<PAGE>   1

                                                                   EXHIBIT 10.32

                               EXCHANGE AGREEMENT

     AGREEMENT (this "Agreement") made as of this  -- day of    --   , 2001 by
and among Odyssey Re Holdings Corp. ("Odyssey"), a Delaware corporation, with
its principal executive office at 140 Broadway, 39th Floor, New York, New York,
TIG Insurance Company ("TIG"), a California corporation, with its principal
executive office at 5205 North O'Connor Blvd., Irving, Texas and ORH Holdings
Inc. ("ORH Holdings"), a Delaware corporation, with its principal executive
office at 300 Stamford Place, Stamford, Connecticut (TIG and ORH Holdings
hereinafter are collectively referred to as the "Fairfax Subsidiaries").

     WHEREAS, the Fairfax Subsidiaries are the beneficial owners of all of the
outstanding shares (the "Securities") of common stock of Odyssey America
Reinsurance Corporation ("OARC");

     WHEREAS, based on the representations, warranties and covenants herein
contained, Odyssey wishes to receive and the Fairfax Subsidiaries desire to
transfer the said OARC securities; and

     WHEREAS, Odyssey Holdings, intends to undertake an initial public offering
of its stock as contemplated by the registration statement (No. 333-57642) dated
          , 2001.

     NOW, THEREFORE, in consideration of the mutual promises hereinafter
contained, the parties hereto hereby agree as follows:

1.   EXCHANGE OF THE SECURITIES

     1.1   Subject to the terms and conditions hereof, as soon as practicable
following the execution of the Agreement, Odyssey shall receive from the Fairfax
Subsidiaries, and the Fairfax Subsidiaries shall transfer to Odyssey, all of the
Securities.

     1.2   The aggregate exchange consideration for the Securities shall be (a)
$225 million in cash, (b) one or more term notes (the "Notes"), issued to and
registered in the names of the Fairfax Subsidiaries in the form of Exhibit A
hereto, in aggregate principal amount of $200 million and (c) 48,000,000 shares
(the "Exchange Shares") of common stock of Odyssey (collectively, the "Exchange
Consideration") registered in the names of the Fairfax Subsidiaries.

     1.3   As soon as practicable following the execution of this Agreement,
Fairfax Subsidiaries shall deliver or cause to be delivered to Odyssey:

     (a)   stock certificates evidencing the Securities endorsed in blank, or
           accompanied by stock powers duly executed in blank, in form
           satisfactory to Odyssey (see the form of stock powers attached); and

     (b)   a receipt for the Exchange Consideration.

     1.4   As soon as practicable following the execution of this Agreement,
Odyssey shall deliver to the Fairfax Subsidiaries the Exchange Consideration.

     1.5   The cash, the Notes and the Exchange Shares comprising the Exchange
Consideration shall be allocated between the Fairfax Subsidiaries, and
registered in their respective names, in such manner as they shall request prior
to payment.

2.   REPRESENTATIONS AND WARRANTIES BY THE FAIRFAX SUBSIDIARIES

     The Fairfax Subsidiaries hereby jointly and severally represent and warrant
to Odyssey as follows:

     2.1   Each of TIG and ORH Holdings are corporations which are duly
organized, validly existing and in good standing under the laws of the State of
California and Delaware, respectively, with all necessary power and authority to
enter into and perform their obligations under this Agreement.
<PAGE>   2

     2.2   This Agreement has been duly and validly authorized, executed and
delivered by the Fairfax Subsidiaries and is binding on and enforceable against
the Fairfax Subsidiaries in accordance with its terms.

     2.3   Each Fairfax Subsidiary is the sole and exclusive beneficial owner
and owner of record of all rights, title and interest in and to the Securities
it is delivering pursuant to this Agreement, free and clear of all claims and
encumbrances of any nature whatsoever.

     2.4   The Securities constitute all of the issued and outstanding capital
stock of the OARC.

     2.5   Upon consummation of the transactions contemplated by this Agreement
and registration of the Securities in the name of Odyssey in the stock records
of OARC, Odyssey will own all of the issued and outstanding capital stock of
OARC free and clear of all claims and encumbrances.

     2.6   Upon consummation of the transactions contemplated by this Agreement,
the Securities will be fully paid and nonassessable.

3.   REPRESENTATIONS AND WARRANTIES BY ODYSSEY

     Odyssey represents and warrants to the Fairfax Subsidiaries as follows:

     3.1   Odyssey is a corporation duly organized, validly existing and in good
standing under the laws of the State of Delaware, with all necessary power and
authority to enter into and perform its obligations under this Agreement.

     3.2   This Agreement has been duly and validly authorized, executed and
delivered by Odyssey and is binding on, and enforceable against, Odyssey in
accordance with its terms, subject to applicable bankruptcy laws.

     3.3   Odyssey is receiving and holding the Securities for investment
purposes only and not for, or with a view to or for resale in connection with,
any distribution thereof within the meaning of the Securities Act of 1933, as
amended.

     3.4   The Exchange Shares issued to the Fairfax Subsidiaries as part of the
Exchange Consideration have been validly authorized and will be issued free and
clear of all claims and encumbrances of any nature whatsoever.

     3.5   Upon transfer of the Exchange Consideration, the Fairfax Subsidiaries
will be the owners of record of the Exchange Shares free of claims and
encumbrances.

     3.6   Upon transfer of the Exchange Consideration, the Exchange Shares will
be fully paid and nonassessable.

     3.7   The issuance of the Notes as contemplated by this Agreement has been
duly authorized and upon consummation of the transactions contemplated by this
agreement will have been duly executed and delivered and will be binding on and
enforceable against Odyssey in accordance with their terms, subject to
applicable bankruptcy laws.

4.   SURVIVAL OF REPRESENTATIONS AND WARRANTIES

     The parties hereto each agree that all representations, warranties,
covenants and agreements contained herein shall survive the execution and
delivery of this Agreement, the exchange of the Securities, the transfer of the
Exchange Consideration, and any investigation or audit made by any party hereto.

5.   GENERAL

     5.1   Each of the parties hereto shall use all efforts to take, or cause to
be taken, all appropriate action and do or cause to be done, all things
necessary, proper or advisable under applicable law, and execute and deliver
such documents and other papers, as may be required to carry out the provisions
of this agreement and consummate and make effective the transactions
contemplated by this Agreement.

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     5.2   This Agreement constitutes the entire agreement between the
undersigned parties with respect to the subject matter hereof. It may not be
altered, amended or supplemented except by an agreement in writing signed by
each of the parties hereto. It shall be governed by and construed in accordance
with the laws of the State of New York. It shall be binding upon the parties
hereto and their respective successors and assigns. This Agreement may be
executed in counterparts, each of which shall be deemed an original and both of
which shall constitute one and the same instrument.

6.   NOTICES

     All notices, requests, claims, demands and other communications hereunder
shall be in writing and shall be given or made (and shall be deemed to have been
duly given or made upon receipt) by delivery in person, by courier service, by
facsimile or by registered or certified mail (postage prepaid, return receipt
requested) to the following parties at the following addresses:

                       Odyssey Re Holdings Corp
                       140 Broadway, 39th Floor
                       New York, New York 10005
                       Attention: Donald L. Smith, Esq., General Counsel
                       ORH Holdings Inc.
                       300 Stamford Place
                       Stamford, Connecticut 06902
                       Attention: Donald L. Smith, Esq., General Counsel
                       TIG Insurance Company
                       5205 North O'Connor Blvd.
                       Irving, Texas 75039
                       Attention: William Huff, Esq., General Counsel
                       with a copy to:
                       Shearman & Sterling
                       599 Lexington Avenue
                       New York, New York 10022
                       Facsimile: (212) 848-7179
                       Attention: Brice T. Voran, Esq.

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<PAGE>   4

                                          ODYSSEY RE HOLDINGS CORP.

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

                                          TIG INSURANCE COMPANY

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

                                          ORH HOLDINGS INC.

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

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<PAGE>   5

                                   EXHIBIT A

                               FORM OF TERM NOTES

                                   TERM NOTE

THIS NOTE WAS ORIGINALLY ISSUED IN A TRANSACTION EXEMPT FROM REGISTRATION UNDER
THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"), AND MAY NOT BE
REOFFERED, RESOLD, PLEDGED OR OTHERWISE TRANSFERRED IN THE ABSENCE OF SUCH
REGISTRATION OR AN APPLICABLE EXEMPTION THEREFROM. THIS NOTE OR A PORTION OR
PORTIONS THEREOF SHALL ONLY BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED
AS PROVIDED HEREIN IN A MINIMUM PRINCIPAL AMOUNT OF $5,000,000 TO AN
INSTITUTIONAL ACCREDITED INVESTOR, AS DEFINED IN RULE 501(A) (1), (2), (3) OR
(7) UNDER THE SECURITIES ACT, IN A TRANSACTION EXEMPT FROM REGISTRATION UNDER
THE SECURITIES ACT, IN ACCORDANCE WITH ALL APPLICABLE SECURITIES LAWS OF THE
STATES OF THE UNITED STATES. THE HOLDER AND EACH SUBSEQUENT HOLDER OF THIS NOTE
OR ANY PORTION THEREOF IS REQUIRED TO NOTIFY ANY PURCHASER OF THIS NOTE OR ANY
PORTION THEREOF OF THE RESTRICTIONS REFERRED TO ABOVE.

$200,000,000                                                      May  -- , 2001

     FOR VALUE RECEIVED, the undersigned, ODYSSEY RE HOLDINGS CORP., a Delaware
corporation (herein, called "Maker"), unconditionally promises to pay to the
order of    --   , an    --   corporation, or registered assigns (   --   and
all subsequent holders of this Note or any portion thereof are referred to
hereinafter, individually and collectively, as the context may require, as a
"Holder"), the principal sum of Two Hundred Million Dollars, $200,000,000.00,
with interest from the date the Offering (as defined in Section 13 below) is
consummated (the "Effective Date") (as hereinafter provided, in the original
aggregate principal amount of $200,000,000 including as it may be divided,
reduced, reissued, renewed, substituted, restated, amended, supplemented or
otherwise modified from time to time, being the "Note"), both principal and
interest to be payable by wire transfer in immediately available funds to the
Holder at such account as the Holder may designate from time to time, on the
terms and conditions set forth below.

     All capitalized terms used herein are defined in Section 13 of this Note,
unless the context otherwise dictates.

1.   PRINCIPAL PAYMENTS; INTEREST CHARGES; FEES.

     a.    Principal Payments.  Three (3) annual payments of principal of
Sixty-Six Million Six Hundred Sixty-Six Thousand Six Hundred Sixty-Six and
67/100 Dollars ($66,666,666.67) each, shall be due and payable, together with
accrued interest, on each June 30, commencing June 30, 2002 through June 30,
2004.

     b.    Interest.  Interest shall accrue on the unpaid principal balance of
this Note and shall be paid quarterly, on the 15th day of each June, September,
December and March, beginning June 30, 2001. Interest shall be payable for the
actual number of days outstanding, based upon a 360-day year. All payments shall
be applied first to interest that has become due and payable, and then to
principal. The interest rate on this Note shall be Three-Month LIBOR plus 225
basis points.

     Any such date upon which the interest rate is to be determined shall be
defined as an "Interest Rate Determination Date." All payments, both interest
and principal, shall be paid in lawful money of the United States.

     c.    Past-Due Principal and Interest Payments.  All past-due installments
of interest and principal, or any portion thereof, not paid when due (whether at
maturity, by acceleration, or otherwise), if permitted by applicable law, shall
bear interest until such overdue amounts shall be paid at a rate per annum equal
to the sum of 3% plus the rate of interest otherwise applicable pursuant to
clause (b) immediately above, or if such rate is not permitted by applicable
law, the maximum rate permitted by applicable law.
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<PAGE>   6

2.   CONDITION PRECEDENT TO OBLIGATIONS UNDER THE NOTE.  All duties and
obligations of Maker under this Note, and all the rights of Holder under this
Note, are conditioned upon consummation of the Offering. If the Offering is not
consummated by July 1, 2001, this Note shall be null and void.

3.   WARRANTIES AND REPRESENTATIONS.  Maker warrants and represents that, as of
the date hereof and until this Note is fully paid, performed and satisfied, the
following representations and warranties are and shall remain true:

     a.    Corporate Existence and Power.  Maker is a corporation duly
incorporated and validly existing under the laws of the State of Delaware, and
has all corporate power and all material governmental licenses, authorizations,
consents and approvals required to carry on its business as now conducted.

     b.    Corporate and Governmental Authorization; Contravention.  The
execution, delivery and performance by Maker of this Note are within Maker's
corporate powers, have been duly authorized by all necessary corporate action,
have not been disapproved by the Delaware Commissioner of Insurance, require no
action by or in respect of, or filing with, any other governmental body, agency
or official and do not contravene, or constitute a default under, any provision
of applicable law or regulation or of the certificate of incorporation or
by-laws of Maker or of any material agreement, judgment, injunction, order,
decree or other instrument binding upon Maker or any of its Restricted
Subsidiaries, or result in the creation or imposition of any Lien on any asset
of Maker or its Restricted Subsidiaries.

     c.    Binding Effect.  This Note, when executed and delivered in accordance
with its terms, will constitute a valid and binding obligation of Maker,
enforceable in accordance with its terms, except as the same may be limited by
bankruptcy, insolvency or similar laws affecting creditors' rights generally and
by general principles of equity.

     d.    Use of Proceeds from the Offering.  Maker shall use the net proceeds
of the Offering in the manner described in the Registration Statement on Form
S-1 (Registration No. 333-57642), as amended, as filed by the Maker with the
Securities and Exchange commission to register the securities offered in the
Offering.

     e.    Obligations to Be Pari Passu.  Maker's obligations under this Note
rank pari passu as to priority of payment and in all other respects with all
other unsecured and unsubordinated Debt of Maker.

4.   COVENANTS.  Maker agrees that so long as any amount payable under any Note
remains unpaid:

     a.    Information Delivery.  Maker will deliver to Holder:

           (i)   forthwith upon learning of the occurrence of any Default, a
     certificate of the chief financial officer or the chief accounting officer
     of Maker setting forth the details thereof and the action which Maker is
     taking or proposes to take with the respect thereto; and

           (ii)   from time to time such additional information regarding the
     financial position or business of Maker as any Holder may reasonably
     request.

     b.    Payment of Obligations.  Maker will pay and discharge, and will cause
each Restricted Subsidiary to pay and discharge, at or before maturity, all
their respective material obligations and liabilities, including, without
limitation, tax liabilities, except where the same may be contested in good
faith by appropriate proceedings, and will maintain, and will cause each
Restricted Subsidiary to maintain, in accordance with generally accepted
accounting principles, appropriate reserves for the accrual of any of the same.

     c.    Conduct of Business and Maintenance of Existence.  Maker will
continue, and will cause each Restricted Subsidiary to continue, to engage in
business of the same general type as now conducted by Maker and its Restricted
Subsidiaries, taken as a whole, and will preserve, renew and keep in full force
and effect, and will cause each Restricted Subsidiary to preserve, renew and
keep in full force and effect, their respective corporate existence and their
respective rights, privileges, licenses and franchises which, in the judgment of
the Board of Directors of Maker, are necessary or desirable in the normal
conduct of business.

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<PAGE>   7

     d.    Compliance with Laws.  Maker will comply, and cause each Subsidiary
to comply, in all material respects with all applicable laws, ordinances, rules,
regulations and requirements of governmental authorities except where the
necessity of compliance therewith is contested in good faith by appropriate
proceedings.

     e.    Inspection of Property, Books and Records.  Maker will keep, and will
cause each Restricted Subsidiary to keep, proper books of record and account in
which full, true and correct entries shall be made of all dealings and
transactions in relations to its business and activities; and will permit, and
will cause each Restricted Subsidiary to permit, representatives of Holders to
visit and inspect any of their respective properties, to examine and make
abstracts from any of their respective books and records and to discuss their
respective affairs, finances and accounts with their respective officers,
employees, actuaries and independent public accountants, all upon reasonable
notice, at such reasonable times during ordinary business hours and as often as
may reasonably be desired; provided that neither Maker nor any of its
Subsidiaries shall be required to disclose any information subject to its
attorney-client privilege.

     f.    Negative Pledge.  Neither Maker nor any Restricted Subsidiary will
create, assume or suffer to exist any Lien on any asset now owned or thereafter
acquired by it, except:

           (i)   Liens existing on the date of this Note securing Debt
     outstanding on the date of this Note in an aggregate principal amount not
     exceeding $10,000,000;

           (ii)   any Lien existing on any asset of any corporation at the time
     such corporation becomes a Restricted Subsidiary and not created in
     contemplation or as a result of such event;

           (iii)  any Lien on any asset securing Debt incurred or assumed for
     the purpose of financing all or any part of the cost of acquiring such
     asset, provided that such Lien attaches to such asset concurrently with or
     within 90 days after the acquisition thereof;

           (iv)  any Lien on any asset of any corporation existing at the time
     such corporation is merged or consolidated with or into Maker or a
     Restricted Subsidiary and not created in contemplation or as a result of
     such event;

           (v)   any Lien existing on any asset prior to the acquisition thereof
     by Maker or a Restricted Subsidiary and not created in contemplation or as
     a result of such acquisition;

           (vi)  any Lien arising out of the refinancing, extension, renewal or
     refunding of any Debt secured by any Lien permitted by any of the foregoing
     subclauses of this Section 4.i, provided that such Debt is not increased
     beyond the then outstanding principal amount thereof and is not secured by
     any additional assets;

           (vii) Liens incidental to the conduct of its business or the
     ownership of its assets which (A) do not secure Debt, (B) do not secure any
     obligation in an amount exceeding $5,000,000 and (C) do not in the
     aggregate materially detract from the value of its assets or materially
     impair the use thereof in the operation of its business;

           (viii) Liens created by any Restricted Subsidiary as security for
     Debt owing to Maker;

           (ix)  Liens created by Maker as security for Debt owing to
     Subsidiaries, but only if the only security for such Debt consists of
     Investments acquired by Maker solely form the proceeds of such Debt;

           (x)   Liens on cash and cash equivalents securing Derivative
     Financial Products, provided that the aggregate amount of cash and cash
     equivalents subject to such Liens may at no time exceed $50,000,000;

           (xi)  in addition to the Liens permitted by sub clauses (i) through
     (x) and (xii) of this Section 4.f, any Lien on any asset securing Debt of
     Maker or any Restricted Subsidiary, in an aggregate outstanding principal
     amount at no time exceeding $5,000,000; and

           (xii) in addition to the Liens permitted by sub clauses (i) through
     (xi) of this Section 4.f, any Lien on real property leased by Maker or any
     Restricted Subsidiary pursuant to a capital lease (which capital lease was
     entered into in connection with a sale leaseback transaction where Maker or
     such
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<PAGE>   8

     Restricted Subsidiary, as the case may be, was the seller) securing Debt of
     Maker or such Restricted Subsidiary, as the case may be, in an aggregate
     outstanding principal amount at no time exceeding $25,000,000.

     g.    Consolidations, Mergers and Sales of Assets.  Maker will not (i)
consolidate or merge with or into any other Person or (ii) sell, lease or
otherwise transfer, directly or indirectly, all or substantially all of the
assets of Maker and its Subsidiaries, taken as a whole, to any other Person;
provided that Maker may merge with another Person if (A) Maker is the
corporation surviving such merger and (B) immediately after giving effect to
such merger, no Default shall have occurred and be continuing.

     h.    Leverage.  Consolidated Debt will at no time be greater than 50% of
Adjusted Consolidated Net Worth.

     i.    Obligation to be Pari Passu.  Maker's obligations under this Note
will rank at all times pari passu as to priority of payment and in all other
respects with all other unsecured and unsubordinated Debt of Maker.

5.   EVENTS OF DEFAULT.  If one or more of the following events ("Events of
Default") shall have occurred and be continuing;

     a.    Maker shall fail to pay (i) any installment of principal due
hereunder on the date such payment shall be due and payable under the terms of
this Note or (ii) interest on any other sum of money due under this Note or due
to an affiliate of the Holder within thirty days after the due date therefore;

     b.    Maker shall fail to observe or perform any covenant contained in
Sections 4.b through 4.h inclusive;

     c.    Maker shall fail to observe or perform any covenant or agreement
contained in this Note (other than those covered by clauses (a) or (b) above)
for 30 days after written notice thereof has been given to Maker by the Holder;

     d.    Any representation, warranty, certification or statement made by
Maker in this Note or in any certificate, financial statement or other document
delivered pursuant to this Note shall prove to have been incorrect in any
material respect when made (or deemed made);

     e.    Maker or any Subsidiary (other than a Newly Acquired Subsidiary)
shall fail to make any payment in respect of any Debt (other than the Note and
any Debt solely of a Newly Acquired Subsidiary existing at the time such Person
becomes a Subsidiary and not created in contemplation of such event ("Newly
Acquired Subsidiary Debt")) having a principal amount then outstanding of not
less than $15,000,000 when due and such failure shall continue beyond any
applicable grace period or Maker or any Subsidiary (other than a Newly Acquired
Subsidiary) shall fail to make any payment in an amount at least equal to
$15,000,000 in respect of any Derivative Financial Product when due and such
failure shall continue beyond any applicable grace period;

     f.    Any event or condition shall occur which results in the acceleration
of the maturity of any Debt (other than the Note and Newly Acquired Subsidiary
Debt) having a principal amount then outstanding of not less than $15,000,000 of
Maker or any Subsidiary or enables (or, with the giving of notice or lapse of
time or both, would enable) the holder of such Debt or any Person acting on such
holder's behalf to accelerate the maturity thereof;

     g.    Maker or any Restricted Subsidiary (other than a Newly Acquired
Subsidiary) shall commence a voluntary case or other proceeding seeking
rehabilitation, dissolution, conservation, liquidation, reorganization or other
relief with respect to itself or its debts under any bankruptcy, insolvency or
other similar law now or hereafter in effect or seeking the appointment of a
trustee, receiver, liquidator, rehabilitator, dissolver, conservator, custodian
or other similar official of it or any substantial part of its property, or
shall consent to any such relief or to be appointment of or taking possession by
any such official in an involuntary case or other proceeding commenced against
it, or shall make a general assignment for the benefit of creditors, or

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<PAGE>   9

shall fail generally to pay its debts as they become due, or shall take any
corporate action to authorize any of the foregoing;

     h.    An involuntary case or other proceeding shall be commenced against
Maker or any Restricted Subsidiary (other than a Newly Acquired Subsidiary)
seeking rehabilitation, dissolution, conservation, liquidation, reorganization
or other relief with respect to it or its debts under any bankruptcy, insolvency
or other similar law now or hereafter in effect or seeking the appointment of a
trustee, receiver, liquidator, rehabilitator, dissolver, conservator, custodian
or other similar official of it or any substantial part of its property, and
such involuntary case or other proceeding shall remain undismissed and unstayed
for a period of 60 days; or an order for relief shall be entered against Maker
or any such Restricted Subsidiary under the federal bankruptcy laws as now or
hereafter in effect; or any governmental body, agency or official shall apply
for, or commence a case or other proceeding to seek, an order for the
rehabilitation, conservation, dissolution or other liquidation of Maker or any
such Restricted Subsidiary or of the assets or any substantial part thereof of
Maker or any such Restricted Subsidiary or any other similar remedy; or

     i.    A judgment or order for the payment of money in excess of $50,000,000
(after (without duplication) the actual amounts of insurance recoveries, offsets
and contributions received and amounts thereof not yet received but which the
insurer thereon has acknowledged in writing its obligation to pay) shall be
rendered against Maker or any Restricted Subsidiary and such judgment or order
shall continue unsatisfied and unstayed for a period of 90 days after entry of
such judgment (and, for purposes of this clause (i), a judgment shall be stayed
if, among other things, an appeal is timely filed and such judgment cannot be
enforced); then, and in every such event, Holder may, by notice to Maker,
declare this Note (together with accrued interest thereon) to be, and this Note
(together with accrued interest thereon) shall thereupon become, immediately due
and payable without presentment, demand, protest or other notice of any kind,
all of which are hereby waived by Maker; provided that in the case of any of the
Events of Default specified in clauses (g) or (h) above with respect to Maker,
without any notice to Maker or any other act by the Holder, the Note (together
with accrued interest thereon) shall become immediately due and payable without
presentment, demand, protest or notice of any kind, all of which are hereby
waived by Maker.

6.   WAIVER OF DEMAND AND PRESENTMENT.  Maker and all other parties now or
hereafter liable for payment hereof, whether as endorser, guarantor, surety or
otherwise, severally waive demand, presentment, notice of dishonor, notice of
default, notice of intent to accelerate, diligence in collecting, grace, notice
and protest, and consent to all extensions which from time to time may be
granted by the Holder, except as expressly otherwise required to be given
pursuant to the terms of this Note.

7.   NO WAIVER.  Failure by Holder to exercise any right, remedy or option under
this Note or any supplement hereto or in any other agreement between Maker and
Holder or delay by Holder in exercising the same will not operate as a waiver by
Holder of its right to exercise any such right, remedy or option. No waiver by
Holder will be effective unless it is in writing and then only to the extent
specifically stated. This Note cannot by changed or terminated orally.

8.   REGISTRATION AND TRANSFER; SUBSTITUTION OF NOTES; COMMUNICATIONS WITH
MAKER, ETC.

     a.    The Maker shall keep at its principal office a register in which the
Maker shall provide for the registration of Notes and for the registration of
transfer of Notes. Each Holder may, at its option and either in person or by its
duly authorized attorney, surrender the same for registration or transfer or
exchange at such office of the Maker and, without expense to such Holder (other
than transfer taxes, if any), receive in exchange therefore one or more Note or
Notes, dated as of the date to which interest has been paid on the Note or Notes
so surrendered (or if no interest has theretofore been paid, dated as of the
Effective Date), in denominations which are an integral multiple of $500,000 and
are not less than $5,000,000 for the same aggregate unpaid principal amount as
the Note or Notes so surrendered for transfer or exchange, registered in such
name or names and in such denomination as may be designated by such Holder. The
Maker, however, shall not be obligated to register any transfer of any Note or
Notes so surrendered unless such is accompanied by (i) a certificate of the
proposed transferee of such Note or Notes stating that it is an institutional
investor which is an "accredited investor" within the meaning of Rule 501(a)
(1), (2), (3) or (7) under the Securities Act, and that it is purchasing the
Note or Notes for its own account, for investment,
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<PAGE>   10

and not with a view to, or for offer or sale in connection with, any
distribution thereof or with any present intention of distributing or selling
the Note or Notes, subject to the disposition of the property of such proposed
transferee being at all times within its controls and (ii) an opinion of counsel
satisfactory to the Maker that an exemption from the registration requirements
under the Securities Act, the Trust Indenture Act of 1939 and applicable blue
sky laws is available.

     Every Note presented or surrendered for registration of transfer or
exchange shall be duly endorsed, or shall be accompanied by a written instrument
of transfer fully executed, by the registered Holder of such Note or its
attorney duly authorized in writing.

     Every Note so made and delivered in exchange for this Note shall in all
other respects be in the same form and have the same terms as this Note, and
each such exchange or transfer shall be made in such a manner that no gain or
loss of principal or interest shall result therefrom. No transfer or exchange of
any Note shall be valid unless made in such manner.

     b.    Upon receipt by the Maker of evidence reasonably satisfactory to it
of the loss, theft, destruction or mutilation of any Note, and (in the case of
any such loss, theft or destruction) upon receipt of indemnity reasonably
satisfactory to the Maker, and (in the case of any such mutilation) upon
surrender and cancellation of such Note, the Maker will make and deliver, in
lieu of such lost, stolen, destroyed or mutilated Note, a substitute Note of
like tenor and unpaid principal amount and dated as of the date to which
interest has been paid (or if no interest has theretofore been paid, dated as of
the Effective Date) on such stolen, destroyed or mutilated Note.

     c.    All communications, demands and requests relating to the exercise of
rights and remedies and notices in connection therewith to be given by or to any
Holder or the Designated Holder shall be given by or to the Original Holder (as
hereinafter defined), unless and until such Original Holder and such other
Holders as shall, when considered with the Original Holder, hold at least 51% of
the aggregated unpaid principal amount of the Note, designate effective upon not
less than five business days' prior written notice thereof to the Maker (the
Original Holder or such designated other Holder being the "Designated Holder").
Thereafter, subsequent Designated Holders may be appointed by the Holders
holding at least 51% of the aggregate unpaid principal amount of the Notes,
provided, that there shall only be one Designated Holder at any one time, and
provided, further, that the Maker shall be given at least five business days'
prior written notice of the effectiveness of any such designation. The
Designated Holder (if the Original Holder, individually, and if not the Original
Holder, with the consent or upon the direction of the Holders of at least 51% of
the aggregated outstanding unpaid principal balance of the Notes) shall (i) make
all determinations as to the exercise and enforcement of any rights and remedies
of the Holders against the Maker in accordance with the terms hereof, and (ii)
subject to the immediately succeeding sentence, be authorized and empowered to
grant any extension, renewals amendments, waivers, modifications, releases and
consents of or to any of the provisions of this Note on behalf of all of the
Holders hereunder. Notwithstanding anything contained in the immediately
preceding sentence, any extension, renewal, amendment, waiver, modification,
release or consent of or to any provision of the Notes, which alters (A) the
principal amount, the final maturity, or the due dates for interest or principal
payments hereunder, or provides for the reduction of the interest rate
applicable thereto or any other amounts payable hereunder, (B) the definition of
"Original Holder" or "Designated Holder" or (C) the provisions contained in this
clause (c), shall not, in any of the foregoing cases, be effective unless it is
evidenced by a writing agreed to and signed by all of the Holders of the Notes.
Without limiting the foregoing in any manner, the Maker shall be entitled to
rely on any such extension, renewal, amendment, waiver, modification, release or
consent believed by it in good faith to have been executed and delivered by the
appropriate persons in accordance with this Section 8 without any inquiry as to
such person's authority to so execute and deliver any such instrument, document
or agreement. "Original Holder" as used in this clause (c) shall mean    --
or, if not    --   any one affiliate thereof which is the Holder of the entire
aggregate unpaid principal amount of the Notes (provided that if the entire
aggregate unpaid principal amount of the Notes is held by more than one such
affiliate, such Holder designated    --   shall be the Original Holder).

                                        6
<PAGE>   11

9.   NO ASSIGNMENT.  Maker may not assign, transfer or otherwise dispose of any
rights or obligations hereunder, by operation of law or otherwise, and any such
assignment, transfer or other disposition without Holder's written consent shall
be void. All of the rights, privileges, remedies and options given to Holder
hereunder shall inure to the benefit of Holder's successors and assigns and, in
addition, shall insure to the benefit of and be enforceable by each person who
shall from time to time become a Holder of the Note, and all the terms,
conditions, covenants, provisions and warranties herein shall inure to the
benefit of and bind the representatives, successors and assigns of Maker and
Holder, respectively. Holder may not assign, transfer or otherwise dispose of
the Note without having first given forty-five (45) days prior written notice of
its intent to do so. In addition, the assigning Holder shall give Maker at least
three business days prior written notice of the effective date of any such
assignment (as set forth in such notice), all payments required to be made by
assigned shall be made by the Maker to the designated assignee. The assigning
Holder and such assignees shall make directly among themselves all appropriate
adjustments in payments made under the Note (or the assigned portions thereof)
for periods prior to the effective date of such assignment.

10. PREPAYMENT.  The Maker may, at its option, at any time and from time to
time, prepay all or any part of the principal balance of this Note, without
penalty or premium, to the Holders ratably (based on the outstanding principal
balance of such Holder's respective Notes), provided that concurrently with each
such prepayment the Maker shall pay accrued interest on the principal so prepaid
to the date of such prepayment.

11. CONFIDENTIALITY.  Each of Holders hereby agrees not to (a) disclose to any
person, or (b) use for any purpose other than evaluating its investment in the
Note, any non-public information provided by the Maker pursuant to or in
connection with this Note, any non-public information provided by the Maker
pursuant to or in connection with this Note (including, without limitation,
pursuant to Section 4.a hereof), or which is otherwise obtained by any such
Holder in connection with its dealings with Maker relating to this Note, without
the prior written authorization of Maker, provided that such Holder may disclose
any such information: (i) to such of its officers, directors, employees,
auditors, accountants, attorneys or advisors as are advised of the
confidentiality of such information, (ii) as any be required to be disclosed by
such Holder pursuant to any law or regulation applicable to such Holder or in
any judicial or arbitration proceeding relating to this Note (and in the event
of any such disclosure, such Holder's only duty shall be to inform the Maker
thereof), and (iii) any purchaser or prospective purchaser of the Note, provided
that prior to making any such disclosure such purchaser or prospective purchaser
shall agree to hold such information confidential on terms similar to those
hereinabove set forth.

12. DEFINITIONS.  The following terms, as used herein, have the following
meanings:

     a.    "Adjusted Consolidated Net Worth" means at any date the consolidated
shareholders' equity of Maker and its Consolidated Subsidiaries, plus any
unrealized losses or less any unrealized gains (in each case to the extent
reflected in the determination of such consolidated shareholders' equity)
related, directly or indirectly, to securities available for sale, as determined
in accordance with Statement of Financial Accounting Standards No. 115 (or any
successor statements or amendments thereto) (in each case as affected by any
subsequent relevant pronouncements of the Financial Accounting Standards Board
or, if and to the extent applicable, the Securities and Exchange Commission).

     b.    "Consolidated Debt" means at any date the Debt of Maker and its
Consolidated Subsidiaries, determined on a consolidated basis as of such date.

     c.    "Consolidated Subsidiary" means at any date any Subsidiary or other
entity the accounts of which would be consolidated with those of Maker in its
consolidated financial statements if such statements were prepared as of such
date.

     d.    "Debt" of any Person means at any date, without duplication, (i) all
obligations of such Person for borrowed money, (ii) all obligations of such
Person evidenced by bonds, debentures, notes or other similar instruments, (iii)
all obligations of such Person to pay the deferred purchase price of property or
services, except trade accounts payable arising in the ordinary course of
business, (iv) all obligations of such Person as lessee under capital leases,
(v) all non-contingent obligations of such Person to reimburse any bank or other
Person in respect of amounts paid under a letter of credit or similar
instrument, (vi) all Debt of others

                                        7
<PAGE>   12

secured by a Lien on any asset of such Person, whether or not such Debt is
assumed by such Person, and (vii) all Debt of others Guaranteed by such Person,
but, in the case of Guarantees of Debt or other obligations comprised of
industrial revenue bonds, real estate partnerships or mortgage loan pass-through
certificates, only to the extent that the aggregate amount of such Guarantees
exceeds $150,000,000.

     e.    "Default" means any condition or event which constitutes an Event of
Default or which with the giving of notice or lapse of time or both would,
unless cured or waived, become an Event of Default.

     f.    "Derivative Financial Products" of any Person means all obligations
(including whether pursuant to any master agreement or any particular agreement
or transaction) of such Person in respect of any rate swap transaction, basis
swap, forward rate transaction, interest rate future, commodity swap, commodity
option, equity or equity index swap, equity or equity index option, bond option,
interest rate option, foreign exchange transaction, cap transaction, floor
transaction, collar transaction, currency swap transaction, cross-currency rate
swap transaction, currency future, currency option or any other similar
transaction (including any option with respect to any of the foregoing) or any
obligation thereof.

     g.    "Event of Default" has the meaning set forth in Section 5.

     h.    "Guarantee" by any Person means any obligation, contingent or
otherwise, of such Person directly or indirectly guaranteeing any Debt or
obligation of any other Person and, without limiting the generality of the
foregoing, any obligation, direct or indirect, contingent or otherwise, of such
Person (i) to purchase or pay (or advance or supply funds for the purchaser or
payment of) such Debt or other obligation (whether arising by virtue of
partnership arrangements, by agreement to keep-well, to purchase assets, goods,
securities or services, to take-or-pay, or to maintain financial statement
conditions or otherwise) or (ii) entered into for the purpose of assuring in any
other manner the obligee of such Debt or other obligation of the payment thereof
or to protect such obligee against loss in respect thereof (in whole or in
part), provided that the term Guarantee shall not include endorsements for
collection or deposit in the ordinary course of business. The term "Guarantee"
used as a verb has a corresponding meaning.

     i.    "Investment" means any investment in any Person, whether by means of
share purchase, capital contribution, loan, time deposit or otherwise.

     j.    "Lien" means, with respect to any asset, any mortgage, lien, pledge,
charge, security interest or encumbrance of any kind in respect of such asset.
For the purposes of this Note, Maker or any Subsidiary shall be deemed to own
subject to a Lien any asset which it has acquired or holds subject to the
interest of a vendor or lessor under any conditional sale agreement, capital
lease or other title retention agreement relating to such asset. The term "Lien"
does not include any judgment Lien resulting from a judgment which has not
become final and unappealable.

     k.    "Newly Acquired Subsidiary" means any Subsidiary that is not a
Subsidiary on the date hereof but that becomes a Subsidiary after the date
hereof, but only during the 180 days after the first date on which such
Subsidiary became a Subsidiary.

     l.    "Offering" means the offer by the Maker of    --   shares of its
Common Stock, no par value (the "Common Shares"). (   --   Common Shares if an
over-allotment option granted to underwriters is exercised) in an initial public
offering described in the Registration Statement on Form S-1 (Registration No.
333-57642), as amended, as filed by the Maker with the Securities and Exchange
Commission.

     m.   "Person" means an individual, a corporation, a partnership, an
association, a trust or any other entity or organization, including a government
or political subdivision or an agency or instrumentality thereof.

     n.    "Restricted Subsidiary" means, as of any date, a Subsidiary which
meets the definitional requirements of a "significant subsidiary", as such term
is defined in the rules set forth in Regulation S-X under the Securities
Exchange Act of 1934, as amended (applying the tests set forth in such rules
with reference to the consolidated balance sheets and related consolidated
statements of income of Maker and its Consolidated Subsidiaries as of the last
day of its most recently completed fiscal quarter and for the twelve-month
period then ended).

                                        8
<PAGE>   13

     o.    "Subsidiary" means any corporation or other entity of which
securities or other ownership interests having ordinary voting power to elect a
majority of the board of directors or other persons performing similar functions
are at the time directly or indirectly owned by Maker.

     p.    "Three-Month LIBOR" means an interest rate per annum equal to the
rate per annum obtained by the arithmetic mean (rounded upwards to the nearest
1/16th of 1%) of the offered rates for three-month deposits in U.S. Dollars on
the Interest Rate Determination Date, as such rates appear on the "Reuters
Screen LIBO Page" at approximately 11:00 A.M. (London time) on the Interest Rate
Determination Date, if at least two such offered rates appear on the Reuters
Screen LIBO Page. If fewer than two offered rates appear on the Reuters Screen
LIBO Page on such Interest Rate Determination Date, Maker will request the
principal London offices of each of four major banks in the London interbank
market, as selected by Maker with the approval of the Designated Holder, to
provide Maker with its offered quotations for three-month deposits in U.S.
Dollars, on the Interest Rate Determination Date, to prime banks in the London
interbank market at approximately 11:00 A.M. (London time) on such Interest Rate
Determination Date and in a principal amount not less than U.S.$1,000,000 that
is representative of a single transaction in such market at such time. If at
least two such quotations are provided, LIBOR will be the arithmetic mean
(rounded upwards to the nearest 1/16th of 1%) of such quotations. If fewer than
two quotations are provided, LIBOR with respect to such Interest Rate
Determination Date will be the arithmetic mean (rounded upwards to the nearest
1/16th of 1%) of the Interest Rate Determination Date quoted at approximately
11:00 A.M. (New York City time) on such Interest Rate Determination Date by
three major banks in New York City selected by Maker with the approval of the
Designated Holder for three-month loans in U.S. Dollars to leading European
banks, on the Interest Rate Determination Date, and in a principal amount not
less than U.S.$1,000,000 that is representative of a single transaction in such
market at such time; provided, however, that if fewer than three banks selected
as aforesaid by Maker with the approval of the Designated Holder are quoting
rates as mentioned in this sentence, LIBOR for such Interest Rate Determination
Date will be equivalent to LIBOR for the immediately preceding Interest Rate
Determination Date.

13. MISCELLANEOUS.

     a.    Each provision of this Note shall be interpreted in such manner as to
be valid under applicable law, but if any provision hereof shall be invalid
under applicable law, such provision shall be ineffective to the extent of such
invalidity, without invalidating the remainder of such provision or the
remaining provisions hereof. Any reference herein to "Maker" shall be limited to
Odyssey Re Holdings Corp. and shall not mean any of its affiliates or
subsidiaries.

     b.    This Note and payments due hereunder are being delivered and accepted
in the State of New York, without relief from valuation or appraisement laws,
and shall be deemed to have been made at New York, New York. This Note shall be
interpreted, and the rights and liabilities of the parties hereto determined, in
accordance with the laws of the State of New York and all other laws of
mandatory application.

     c.    Maker agrees that any action, unit or proceeding in respect of or
arising out of this Note, its validity or performance, at the sole option of the
Holder, its successors and assigns, and without limitation on the ability of the
Holder, its successors and assigns, to exercise all rights as to initiate and
prosecute in any applicable jurisdiction actions related to repayment of the
obligations, shall be initiated and prosecuted as to all parties and their
successors and assigns at New York, New York. The Holder and Maker each consents
to and submits to the exercise of jurisdiction over its person by any court
situated at New York, New York having jurisdiction over the subject matter,
waives personal service of any and all process upon it, and consents that all
such service of process be made by certified mail directed to Maker and the
Holder at their respective addresses set forth in clause (e) below or as
otherwise provided under the laws of the State of New York. Maker waives and
objection based on forum non convenience, and any objection to venue of any
action instituted hereunder, and consents to the granting of such legal or
equitable relief as is deemed appropriate by the court.

                                        9
<PAGE>   14

     d.    Maker and the Holder each waives trial by jury with respect to any
action, claim, suit or proceeding in respect of or arising out of this Note
and/or the conduct of the relationship between the Holder and Maker.

     e.    Any notice required, permitted or contemplated hereunder shall be in
writing and addressed to the party to be notified at the address set forth below
or at such other address as each party may designate for itself from time to
time by notice hereunder, and shall be deemed validly given (i) three days
following deposit in the U.S. mail, with proper postage prepaid, or (ii) the
next business day after such notice was delivered to a regularly scheduled
overnight delivery carrier with delivery fees either prepaid or an arrangement,
satisfactory with such carrier, made for the payment thereof, or (iii) upon
receipt of notice given by telecopy, mailgram, telex or personal delivery;

     If to Maker:

    Odyssey Re Holdings Corp.
    140 Broadway, 39th Floor,
    New York, New York 10005
    Attention: Donald L. Smith, General Counsel

    If to the Holder:
    --

    with a copy to:
    --

     f.    If this Note is not paid when due, whether at maturity or by
acceleration, or if it is collected through a bankruptcy or other court, whether
before or after maturity, Maker agrees to pay all costs of collection including,
but not limited to, reasonable attorneys' fees incurred by the Holder hereof.

     g.    This Note contains a complete statement of all the arrangements
between the Maker and the Holder with respect to this Note, supersedes all
existing agreements between maker and Holder concerning this Note, and cannot be
changed or terminated except by a written instruments signed by each of the
parties hereto.

     h.    The headings in this Note are solely for convenience of reference and
shall not affect its interpretation.

     i.    Since the parties to this Note will be irrevocably damaged if this
Note is not specifically enforced, either party shall be entitled to an
injunction restraining any violation by the other, without any bond or other
security being required.

     j.    This Note shall terminate upon the payment in full of the outstanding
principal and accrued interest thereon.

                                        10
<PAGE>   15

     IN WITNESS WHEREOF, the undersigned has executed and delivered this Note on
the day and year first above written.

<TABLE>
<S>                                           <C>
                                              ODYSSEY RE HOLDINGS CORP.

                                              By: -------------------------------------------------------

                                              Name: ----------------------------------------------------

                                              Title:
                                              ------------------------------------------------------

                                              By: -------------------------------------------------------

                                              Name: ----------------------------------------------------

                                              Title:
                                              ------------------------------------------------------

                                              Signed and Acknowledged in the presence of:

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

                                              Name: ----------------------------------------------------
</TABLE>

<TABLE>
<S>                                        <C>  <C>
STATE OF NEW YORK -----------------
                                                  SS:
COUNTY OF ----------------------------
</TABLE>

     The foregoing instrument was acknowledged before me this      day of
          , 2001, by           , of Odyssey Re Holdings Corp., a Delaware
corporation, on behalf of the corporation.

                                          --------------------------------------
                                          Notary Public

                                          My Commission Expires ----------------

                                        11
<PAGE>   16

                                   EXHIBIT B

                              FORM OF STOCK POWERS

     FOR EXCHANGE CONSIDERATION RECEIVED, TIG hereby transfers unto Odyssey
16,700 shares of common stock of OARC standing in the name of TIG on the books
of said Corporation represented by Certificate No. ( ______________ ) herewith
 ______________ , and do hereby irrevocably constitute and appoint
 ____________________________ , attorney to transfer the said stock on the books
of said Corporation with full power of substitution in the premises.
Dated:

                                          TIG INSURANCE COMPANY

                                          By:
                                          --------------------------------------
                                              Name:
                                              Title:
In presence of:

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

                                        1
<PAGE>   17

     FOR EXCHANGE CONSIDERATION RECEIVED, ORH Holdings hereby transfers unto
Odyssey 4,175 shares of common stock of OARC standing in the name of ORH
Holdings on the books of said Corporation represented by Certificate No.
( ______________ ) herewith  ______________ , and do hereby irrevocably
constitute and appoint  ____________________________ , attorney to transfer the
said stock on the books of said Corporation with full power of substitution in
the premises.
Dated:
                                          ORH HOLDINGS INC.

                                          By:
                                          --------------------------------------
                                              Name:
                                              Title:
In presence of:

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

                                        2