time after the date that the number of Common
Shares issuable pursuant to the Public Offering and the RenRe Investment has
been determined:

                  (A) declares or pays a dividend or makes any other
            distribution with respect to its capital stock in Common Shares such
            that the number of Common Shares outstanding is increased,

                  (B) subdivides or splits-up its outstanding Common Shares,
            such that the number of Common Shares outstanding is increased,

                  (C) combines its outstanding Common Shares into a smaller
            number of Common Shares or


                                       3
<PAGE>

                  (D) effects any reclassification of the Common Shares other
            than a change in par value (including any such reclassification in
            connection with an amalgamation or merger in which the Company is
            the surviving entity or a reincorporation of the Company),

the number of Common Shares purchasable upon exercise of the RenRe Option shall
be proportionately adjusted so that RenRe will be entitled to receive the kind
and number of Common Shares or other securities of the Company which it would
have been entitled to receive after the happening of any of the events described
above if the RenRe Option had been exercised immediately prior to the happening
of such event or any record date with respect thereto. An adjustment made
pursuant to this paragraph 3(a) shall become effective immediately after the
effective date of such event retroactive to the record date, if any, for such
event.

      (b) In case the Company issues rights, options or warrants to all holders
of its outstanding Common Shares entitling them to subscribe for or purchase
Common Shares at a price per share which is lower at the record date mentioned
below than the then Current Market Value (as defined in Section 3(d)), the
number of RenRe Option Shares that RenRe may purchase thereafter upon the
exercise of the RenRe Option will be determined by multiplying the number of
RenRe Option Shares theretofore purchasable upon exercise of the RenRe Option by
a fraction, of which the numerator is the sum of (A) the number of Common Shares
outstanding on the record date for determining shareholders entitled to receive
such rights, options or warrants plus (B) the number of additional Common Shares
offered for subscription or purchase, and of which the denominator shall be the
sum of (A) the number of Common Shares outstanding on the record date for
determining shareholders entitled to receive such rights, options or warrants
plus (B) the number of shares which the aggregate offering price of the total
number of Common Shares so offered would purchase at the Current Market Value
(as defined below in Section 3(d)) per share of Common Shares at such record
date. Such adjustment shall be made whenever such rights, options or warrants
are issued, and shall become effective immediately after the record date for the
determination of shareholders entitled to receive such rights, options or
warrants.

      (c) In the event the Company distributes to all holders of its Common
Shares any of the capital stock of any of its subsidiaries (each, a
"Subsidiary"), the RenRe Option will upon such distribution be deemed to be an
option to purchase the kind and number of shares of the capital stock of the
Subsidiary which RenRe would have been entitled to receive after such
distribution had the RenRe Option been exercised immediately prior to such
distribution or any record date with respect thereto. The roll-over of the RenRe
Option into an option to purchase shares of capital stock of the applicable
Subsidiary pursuant to this Section 3(c) will become effective immediately after
the effective date of the distribution of shares of the capital stock of the
applicable Subsidiary to shareholders of the Company described above.

      (d) For the purpose of any computation under Section 3(b), the "Current
Market Value" of such Common Shares on a specified date is deemed to be the
average of the daily closing prices per share for the ten consecutive Trading
Days (as defined below) ending on the day before the applicable record date.
"Trading Day" means each Monday, Tuesday, Wednesday, Thursday and Friday, other
than any day on which the Common Shares are not traded on the applicable
securities exchange or on the applicable securities market. The closing price
for each day is the reported last sale price regular way or, in case no such
reported sale


                                       4
<PAGE>

takes place on such day, the average of the reported closing bid and asked
prices regular way, in either case on the New York Stock Exchange or, if the
Common Shares are not listed or admitted to trading on such Exchange, on the
principal national securities exchange on which the Common Shares are listed or
admitted to trading or, if not listed or admitted to trading on any national
securities exchange, on the NASDAQ National Market or, if the Common Shares are
not listed or admitted to trading on any national securities exchange or quoted
on the NASDAQ National Market, the average of the closing bid and asked prices
in the over-the-counter market as furnished by any New York Stock Exchange
member firm reasonably selected from time to time by the Board of Directors of
the Company for that purpose.

      (e) In the event the Company shall, in any calendar year, by dividend or
otherwise, distribute to all or substantially all holders of its Common Shares
(the "Current Distribution") (i) any dividend or other distribution of cash,
evidences of indebtedness, or any other assets or properties (other than as
described in Sections 3(a)-(c) above) or (ii) any options, warrants or other
rights to subscribe for or purchase any of the foregoing, with a fair value (as
determined in good faith by the Company's Board of Directors) per Common Share
that, when combined with the aggregate amount per Common Share paid in respect
of all other such distributions to all or substantially all holders of its
Common Shares within such calendar year, exceeds (1) for calendar year 2003, the
Initial Dividend (as defined below) or (2) for any subsequent calendar year, an
amount equal to the Initial Dividend increased at a rate of 10% per annum from
January 1, 2003, compounded annually on December 31 of each year commencing in
2003 (such excess of the Current Distribution being herein referred to as the
"Excess Distribution Amount"), the per share RenRe Option Price in effect
immediately prior to the close of business on the date fixed for such payment
shall be reduced by the Excess Distribution Amount, such reduction to become
effective immediately prior to the opening of business on the day following the
date fixed for such payment. The "Initial Dividend" means the distributions
described in items (i) and (ii) above per Common Share paid by the Company to
all or substantially all holders of its Common Shares during the 2003 calendar
year as determined by the Company's Board of Directors, up to a maximum of $0.44
per Common Share.

      (f) Whenever the number of Common Shares purchasable by RenRe upon the
exercise of the RenRe Option is adjusted, as herein provided, the RenRe Option
Price shall be adjusted by multiplying the RenRe Option Price immediately prior
to such adjustment by a fraction, of which the numerator shall be the number
of RenRe Option Shares purchasable upon the exercise of the RenRe Option
immediately prior to such adjustment, and of which the denominator shall be the
number of RenRe Option Shares purchasable immediately thereafter.

      (g) No adjustment in the number of RenRe Option Shares purchasable upon
the exercise of the RenRe Option need be made under Section 3(b) and (c) if the
Company issues or distributes, pursuant to this Agreement, to RenRe the shares,
rights, options, warrants, securities or assets referred to in those paragraphs
which RenRe would have been entitled to receive had the RenRe Option been
exercised prior to the happening of such event or the record date with respect
thereto. No adjustment need be made for a change in the par value of the RenRe
Option Shares.

      (h) For the purpose of this Section 3, the term "Common Shares" shall mean
(i) the class of stock consisting of the Common Shares of the Company, or (ii)
any other class of stock


                                       5
<PAGE>

resulting from successive changes or reclassification of such shares other than
consisting solely of changes in par value. In the event that at any time, as a
result of an adjustment made pursuant to Section 3(a) above, RenRe will become
entitled to receive any securities of the Company other than Common Shares,
thereafter the number of such other securities so receivable upon exercise of
the RenRe Option and the RenRe Option Price of such securities will be subject
to adjustment from time to time in a manner and on terms as nearly equivalent as
practicable to the provisions with respect to the RenRe Option Shares contained
in paragraphs (a) through (f), inclusive, above; provided, however, that the
RenRe Option Price will at no time be less than the aggregate par value of the
Common Shares or other securities of the Company obtainable upon exercise of the
RenRe Option.

      (i) In the case of Section 3(b), upon the expiration of any rights,
options or warrants or if any thereof shall not have been exercised, the RenRe
Option Price and the number of Common Shares purchasable upon the exercise of
the RenRe Option shall, upon such expiration, be readjusted and shall thereafter
be such as they would have been had they been originally adjusted (or had the
original adjustment not been required, as the case may be) as if (A) the only
Common Shares so issued were the Common Shares, if any, actually issued or sold
upon the exercise of such rights, options or warrants and (B) such Common
Shares, if any, were issued or sold for the consideration actually received by
the Company upon such exercise plus the aggregate consideration, if any,
actually received by the Company for the issuance, sale or grant of all such
rights, options or warrants whether or not exercised; provided, further, that no
such readjustment may have the effect of increasing RenRe Option Price or
decreasing the number of Common Shares purchasable upon the exercise of the
RenRe Option by an amount in excess of the amount of the adjustment initially
made in respect to the issuance, sale or grant or such rights, options or
warrants.

      (j) In the case of Section 3(b), on any change in the number of Common
Shares deliverable upon exercise of any such rights, options or warrants, other
than a change resulting from the antidilution provisions hereof, the number of
RenRe Option Shares thereafter purchasable upon the exercise of the RenRe Option
shall forthwith be readjusted to such number as would have been obtained had the
adjustment made upon the issuance of such rights, options or warrants not
converted prior to such change (or rights, options or warrants related to such
securities not converted prior to such change) been made upon the basis of such
change.

      (k) The Company may at its option, at any time during the term of the
RenRe Option, reduce the then current RenRe Option Price to any amount and for
any period of time deemed appropriate by the Board of Directors of the Company,
including such reductions in the exercise price as the Company considers to be
advisable in order that any event treated for Federal income tax purposes as a
dividend of stock or stock rights shall not be taxable to the recipients.

4. The Company undertakes to use commercially reasonable efforts to increase its
authorized share capital prior to the dates upon which the RenRe Option shall
become exercisable to a level sufficient to satisfy any exercise of the RenRe
Option.

5. (a) For so long as the RenRe Option is exercisable hereunder, each party
hereto shall (i) use its commercially reasonable efforts to obtain all
authorizations, consents, orders and approvals of all governmental authorities
and officials that may be or become necessary for the


                                       6
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performance of its obligations pursuant to this Agreement and (ii) cooperate
reasonably with the other party in promptly seeking to obtain all such
authorizations, consents, orders and approvals. The parties hereto agree to
cooperate reasonably, complete and file any joint applications for any
authorizations from any governmental authorities reasonably necessary or
desirable to effectuate the transactions contemplated by this Agreement. The
parties hereto agree that they will keep each other apprised of the status of
matters relating to the exercise of the RenRe Option, including reasonably
promptly furnishing the other with copies of notices or other communications
received by the Company or RenRe, from all third parties and governmental
authorities with respect to the RenRe Option.

      (b) For so long as the RenRe Option is exercisable, the Company and RenRe
agree to reasonably promptly prepare and file, if necessary, any filing under
the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended (the "HSR
Act") with the Federal Trade Commission (the "FTC") and the Antitrust Division
of the Department of Justice (the "DOJ") in order to enable RenRe to exercise
such RenRe Option pursuant to this Agreement. Each party hereby covenants to
cooperate reasonably with the other such party to the extent reasonably
necessary to assist in making reasonable supplemental presentations to the FTC
or the DOJ, and, if requested by the FTC or the DOJ, to reasonably promptly
amend or furnish additional information thereunder.

      (c) Any reasonable out-of-pocket costs and expenses arising in connection
with actions taken pursuant to this Section 5 shall be borne by RenRe.

6. (a) The RenRe Option and the RenRe Option Shares may not be assigned or
otherwise transferred, disposed of or encumbered by RenRe (or any subsequent
transferee) in whole or in part except as provided in this Section 6.
Notwithstanding anything to the contrary in this Agreement, RenRe may, at any
time, assign or otherwise transfer, dispose or encumber the RenRe Option or the
RenRe Option Shares in whole or in part to any direct or indirect wholly owned
subsidiary of RenRe, provided that such transferee shall enter into an option
agreement with the Company that is substantially identical to this Agreement.

      (b) In the event of a merger of RenRe into another person, or a sale,
transfer or lease to another person of all or substantially all the assets of
RenRe, the RenRe Option or the RenRe Option Shares may be transferred as part of
such transaction to the other party to such transaction.

      (c) On and after the date which is the second anniversary of the closing
date of the Public Offering, RenRe may transfer the RenRe Option or the RenRe
Option Shares, in whole or in part, in one or more private transaction(s) to up
to three institutional accredited investors; provided, however, that any
proposed transfer is conditioned upon

            (i) receipt by the Company of evidence satisfactory to it, which may
      include an opinion of United States counsel that such transfer would not
      require registration under the Securities Act or state securities laws and
      upon the obtainment of any required government approvals (which approvals
      the Company agrees to use commercially reasonable efforts to assist in
      obtaining); and


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            (ii) the proposed transferee executing and delivering instruments
      reasonably acceptable to the Company acknowledging

                  (A) that the RenRe Option and the RenRe Option Shares have not
            been registered under the Securities Act and, accordingly, the
            transferee may not offer, sell, assign, pledge or otherwise transfer
            the RenRe Option or any RenRe Option Shares except pursuant to an
            effective registration statement under the Securities Act covering
            such RenRe Option Shares or pursuant to an available exemption from
            the registration requirements of the Securities Act and in
            compliance with all applicable state securities laws;

                  (B) that the Company is entitled to decline to register any
            transfer (as defined in the Company's bye-laws) of RenRe Option
            Shares, and any transfer of RenRe Option and RenRe Option Shares
            shall be void, unless (i) such transfer is made pursuant to and in
            accordance with Rule 144 (provided that the Company (or its
            designated agent for such purpose) may request a certificate
            satisfactory to it of compliance by the transferor with the
            requirements of Rule 144), (ii) such transfer is made pursuant to
            another available exemption from the registration requirements of
            the Securities Act (provided that, if not already a party hereto,
            the intended transferee agrees to abide by the provisions of this
            Section 6(c)(ii), and provided, further, that, if the Company
            requests, the transferor first provides the Company (or such agent)
            with evidence satisfactory to it, which may include an opinion of
            U.S. counsel satisfactory to the Company, to the effect that such
            transfer is made pursuant to another available exemption from the
            registration requirements of the Securities Act), (iii) such
            transfer is made pursuant to an effective registration statement
            under the Securities Act covering the RenRe Option Shares being
            transferred, including a registration statement filed pursuant to
            the Standstill Agreement and in all cases pursuant to this clause
            (B) such transfer is in compliance with all applicable state
            securities laws (the Company being entitled to waive or modify the
            foregoing transfer requirements, generally or in any particular
            case, to the extent that it determines, on advice of U.S. counsel,
            that compliance with such requirements is not necessary to ensure
            compliance with the Securities Act or any applicable state
            securities laws, or such modification is necessary to ensure
            compliance with the Securities Act or any applicable state
            securities laws, as the case may be) and (iv) such transferee agrees
            to be bound by the provisions of this Agreement;

                  (C) that, except as provided below, no RenRe Option Share
            shall be held in book-entry form, and each certificate representing
            a RenRe Option Share shall be evidenced by a certificate bearing a
            restrictive legend (the "Legend") substantially in the form set
            forth below:

            THE COMMON SHARES EVIDENCED HEREBY HAVE NOT BEEN REGISTERED UNDER
            THE U.S. SECURITIES ACT OF 1933 (THE "SECURITIES ACT") AND MAY NOT
            BE OFFERED, SOLD, ASSIGNED, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT
            PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES


                                       8
<PAGE>

            ACT OR AN AVAILABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF
            THE SECURITIES ACT AND COMPLIANCE WITH APPLICABLE STATE SECURITIES
            LAWS. SUCH SHARES MAY NOT BE HELD IN BOOK-ENTRY FORM. SUCH SHARES
            ARE ALSO SUBJECT TO RESTRICTIONS ON TRANSFER (AS DEFINED IN THE BYE-
            LAWS OF THE COMPANY) SET FORTH IN THE TRANSFER RESTRICTIONS,
            REGISTRATION RIGHTS AND STANDSTILL AGREEMENT, DATED AS OF SEPTEMBER
            __, 2002, BETWEEN RENAISSANCERE HOLDINGS LTD. AND PLATINUM
            UNDERWRITERS HOLDINGS, LTD. (THE "COMPANY"), WHICH MAY REQUIRE,
            AMONG OTHER THINGS, THE PRIOR RECEIPT BY THE COMPANY FROM THE
            TRANSFEROR OR THE TRANSFEREE OF EVIDENCE SATISFACTORY TO IT, WHICH
            MAY INCLUDE AN OPINION OF U.S. COUNSEL OR UNDERTAKINGS TO BE BOUND
            BY SUCH AGREEMENT. SUCH SHARES ARE ALSO SUBJECT TO RESTRICTIONS IN
            THE BYE-LAWS OF THE COMPANY, INCLUDING RESTRICTIONS ON TRANSFER AND
            VOTING INTENDED TO ENSURE THAT NO PERSON BECOMES OR IS DEEMED TO
            BECOME A 10% SHAREHOLDER OF THE COMPANY (AS EXPLAINED IN SUCH
            BYE-LAWS).

                  (D) that the transferee shall become a party to the Transfer
            Restrictions, Registration Rights and Standstill Agreement, with the
            attendant rights and obligations thereunder; provided, further, that
            any proposed transfer may be disapproved by the Board of Directors
            of the Company if, in their reasonable judgment, they have reason to
            believe that such transfer may expose the Company, any subsidiary
            thereof, any shareholder or any person ceding insurance to the
            Company or any such subsidiary to adverse tax or regulatory
            treatment in any jurisdiction. In connection with or following any
            transfer of RenRe Option Shares in accordance with clause (i) or
            (iii) of Section 6(c)(ii)(B) (except in the case of a transfer of
            RenRe Option Shares to an "affiliate" of RenRe, as such term is
            defined in the Securities Act, in accordance with clause (i) of
            Section 6(c)(ii)(B)), and upon the surrender of any certificate or
            certificates representing such RenRe Option Shares to the Company
            (or such agent), the Company shall cause to be issued in exchange
            therefor a new certificate or certificates that represent the same
            Common Shares and do not bear the Legend (or shall permit such
            shares to be held in book-entry form). The Company shall use
            commercially reasonable efforts to cause each RenRe Option Share
            transferred as contemplated by clause (i) or (iii) of Section
            6(c)(ii)(B) to be duly listed on each securities exchange, and to be
            accepted for quotation in each interdealer quotation system, on or
            in which any Common Shares are listed or quoted at the time of such
            transfer (provided that the approval for such listing or quotation
            has been obtained by the Company), in each case so that the RenRe
            Option Share so transferred will be freely transferable on each such
            exchange and in each such system to the same extent as the Common
            Shares then listed thereon or quoted therein; and

                  (E) such transferee shall not become a "10% Shareholder" (as
            defined in Section 6(d) below) immediately after such transfer
            (assuming for purposes of


                                       9
<PAGE>

            this determination that the RenRe Option Shares were actually owned
            by the transferee); and

            (iii) such transfer not resulting, directly or indirectly, in a
      transfer to any Specified Person (as defined below) of more than 9.9% of
      the Common Shares outstanding at the time of such transfer, or the right
      to acquire pursuant to the RenRe Option more than 9.9% of the Common
      Shares outstanding at the time of such transfer, except in the following
      circumstances: (A) in connection with any tender offer or exchange offer
      made to all holders of outstanding Common Shares; (B) to any Wholly Owned
      Subsidiary (as defined in the Standstill Agreement) of RenRe provided that
      such Wholly Owned Subsidiary agrees in writing with the Company to the
      same transfer restrictions as are contained in this Section 6(c); or (C) a
      transfer by operation of law upon consummation of a merger or
      consolidation of RenRe into another Person (as defined in the Investment
      Agreement). For purposes of this Section 6(c)(iii), "Specified Person"
      means any Person that generates 50% or more of its gross revenue in its
      most recent fiscal year for which financial statements are available by
      writing property or casualty insurance or reinsurance.

      (d) In connection with any transfer of all or a portion of the RenRe
Option pursuant to Section 6(c), the Company shall prepare an option agreement
substantially identical to this Agreement (or, in the case of a partial
transfer, option agreements) issuable to the transferee (and transferor, in the
case of partial transfer) upon surrender to the Company of the existing option
agreement upon consummation of the transfer. Upon said consummation, the
transferee shall have such rights and obligations with respect to the number of
RenRe Option Shares covered by the portion of the RenRe Option transferred to
such transferee as the rights and obligations of RenRe hereunder. As used
herein, "10% Shareholder" means a person who owns, in aggregate, (i) directly,
(ii) with respect to persons who are United States persons, by application of
the attribution and constructive ownership rules of Sections 958(a) and 958(b)
of the Code or (iii) beneficially, directly or indirectly, within the meaning of
Section 13(d)(3) of the United States Securities Exchange Act of 1934, issued
shares of the Company carrying 10% or more of the total combined voting rights
attaching to all issued shares.

      (e) Any transferee of all or part of the RenRe Option pursuant to Section
6(c) hereof (or any subsequent transferee who holds any portion of the RenRe
Option as a result of a transfer pursuant to this Section 6(e)) may transfer, in
whole but not in part, its portion of the RenRe Option to a subsequent
transferee; provided that any such transfer shall be subject to the terms and
conditions set forth in Sections 6(c) and 6(d) hereof.

7. The issuance of share certificates upon the exercise of the RenRe Option
shall be without charge to RenRe. The Company shall pay, and indemnify RenRe
from and against, any issuance, stamp, documentary or other taxes (other than
transfer taxes and income taxes), or charges imposed by any governmental body,
agency or official by reason of the exercise of the RenRe Option or the
resulting issuance of Common Shares.

8. This Agreement may not be amended except in a written instrument signed by
the Company and RenRe.


                                       10
<PAGE>

9. All notices, requests, claims, demands and other communications hereunder
shall be in writing and shall be deemed to have been duly given if delivered by
hand (with receipt confirmed), or by certified mail, postage prepaid and return
receipt requested, or by facsimile addressed as follows (or to such other
address as a party may designate by written notice to the others) and shall be
deemed given on the date on which such notice is received:

                If to RenRe:

                RenaissanceRe Holdings Ltd.
                Renaissance House
                8-12 East Broadway
                Pembroke HM19 Bermuda
                Attention: Stephen H. Weinstein, General Counsel
                Facsimile: (441) 296-5037

                with a copy to:

                John S. D'Alimonte
                Wilikie Farr & Gallagher
                787 Seventh Avenue
                New York, New York 10019
                Facsimile: (212) 728-8111

                If to the Company:

                Platinum Underwriters Holdings, Ltd.
                Clarendon House
                2 Church Street
                Hamilton HM11
                Bermuda
                Attention: General Counsel
                Facsimile: (441) 292-4720

                with a copy to:

                Linda E. Ransom
                Dewey Ballantine LLP
                1301 Avenue of the  Americas
                New York, New York 10019
                Facsimile: (212) 259-6333

10. This Agreement, the Standstill Agreement, the Services Agreement, the
Confidentiality Agreement (which Confidentiality Agreement shall terminate as of
Closing) and the Investment Agreement constitute the entire agreement between
the parties hereto with respect to the subject matter hereof and supersede all
prior agreements and understandings, oral and written, between the parties
hereto with respect to the subject matter hereof.


                                       11
<PAGE>

11. This Agreement shall inure to the benefit of and be binding upon the parties
hereto, and their respective successors and permitted assigns. Nothing in this
Agreement, expressed or implied, is intended to confer on any person other than
the parties hereto, and their respective successors and permitted assigns, any
rights, remedies, obligations or liabilities under or by reason of this
Agreement.

12. This Agreement may not be assigned by any party hereto, except to a party to
whom RenRe transfers the RenRe Option or RenRe Option Shares in accordance with
Section 6 of this Agreement or Section 2 of the Standstill Agreement, and then
only in accordance with those sections.

13. The headings contained in this Agreement are for convenience only and do not
affect the meaning or interpretation of this Agreement.

14. (a) This Agreement shall be governed by, and construed in accordance with,
the law of the State of New York (without regard to principles of conflict of
laws).

      (b) The parties hereto shall promptly submit any dispute, claim, or
controversy arising out of or relating to this Agreement, including effect,
validity, breach, interpretation, performance, or enforcement (collectively, a
"Dispute") to binding arbitration in New York, New York at the offices of
Judicial Arbitration and Mediation Services, Inc. ("JAMS") before an arbitrator
(the "Arbitrator") in accordance with JAMS' Comprehensive Arbitration Rules and
Procedures and the Federal Arbitration Act, 9 U.S.C. Sections 1 et seq. The
Arbitrator shall be a former judge selected from JAMS' pool of neutrals. The
parties agree that, except as otherwise provided herein respecting temporary or
preliminary injunctive relief, binding arbitration shall be the sole means of
resolving any Dispute. Judgment on any award of the Arbitrators may be entered
by any court of competent jurisdiction.

      (c) The costs of the arbitration proceeding and any proceeding in court to
confirm or to vacate any arbitration award or to obtain temporary or preliminary
injunctive relief as provided in paragraph (d) below, as applicable (including,
without limitation, actual attorneys' fees and costs), shall be borne by the
unsuccessful party and shall be awarded as part of the Arbitrator's decision,
unless the Arbitrator shall otherwise allocate such costs in such decision.

      (d) This Section 14 shall not prevent the parties hereto from seeking or
obtaining temporary or preliminary injunctive relieve in a court for any breach
or threatened breach of any provision hereof pending the hearing before and
determination of the Arbitrator. The parties hereby agree that they shall
continue to perform their obligations under this Agreement pending the hearing
before and determination of the Arbitrator, it being agreed and understood that
the failure to so provide will cause irreparable harm to the other party hereto
and that the putative breaching party has assumed all of the commercial risks
associated with such breach or threatened breach of any provision hereof by such
party.

      (e) The parties agree that the State and Federal courts in The City of New
York shall have jurisdiction for purposes of enforcement of their agreement to
submit Disputes to arbitration and of any award of the Arbitrator.


                                       12
<PAGE>

15. Capitalized terms used but not defined in this Agreement have the meanings
specified in the Investment Agreement.

16. This Agreement becomes effective contingent upon the consummation of the
Public Offering automatically and with no action on the part of any person.


                                       13
<PAGE>

            IN WITNESS WHEREOF, the parties have caused this Agreement to be
signed and attested by its duly authorized officers and to be dated as of
November 1, 2002.

                                         PLATINUM UNDERWRITERS HOLDINGS, LTD.


                                         By: /s/ Jerome T. Fadden
                                            ------------------------------------
                                            Name   Jerome T. Fadden
                                            Title  President & CEO


                                         RENAISSANCERE HOLDINGS LTD.

                                         By: /s/ John M. Lummis
                                            ------------------------------------
                                            Name   John M. Lummis
                                            Title  Executive Vice President and
                                                   Chief Financial Officer


                                                          RenRe Option Agreement