Document:

EX-10.2

AMENDED AND RESTATED OPTION AGREEMENT

This AMENDED AND RESTATED OPTION AGREEMENT (this “Agreement”), dated as of January 10, 2005,
amends and restates the OPTION AGREEMENT, dated November 1, 2002 (the “Option Agreement”), between
(i) PLATINUM UNDERWRITERS HOLDINGS, LTD., a company organized under the laws of the Islands of
Bermuda (the “Company”), (ii) ST. PAUL REINSURANCE COMPANY LIMITED (the “Optionee”), a company
organized under the laws of England and Wales and a wholly owned subsidiary of THE ST. PAUL
TRAVELERS COMPANIES, INC., a company incorporated under the laws of the State of Minnesota in the
United States of America and formerly known as The St. Paul Companies, Inc. (“St. Paul Travelers”),
and (iii) ST. PAUL TRAVELERS.

RECITALS:

WHEREAS, the Company completed an initial public offering (the “Public Offering”) of its
common shares, par value U.S.$0.01 per share (the “Common Shares”), on November 1, 2002;

WHEREAS, St. Paul Travelers and the Company entered into a Formation and Separation Agreement,
dated as of October 28, 2002 (the “Formation and Separation Agreement”), pursuant to which St. Paul
Travelers agreed to purchase from the Company that number of Common Shares determined as set forth
in the Formation and Separation Agreement;

WHEREAS, pursuant to the Formation and Separation Agreement, the Company, the Optionee and St.
Paul Travelers entered into the Option Agreement pursuant to which the Company granted to the
Optionee, in respect of St. Paul Travelers’ initial investment in the Company, an option (the
“Original Option”) to purchase up to 894,260 Common Shares following the completion of the Public
Offering at an exercise price of $27.00, which equals 120 percent of the Public Offering price per
Common Share;

WHEREAS, the parties hereto desire that the Original Option be amended to provide that any
exercise thereof shall be on a net share settlement basis with payment by the Optionee to the
Company of cash consideration per Common Share issued upon such exercise of the then par value of
such Common Share; and

WHEREAS, the Company has determined that the Company will benefit from a reduction in the
overhang on the market which arises from the Original Option, the Company has no need of the
capital represented by the aggregate Original Option Price, and it is in the best interests of the
Company to amend the Original Option in accordance with the desires of the parties hereto.

NOW, THEREFORE, in consideration of the mutual promises, covenants and agreements set forth
herein and for other good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, the parties hereto hereby agree that the Option Agreement shall be amended and
restated in its entirety as follows:

1

THE OPTION (AS DEFINED BELOW) HAS NOT BEEN REGISTERED UNDER THE U.S. SECURITIES ACT OF 1933.
NEITHER THE 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 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 OPTION ARE SUBJECT TO SUBSTANTIAL RESTRICTIONS ON TRANSFER AS SET FORTH IN SECTION 6 OF THIS
AGREEMENT.

1. (a) The Company grants the Optionee an option (the “Option”) to purchase up to 894,260 Common
Shares (the “Option Shares”) in accordance with the terms of this Agreement.

(b) The Option is exercisable, in whole or in part at any time prior to November 1, 2012 (the
“Exercise Period”), at an exercise price per Common Share (the “Exercise Price”) equal to $27.00
less the then par value of such Common Share, as such Exercise Price is adjusted from time to time
pursuant hereto, which Exercise Price shall be paid by reducing the number of Common Shares
obtainable upon exercise of the Option as provided in Section 1(d) hereof. As additional
consideration, in connection with any exercise of the Option, the Optionee must pay the applicable
Cash Consideration to the Company in accordance with Section 2 below.

(c) The Option may be exercised on any day during the 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”). The 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) Upon any exercise of the Option, the Exercise Price shall be paid by reducing the number
of Option Shares obtainable upon such exercise so as to yield a number of Option Shares issuable
upon such exercise equal to the product of (x) the number of Option Shares issuable as of the
Notice Date (if payment of the Exercise Price were being made in cash) and (y) the Exchange Ratio.
For purposes hereof, (i) “Exchange Ratio” means a fraction, the numerator of which is the excess of
the Market Price per Common Share over the Exercise Price per share as of the Notice Date and the
denominator of which is the Market Price per Common Share; (ii) “Market Price” means the average of
the daily Closing Price per Common Share for each of the five consecutive Trading Days ending on
the Notice Date (the “Pre-Notice Average”) plus the average of the daily Closing Price per Common
Share for each of the five consecutive Trading Days immediately following the Notice Date (the
“Post-Notice Average”) divided by two; provided, however, that the Post-Notice
Average shall not exceed the Pre-Notice Average multiplied by 1.025 nor be less than the Pre-Notice
Average multiplied by 0.975; (iii) “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; (iv) “Closing Price” means the reported
last sale price regular way or, in case no such reported sale 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;
and (v) “Notice Date” means the date upon which the Company receives written notice (which shall be
signed on behalf of the Optionee and delivered or sent to the Company in accordance with Section 9
hereof) from the Optionee of the Optionee’s exercise of the Option, provided that the Company shall
receive such notice no later than 11:59 pm Bermuda time on such date.

(e) No fractional Common Share shall be issued upon any exercise of the Option. In lieu of a
fractional Common Share, the Optionee shall be entitled to receive cash for the value of the
fractional Common Share, which cash payment shall be equal to the product of (i) the fraction
represented by the fractional Common Share that would have been issued absent this Section 1(e) and
(ii) the Market Price.

(f) In connection with any exercise of the Option, the Market Price, the Exercise Price, and
the number of Option Shares to be issued (after giving effect to the payment of the Exercise Price
as provided in Section 1(d) hereof) will be determined by the Company within three Business Days
after the last Trading Day included in the Post-Notice Average (the “Determination Date”).

(g) Notwithstanding anything to the contrary in this Agreement, St. Paul Travelers’ beneficial
ownership interest in the Common Shares may not at any time and under any circumstances be equal to
or exceed that percentage of the Common Shares outstanding that would cause St. Paul Travelers to
be a “United States 25% Shareholder” as defined in the Company’s bye-laws as in effect as of the
completion of the Public Offering. It is agreed and understood that, prior to any exercise of the
Option, St. Paul Travelers shall, if necessary, dispose (or cause the Optionee to dispose, as
applicable) of such number of Common Shares so that, immediately after any exercise of the Option,
St. Paul Travelers will not be a “United States 25% Shareholder.”

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

(i) Neither the Optionee nor St. Paul Travelers is, solely by virtue hereof, entitled to any
rights of a shareholder in the Company either at law or in equity.

(j) 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 Option shall entitle
the Optionee, upon exercise thereof and payment by the Optionee of the Cash Consideration, to
receive all Transaction Consideration that the Optionee would have been entitled to if it had
exercised the Option in full immediately prior to the Transaction (without regard to the
limitations in Section 1(g) hereof). In determining the kind and amount of Transaction
Consideration that the Optionee would be entitled to receive in respect of any Transaction pursuant
to this Section 1(j), the Optionee 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(j) 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 the Optionee shall be entitled to receive Transaction Consideration upon the terms and
conditions provided in this Section 1(j). Notwithstanding the foregoing, if an adjustment is made
pursuant to this Section 1(j) in respect of a Transaction that involves a Change of Control (as
defined below), the Optionee shall be entitled to exercise the Option pursuant to this Section 1(j)
without regard to Section 1(g) 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 Option in accordance with Section 1 hereof, the Optionee shall provide
written notice to the Company of its intention to exercise all or a portion of the Option. Such
notice must indicate the number of Option Shares the Optionee intends to purchase upon exercise of
the Option (prior to giving effect to the payment of the Exercise Price pursuant to Section 1(d)
hereof).

(b) On the Determination Date, the Company shall deliver written notice to the Optionee of the
number of Option Shares to which the Optionee is entitled as a result of the exercise of the
Option. Upon payment by the Optionee to the Company of the Cash Consideration (which may be made
by check, cash or wire transfer), the Company shall promptly (but in no event later than the third
Business Day after receipt of such payment from the Optionee) deliver to the Optionee the Option
Shares, and shall pay to the Optionee the cash in lieu of any fractional Common Share, which may be
paid by check, cash or wire transfer. The “Cash Consideration” means an amount equal to the
product of (i) the number of Option Shares to which the Optionee is entitled as a result of the
exercise of the Option (after giving effect to the payment of the Exercise Price pursuant to
Section 1(d) hereof) and (ii) the then per share par value of a Common Share. Any increase in the
par value of the Common Shares from $0.01 per Common Share which would have the effect of
increasing the Cash Consideration, other than in the case of any of the actions described in
Section 3(a)(B) and 3(a)(C) hereof which includes a proportionate adjustment in the par value,
shall be subject to the prior written consent of the Optionee.

(c) Notwithstanding anything to the contrary in this Agreement, the 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:

(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

(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 Option Shares issuable upon exercise of the Option shall be proportionately
adjusted so that the Optionee 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 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 Section 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 Common 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 Option Shares that the Optionee may purchase thereafter upon the
exercise of the Option (prior to giving effect to the payment of the Exercise Price pursuant to
Section 1(d) hereof) will be determined by multiplying the number of Option Shares theretofore
purchasable upon exercise of the 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 Common Share 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 Option will upon such
distribution be deemed to be an option to acquire the kind and number of shares of the capital
stock of the Subsidiary which the Optionee would have been entitled to receive after such
distribution had the Option been exercised immediately prior to such distribution or any record
date with respect thereto. The roll-over of the Option into an option to acquire 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 daily Closing Price per Common Share
for each of the ten consecutive Trading Days ending on the day before the applicable record date.

(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) through 3(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
Exercise 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 the Optionee upon the exercise of the
Option is adjusted, as herein provided, the Exercise Price shall be adjusted by multiplying the
Exercise Price immediately prior to such adjustment by a fraction, of which the numerator shall be
the number of Option Shares purchasable upon the exercise of the Option immediately prior to such
adjustment, and of which the denominator shall be the number of Option Shares purchasable
immediately thereafter (in each case, prior to giving effect to the payment of the Exercise Price
pursuant to Section 1(d) hereof).

(g) No adjustment in the number of Option Shares issuable upon the exercise of the Option need
be made under Section 3(b) and (c) if the Company issues or distributes, pursuant to this
Agreement, to the Optionee the shares, rights, options, warrants, securities or assets referred to
in those Sections which the Optionee would have been entitled to receive had the Option been
exercised prior to the happening of such event or the record date with respect thereto. Other than
for adjustments in the Cash Consideration (which are subject to Section 2(b) hereof), no adjustment
need be made for a change in the par value of the 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 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, the Optionee 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
Option and the Exercise 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
Option Shares contained in Sections 3(a) through 3(f), inclusive, above; provided,
however, that the Exercise 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 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 Exercise Price and the number of Common Shares
purchasable upon the exercise of the 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 the Exercise Price or decreasing the number of Common Shares purchasable upon
the exercise of the Option by an amount in excess of the amount of the adjustment initially made in
respect of 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 Option Shares thereafter purchasable 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 Option, reduce the then
current Exercise 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 (if necessary) its
authorized share capital to a level sufficient to satisfy any exercise of the Option.

5. (a) For so long as the 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 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 Option, including
reasonably promptly furnishing the other with copies of notices or other communications received by
the Company or the Optionee, from all third parties and governmental authorities with respect to
the Option.

(b) For so long as the Option is exercisable, the Company and the Optionee 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 the Optionee
to exercise such 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 St. Paul Travelers.

6. (a) The Option and the Option Shares may not be assigned or otherwise transferred, disposed of
or encumbered by the Optionee (or any subsequent transferee) in whole or in part except as provided
in this Section 6. Notwithstanding anything to the contrary in this Agreement, the Optionee may,
at any time, assign or otherwise transfer, dispose or encumber the Option or the Option Shares in
whole or in part to St. Paul Travelers or any direct or indirect wholly owned subsidiary thereof,
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 the Optionee into another person, or a sale, transfer or lease
to another person of all or substantially all the assets of the Optionee, the Option or the Option
Shares may be transferred as part of such transaction to the other party to such transaction.

(c) On and after January 10, 2005, the Optionee may transfer the Option or the 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

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

(A) that the transferee may not offer, sell, assign, pledge or otherwise
transfer the Option or any Option Shares except pursuant to an effective
registration statement under the Securities Act of 1933, as amended (the “Securities
Act”), covering such 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 Option Shares, and any transfer of Option and
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 Option Shares
being transferred, including a registration statement filed pursuant to the
Registrations Rights Agreement dated November 1, 2002 between the Company and St.
Paul Travelers (the “Registration Rights 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 Option Share shall be held in book-entry
form, and each certificate representing a 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 MAY NOT BE OFFERED, SOLD, ASSIGNED, PLEDGED OR
OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER
THE U.S. SECURITIES ACT OF 1933 (THE “SECURITIES 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 AMENDED AND RESTATED OPTION AGREEMENTS, EACH DATED
AS OF JANUARY 10, 2005, AMONG THE ST. PAUL TRAVELERS COMPANIES, INC., CERTAIN WHOLLY
OWNED SUBSIDIARIES THEREOF 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 AGREEMENTS. 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 Registration Rights
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 Option Shares in accordance with clause (i) or (iii) of
Section 6(c)(ii)(B) (except in the case of a transfer of Option Shares to an
“affiliate” of the Company, 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 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 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 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 below in
this Section 6(c)) immediately after such transfer (assuming for purposes of this
determination that the 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 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 Post-Closing Subsidiary of St. Paul Travelers (as
defined in the Formation and Separation Agreement) provided that such 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 St. Paul Travelers into another Person (as defined in the Formation and
Separation 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.

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.

(d) In connection with any proposed transfer of all or a portion of the Option pursuant to
Section 6(c), the Company shall prepare an option agreement (or, in the case of a partial transfer,
option agreements) substantially identical to this Agreement with the transferee (and transferor,
in the case of partial transfer) upon surrender to the Company of the existing option agreement
prior to the consummation of the transfer. Upon the execution of such option agreement by the
transferee and the Company and the consummation of the transfer, the transferee shall have such
rights and obligations with respect to the number of Option Shares covered by the portion of the
Option transferred to such transferee as the rights and obligations of the Optionee to such portion
hereunder.

(e) Any transferee of all or part of the Option pursuant to Section 6(c) hereof (or any
subsequent transferee who holds any portion of the Option as a result of a transfer pursuant to
this Section 6(e)) may transfer, in whole but not in part, the 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 Option shall be without charge to
the Optionee. The Company shall pay, and indemnify the Optionee 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 Option or the
resulting issuance of Option Shares.

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

9. All notices, requests, claims, demands and other communications hereunder shall be in writing
and shall be given by facsimile and by e-mail transmission 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 the Optionee:

The St. Paul Travelers Companies, Inc.

385 Washington Street

St. Paul, Minnesota 55102

Attention: General Counsel

Facsimile: (651) 310-5853

E-mail: kspence@spt.com

with a copy to:

Donald R. Crawshaw

Sullivan & Cromwell

125 Broad Street

New York, New York 10004

Facsimile: (212) 558-3588

E-mail: crawshawd@sullcrom.com

If to the Company:

Platinum Underwriters Holdings, Ltd.

The Belvedere Building

69 Pitts Bay Road

Pembroke HM08

Bermuda

Attention: Michael E. Lombardozzi

Executive Vice President, General Counsel

and Secretary

Facsimile: (441) 292-4720

E-mail: mlombardozzi@platinumre.com

with a copy to:

Linda E. Ransom

Dewey Ballantine LLP

1301 Avenue of the Americas

New York, New York 10019

Facsimile: (212) 259-6333

E-mail: lransom@dbllp.com

10. This Agreement, the Formation and Separation Agreement and the Registration Rights Agreement
(which, for the avoidance of doubt, shall apply to any Common Shares issued under this Agreement in
the same manner as to any Common Shares that were issuable under the Option 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. 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. St. Paul Travelers shall, in its capacity as the parent company of the Optionee, cause the
Optionee to comply with the provisions of this Agreement.

13. This Agreement may not be assigned by any party hereto, except to a party to whom the Optionee
transfers the Option or Option Shares in accordance with Section 6 of this Agreement, and then only
in accordance with that section.

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

15. (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. §§ 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
Section 14(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 15 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.

16. Capitalized terms used but not defined in this Agreement have the meanings specified in the
Formation and Separation Agreement.

2

IN WITNESS WHEREOF, each of the parties hereto has caused this AGREEMENT to be duly executed
by a duly authorized officer as of the date and year first above written.

PLATINUM UNDERWRITERS

HOLDINGS, LTD.

By: /s/ Gregory E. A. Morrison

Name: Gregory E.A. Morrison

Title: President and Chief Executive Officer

THE ST. PAUL TRAVELERS COMPANIES, INC.

By: /s/ Samuel Liss

Name: Samuel Liss

Title: Executive Vice President — Business and Development

ST. PAUL REINSURANCE COMPANY LIMITED

By: /s/ Alistair J.S. Gunn

Name: Alistair J. S. Gunn

Title: Director

3EX-10.1

Exhibit 10.1

APPENDIX NO 1

to

LICENCE AGREEMENT NO: 2004-85

between

Endeavour Operating Corporation. ( Licensee )

and

PGS Exploration (UK) Ltd ( PGS )

This is an Appendix (including confirmation of order) to the Agreement referred to above, which is
the PGS Exploration (UK) Ltd General Licence Agreement for Use of PGS Proprietary Data. This
Appendix takes precedence over the Agreement in cases where those differ.

	 	 	 	 	 	 	 
	1.

	 	Survey
	 	:
	 	PGS MC3D Holland MegaSurvey
	 
	 	 	 	 	 	 
	2.

	 	Survey area (sq. km)
	 	:
	 	approx. 30,000 sq. km
	 
	 	 	 	 	 	 
	3.

	 	Location
	 	:
	 	Southern North Sea – Holland
	 
	 	 	 	 	 	 
	4.

	 	Licence commitment
	 	:
	 	15,000 sq. km
	 
	 	 	 	 	 	 
	5.

	 	Licensing price
	 	:
	 	£40 per sq. km

( see Attachment 1 )
	 
	 	 	 	 	 	 
	
 
	 	 	 	 	 	Total licensing price : £600,000
	 
	 	 	 	 	 	 
	6.

	 	Payment schedule
	 	:
	 	45% on signing of Appendix

25% on December 31, 2004 ( or pro rata balance of data

merged at that time )

10% on start of interpretation (Q.1 2005)

10% end April 2005 or completion of 50% of

interpretation of Licensee area in 4) above, whichever

is later.

10% on completion of study and delivery of all products

Final Completion Date & Final Invoicing dependent on

Final Tile request from Endeavour (January 10, 2005 or

deadlines adjusted accordingly).

Payments due 30 days after receipt of invoice
	 
	 	 	 	 	 	 
	7.

	 	Group escalation
	 	:
	 	n/a — single company licence only
	 
	 	 	 	 	 	 
	8.

	 	Licence group
	 	:
	 	n/a – single company licence only
	 
	 	 	 	 	 	 
	9.

	 	Date of commitment
	 	:
	 	23rd December 2004
	 
	 	 	 	 	 	 
	10.

	 	Deliverables available
	 	:
	 	See Attachment 1
	 
	 	 	 	 	 	 
	11.

	 	Any other specific terms
	 	:
	 	See Attachment 1
	 
	 	 	 	 	 	 

1

	 	 	 
	PGS — PGS Exploration (UK) Ltd

	 	LICENSEE – Endeavour International

Corporation
	 
	 	 
	/s/David J. Griffiths

Signature

	 	/s/ Michael D. Cochran

Signature
	 
	 	 
	David J. Griffiths

Print Name

V.P. Contracts & Global Sales

Print Title

1/10/05

Date

	 	Michael D. Cochran

Print Name

EVP — Exploration

Print Title

1/10/5

Date
	 
	 	 

2

Attachment 1 to Appendix no.1

PGS Holland Mega Survey Interpretation Packages

5. Licence Price

With reference to the Deliverables given for the SNS survey as described in Schedule C Licence
Agreement For Use Of North Sea Mega Merge Seismic Data between PGS Exploration (UK) Ltd and NSNV
Inc., dated 16 December 2003.

License to merged MegaSurvey data

License Price includes all Standard Interpretation Delivery Items

License to Horizon Attribute Package (ref. Item 5).

This does not include a licence to the Depth Conversion or ER Mapper Package (price £ 1.50 ea.);
nor cost and shipping of deliverables

10. Deliverables available

The details of the Holland Mega Survey Deliverables are not yet defined, but will include
deliverables similar in form to the Deliverables given for the SNS survey as described in Schedule
C Licence Agreement For Use Of North Sea Mega Merge Seismic Data between PGS Exploration (UK) Ltd
and NSNV Inc., dated 16 December 2003.

This will include:

i). All the Deliverables for the Standard Delivery Items. Details of well data to be advised but
will be similar to that for UK SNS.

The horizons for Holland will be similar to those for UK SNS

ii). The Optional Delivery items, it is anticipated that the Horizon Attribute Package, Depth
Attributes Package and ER Mapper Package will be very similar to SNS UK.

PGS to supply detailed lists of Holland deliverables once these are available.

iii) Merged Data can be supplied in stages as separate tiles as these are merged together on an as
required basis. Similarly, the interpretation can be supplied as whole tiles are completed.

11. Any other Specific Items

i) Uplift on Licensee gaining interest in acreage offshore Holland

	 	 	 	Uplift Payments will apply with respect to PGS Proprietary Data only and at the following standard
rates:

i) Holland

	 	a)	 	Licensee becomes a member of a Bona Fide Group which holds or
acquires an interest in, an exploration or production licence and where the Bona
Fide Group has fully licensed the PGS Proprietary Data relevant to the
geographical area covered by the exploration or production licence.

£ 750 per sq. km ( per company )

	 	b)	 	Licensee becomes a member of a Bona Fide Group which holds or
acquires an interest in an exploration or production licence where the Bona Fide
Group has not fully licensed the PGS Proprietary Data relevant to the
geographical area covered by the exploration or production licence.

£ 3,500 per sq. km ( per group )

	 	c)	 	Licensee acquires an exploration or production licence relevant
to the area covered by the Licensed PGS Proprietary Data.

£ 3,500 sq. km ( per group )

	 	ii)	 	The uplift payments as specified in (i) above shall apply during the first five
(5) years after the Commencement Date, shall reduce to 75% for years six (6) through
ten (10) after the Commencement Date and reduce again to 50% of the rates in (ii) for
years eleven (11) through to fifteen (15). The uplift payments as specified in (ii)
shall cease to apply after fifteen (15) years from the Commencement Date.

	 	2.	 	The reductions to the uplift rates referred to in (ii) above shall cease to apply and the
rates shall return to those set out in (i) above, as applicable in the event that:

	 	(a)	 	there is a change of control of the Licensee (as defined in Article 12) except
in the circumstances described in Article 12.1(iii); or

	 	(b)	 	the Licensee assigns its rights under this Agreement except to an Endeavour
Affiliate as permitted under Article 13.2.

	 	3.	 	Individual Uplift Payments will be paid in cash by Licensee within thirty (30) days of an
invoice from PGS, up to a limit of USD five hundred thousand (USD500,000) per licence area and
subject to a maximum combined total of USD 2 million (USD2,000,000) during the first three (3)
years following the Commencement Date. Payment of the balance of any individual uplift
payment over USD500,000 along with payment of any total amount in excess of USD two million
(USD2,000,000) shall be, deferred. The terms of payment for the deferred amounts shall be
agreed between the Parties, but if the Parties have not agreed in writing on an alternative
method of payment, within two (2) years from the Date of the Appendix, then the deferred
amounts shall be paid in cash to PGS thirty (30) days after two (3) years from the Date of the
Appendix.

ii) Change of Control

For licences involving MegaSurvey data, Clause 12.1(iii) will be applicable.

iii) Data Access to small companies (from Clause 9.3 of original Licence Agreement between PGS
Exploration (UK) Ltd and NSNV Inc dated 16 December 2003 )

Subject to the Licensee having paid any applicable Uplift Payment due under Clause 9.1, a Group
Member with whom the Licensee has entered into a joint venture or other contractual arrangement
providing for joint contractual or equity interests in all or part of any license covered by the
Data shall be entitled to receive from PGS a license to the relevant Data at no additional charge,
where the Group Member complies with the requirements set out in (i) below or, where applicable on
open file or brokerage data, subject to that Group Member having paid an amount to PGS equivalent
to any brokerage payment that PGS may be liable to pay to a third party in respect of granting such
a licence to the Group Member. The licence granted by PGS to Group Member will include data over
the equity licence acreage, plus a reasonable (approximate 2 km) periphery.

	 	(i)	 	where the licence is a Holland licence, such Group Member has not held an
interest in the Southern North Sea (defined as south of 56 deg north of latitude)
except for companies or their Affiliates who do not hold or have not held an interest
in Denmark, Holland or Germany and are qualified as per Clause 9.3 of the Licence
Agreement For Use of North Sea Mega Merge Seismic Data between PGS Exploration (UK) Ltd
and NSNV Inc dated 16 December 2003 for small companies who did not hold more than 2
licenses in the UK prior to UK’s 21st licensing round.

iv) Data Access of rebinned released surveys

At the request of Licensee from time to time, Licensee shall be entitled to receive a copy of Data
from any released surveys which have been rebinned by PGS and may or may not have been merged into
the MegaSurvey prior to delivery of the relevant tile from the MegaSurvey. Such delivery shall be
charged depending on the source of those data (Halliburton PetroBank “Landmark” format = GBP4/km
sq, PGS “Kingdom” format = GBP1/km sq).

v) 2-D / 3-D Post Stack Depth Migration

Licensee is interested in licensing 2-D / 3-D Post Stack Depth Migration data from the Holland
MegaSurvey. PGS has proposed an outline test programme which is under discussion with Licensee with
regard to its scope and pre-funding. Following completion of this test and analysis of the
results, PGS and Licensee will negotiate in good faith for a further work programme of such
migration to be carried out including options for exclusivity for periods of time for Licensee.

The scope of work and price will depend on the results of the test programme

3

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