<PAGE>


                                                                  Exhibit 4.9(a)


               [Form of Warrant Agreement for Warrants Sold Alone]



                        ENDURANCE SPECIALTY HOLDINGS LTD.

                                       and

                               [                  ],


                                as Warrant Agent


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


                                WARRANT AGREEMENT


                                 Dated as of [ ]


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


                            Warrants to Purchase [ ]


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








<PAGE>

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>

                                                                                                       PAGE
                                                                                                       ----

ARTICLE 1 ISSUANCE OF WARRANTS AND EXECUTION AND DELIVERY OF WARRANT CERTIFICATES

<S>                       <C>                                                                           <C>
SECTION 1.01.             Issuance of Warrants...........................................................2
SECTION 1.02.             Execution and Delivery of Warrant Certificates.................................2
SECTION 1.03.             Issuance of Warrant Certificates...............................................3

ARTICLE 2 WARRANT PRICE, DURATION AND EXERCISE OF WARRANTS

SECTION 2.01.             Warrant Price..................................................................4
SECTION 2.02.             Duration of Warrants...........................................................4
SECTION 2.03.             Exercise of Warrants...........................................................4

ARTICLE 3 OTHER PROVISIONS RELATING TO RIGHTS OF HOLDERS OF WARRANT

SECTION 3.01.             No Rights as Warrant Securityholder Conferred by Warrants or Warrant
                          Certificates...................................................................6
SECTION 3.02.             Lost, Mutilated, Stolen or Destroyed Warrant Certificates......................6
SECTION 3.03.             Enforcement of Rights..........................................................6
SECTION 3.04.             Merger, Amalgamation, Consolidation, Conveyance or Transfer....................7

ARTICLE 4 EXCHANGE AND TRANSFER

SECTION 4.01.             Exchange and Transfer..........................................................7
SECTION 4.02.             Treatment of Holders of Warrant Certificates...................................8
SECTION 4.03.             Cancellation of Warrant Certificates...........................................8

ARTICLE 5 CONCERNING THE WARRANT AGENT

SECTION 5.01.             Warrant Agent..................................................................9
SECTION 5.02.             Conditions of Warrant Agent's Obligations......................................9
SECTION 5.03.             Resignation and Appointment of Successor......................................11
</TABLE>


                                       i
<PAGE>

<TABLE>
<CAPTION>

                             ARTICLE 6 MISCELLANEOUS

<S>                     <C>                                                                            <C>
SECTION 6.01.             Amendment.....................................................................12
SECTION 6.02.             Notices and Demands to the Company and Warrant Agent..........................13
SECTION 6.03.             Addresses.....................................................................13
SECTION 6.04.             Applicable Law................................................................13
SECTION 6.05.             Delivery of Prospectus........................................................13
SECTION 6.06.             Obtaining of Governmental Approval............................................13
SECTION 6.07.             Persons Having Rights Under Warrant Agreement.................................13
SECTION 6.08.             Headings......................................................................14
SECTION 6.09.             Counterparts..................................................................14
SECTION 6.10.             Inspection of Agreement.......................................................14
SECTION 6.11.             Notices to Holders of Warrants................................................14

EXHIBIT A - Form of Warrant Certificate................................................................A-1
</TABLE>




                                       ii
<PAGE>


                               WARRANT AGREEMENT(1)

         THIS AGREEMENT dated as of [     ] between ENDURANCE SPECIALTY HOLDINGS
LTD., an exempted company incorporated in Bermuda as a holding company (the
"Company"), and [     ], a [bank] [trust company] duly incorporated and existing
under the laws of [     ], as Warrant Agent (the "Warrant Agent"),

                              W I T N E S S E T H :

         [WHEREAS, the Company has entered into an Indenture dated as of [Date]
(the "Senior Indenture") between the Company and [ ], as Trustee (the "Senior
Indenture Trustee"), and an Indenture dated as of [Date] (the "Subordinated
Indenture") between the Company and [ ], as Trustee (the "Subordinated Indenture
Trustee") (together the "Trustees" or "Trustee" and "Indentures" or
"Indenture"), providing for the issuance from time to time of its unsecured debt
securities to be issued in one or more series as provided in the Indenture; and]

         WHEREAS, the Company proposes to sell [title of such securities being
offered] (the "Offered Securities") with one or more warrants (the "Warrants")
representing the right to purchase [title of such securities purchasable through
exercise of Warrants] (the "Warrant Securities"), the Warrants to be evidenced
by warrant certificates issued pursuant to this Agreement (the "Warrant
Certificates"); and

         WHEREAS, the Company desires the Warrant Agent to act on behalf of the
Company in connection with the issuance, transfer, exchange, exercise and
replacement of the Warrant Certificates, and in this Agreement wishes to set
forth, among other things, the form and provisions of the Warrant Certificates
and the terms and conditions on which they may be issued, transferred,
exchanged, exercised and replaced;

         NOW, THEREFORE, in consideration of the premises and of the mutual
agreements herein contained, the parties hereto agree as follows:


--------
(1)Complete or modify the provisions of this form as appropriate to reflect the
   terms of the Warrants and Warrant Securities. Monetary amounts may be in U.S.
   dollars, in a foreign currency or in a composite currency, including but not
   limited to the euro.


                                       1
<PAGE>


                                   ARTICLE 1
     ISSUANCE OF WARRANTS AND EXECUTION AND DELIVERY OF WARRANT CERTIFICATES

         SECTION 1.01. Issuance of Warrants.

         The Warrants shall be evidenced by one or more Warrant Certificates.
Each Warrant evidenced thereby shall represent the right, subject to the
provisions contained herein and therein, to purchase [_____ shares of the
Warrant Securities] [_____aggregate principal amount of Warrant Securities].

         SECTION 1.02. Execution and Delivery of Warrant Certificates.

         Each Warrant, whenever issued, shall be evidenced by a Warrant
Certificate in registered form substantially in the form set forth in Exhibit A
hereto, shall be dated and may have such letters, numbers or other marks of
identification or designation and such legends or endorsements printed,
lithographed or engraved thereon as the officers of the Company executing the
same may approve (execution thereof to be conclusive evidence of such approval)
and as are not inconsistent with the provisions of this Agreement, or as may be
required to comply with any law or with any rule or regulation made pursuant
thereto or with any rule or regulation of any stock exchange on which the
Warrants may be listed, or to conform to usage. The Warrant Certificates shall
be signed on behalf of the Company by its chairman or vice chairman of the Board
of Directors, the chief financial officer, the president, any vice president,
any assistant vice president, the treasurer or any assistant treasurer of the
Company, which may but need not be attested by its secretary or one of its
assistant secretaries. Such signatures may be manual or facsimile signatures of
such authorized officers and may be imprinted or otherwise reproduced on the
Warrant Certificates.

         No Warrant Certificate shall be valid for any purpose, and no Warrant
evidenced thereby shall be exercisable, until such Warrant Certificate has been
countersigned by the Warrant Agent by manual signature. Such signature by the
Warrant Agent upon any Warrant Certificate executed by the Company shall be
conclusive evidence, and the only evidence, that the Warrant Certificate so
countersigned has been duly issued hereunder.

         In case any officer of the Company who shall have signed any of the
Warrant Certificates either manually or by facsimile signature shall cease to be
such officer before the Warrant Certificates so signed shall have been
countersigned and delivered by the Warrant Agent, such Warrant Certificates may
be countersigned and delivered notwithstanding that the person who signed such
Warrant Certificates ceased to be such officer of the Company; and any Warrant
Certificate may be signed on behalf of the Company by such persons as, at the
actual date of the execution of such Warrant Certificate, shall be the proper
officers of the Company, although at the date of the execution of this Agreement
any such person was not such officer.



                                       2
<PAGE>

         The term "Holder," when used with respect to any Warrant Certificate
shall mean any person in whose name at the time such Warrant Certificate shall
be registered upon the books to be maintained by the Warrant Agent for that
purpose.

         SECTION 1.03. Issuance of Warrant Certificates.

         Warrant Certificates evidencing the right to purchase [_____ shares of
the Warrant Securities] [an aggregate principal amount not exceeding _____
aggregate principal amount of Warrant Securities] (except as provided in
Sections 2.03, 3.02 and 4.01) may be executed by the Company and delivered to
the Warrant Agent upon the execution of this Warrant Agreement or from time to
time thereafter. The Warrant Agent shall, upon receipt of Warrant Certificates
duly executed on behalf of the Company, countersign Warrant Certificates
evidencing [ ]Warrants representing the right to purchase up to [_____shares of
the Warrant Securities] [_____ aggregate principal amount of Warrant Securities]
and shall deliver such Warrant Certificates to or upon the order of the Company.
Subsequent to such original issuance of the Warrant Certificates, the Warrant
Agent shall countersign a Warrant Certificate only if the Warrant Certificate is
issued in exchange or substitution for one or more previously countersigned
Warrant Certificates or in connection with their transfer as hereinafter
provided or as provided in the antepenultimate paragraph of Section 2.03.

         Pending the preparation of definitive Warrant Certificates evidencing
Warrants, the Company may execute and the Warrant Agent shall countersign and
deliver temporary Warrant Certificates evidencing such Warrants (printed,
lithographed, typewritten or otherwise produced, in each case in form
satisfactory to the Warrant Agent). Such temporary Warrant Certificates shall be
issuable substantially in the form of the definitive Warrant Certificates but
with such omissions, insertions and variations as may be appropriate for
temporary Warrant Certificates, all as may be determined by the Company with the
concurrence of the Warrant Agent. Such temporary Warrant Certificates may
contain such reference to any provisions of this Warrant Agreement as may be
appropriate. Every such temporary Warrant Certificate shall be executed by the
Company and shall be countersigned by the Warrant Agent upon the same conditions
and in substantially the same manner, and with like effect, as the definitive
Warrant Certificates. Without unreasonable delay, the Company shall execute and
shall furnish definitive Warrant Certificates and thereupon such temporary
Warrant Certificates may be surrendered in exchange therefor without charge
pursuant to and subject to the provisions of Section 4.01, and the Warrant Agent
shall countersign and deliver in exchange for such temporary Warrant
Certificates definitive Warrant Certificates of authorized denominations
evidencing a like aggregate number of Warrants evidenced by such temporary
Warrant Certificates. Until so exchanged, such temporary Warrant Certificates
shall be entitled to the same benefits under this Warrant Agreement as
definitive Warrant Certificates.



                                       3
<PAGE>




                                    ARTICLE 2
                WARRANT PRICE, DURATION AND EXERCISE OF WARRANTS

         SECTION 2.01. Warrant Price.

         On [ ] the exercise price of each Warrant will be [ ]. During the
period from [ ], through and including [ ], the exercise price of each Warrant
will be [ ] [plus [accrued amortization of the original issue discount] [accrued
interest] from ______.] [In each case, the original issue discount will be
amortized at a [ ]% annual rate, computed on an annual basis using the
"interest" method and using a 360-day year consisting of twelve 30-day months].
Such exercise price of Warrant Securities is referred to in this Agreement as
the "Warrant Price." [The original issue discount for each principal amount of
Warrant Securities is _______].

         SECTION 2.02. Duration of Warrants.

         Subject to Section 4.03(b), each Warrant may be exercised [in whole but
not in part] [in whole or in part] [at any time, as specified herein, on or
after [the date thereof] [______] and at or before [time, location] on [ ] (each
day during such period may hereinafter be referred to as an "Exercise Date")]
[on [list of specific dates] (each, an "Exercise Date")], or such later date as
the Company may designate by notice to the Warrant Agent and the Holders of
Warrant Certificates [in registered form and to the beneficial owners of the
Global Warrant Certificate] (the "Expiration Date"). Each Warrant not exercised
at or before [time, location] on the Expiration Date shall become void, and all
rights of the Holder [and any beneficial owners] of the Warrant Certificate
evidencing such Warrant under this Agreement shall cease.

         SECTION 2.03. Exercise of Warrants.

         [With respect to Warrants evidenced by Warrant Certificates in
registered form, during] [During] the period specified in Section 2.02, any
whole number of Warrants may be exercised by providing certain information as
set forth on the reverse side of the Warrant Certificates evidencing such
Warrants and by paying in full [in lawful money of the United States of America]
[in applicable currency] [in cash] [by certified check or official bank check or
by bank wire transfer, in each case,] [by bank wire transfer] [in immediately
available funds,] the Warrant Price for each Warrant exercised [(plus accrued
interest, if any, on the Warrant Securities to be issued upon exercise of such
Warrant from and including the Interest Payment Date (as defined in the
Indenture), if any, in respect of such Warrant Securities immediately preceding
the Exercise Date to and including the Exercise Date (unless the Exercise Date
is after the Regular Record Date (as defined in the Indenture), if any, for such
Interest Payment Date, but on or before the immediately succeeding Interest
Payment Date for such Warrant Securities, in which event no such accrued
interest shall be payable))] to the Warrant Agent at its corporate trust office
at [address] [or at ], provided that such exercise is subject to receipt within
five business days of such [payment] [wire transfer] by the Warrant Agent of the
Warrant Certificate evidencing each Warrant exercised with the form of election
to purchase Warrant Securities set forth on the reverse side of the Warrant
Certificate properly completed and duly executed. [Cashless Exercise Option].



                                       4
<PAGE>

         The date on which payment in full of the Warrant Price (plus any such
accrued interest) is received by the Warrant Agent shall, subject to receipt of
the Warrant Certificate as aforesaid, be deemed to be the date on which the
Warrant is exercised. The Warrant Agent shall deposit all funds received by it
in payment for the exercise of Warrants in an account of the Company maintained
with it (or in such other account as may be designated by the Company) and shall
advise the Company, by telephone or by facsimile transmission or other form of
electronic communication available to both parties, at the end of each day on
which a payment for the exercise of Warrants is received of the amount so
deposited to its account. The Warrant Agent shall promptly confirm such advice
to the Company in writing.

         If a day on which Warrants may be exercised in the city in which such
Warrants are to be exercised shall be a Saturday or Sunday or a day on which
banking institutions in such city are authorized or required to be closed, then,
notwithstanding any other provision of this Agreement or the Warrant Certificate
evidencing such Warrants, but subject to the limitation that no Warrant may be
exercised after the Expiration Date, the Warrants shall be exercisable on the
next succeeding day which in such city is not a Saturday or Sunday or a day on
which banking institutions in such city are authorized or required to be closed.

         The Warrant Agent shall, from time to time, as promptly as practicable,
advise the Company [and the Trustee] in writing of (i) the number of Warrants
exercised, (ii) the instructions of each Holder of the Warrant Certificates
evidencing such Warrants with respect to delivery of the Warrant Securities to
be issued upon such exercise, (iii) delivery of any Warrant Certificates
evidencing the balance, if any, of the Warrants remaining after such exercise,
and (iv) such other information as the Company or the Trustee shall reasonably
require.

         As soon as practicable after the exercise of any Warrant, but subject
to receipt by the Warrant Agent of the Warrant Certificate evidencing such
Warrant as provided in this Section, the Company shall issue[, pursuant to the
Indenture, in authorized denominations to or upon the order of the Holder of the
Warrant Certificate evidencing each Warrant,] the Warrant Securities to which
such Holder is entitled, in fully registered form, registered in such name or
names as may be directed by such Holder. If fewer than all of the Warrants
evidenced by such Warrant Certificate are exercised, the Company shall execute,
and an authorized officer of the Warrant Agent shall manually countersign and
deliver, a new Warrant Certificate evidencing the number of such Warrants
remaining unexercised.

         The Company shall not be required to pay any stamp or other tax or
other governmental charge required to be paid in connection with any transfer
involved in the issuance of the Warrant Securities, and in the event that any
such transfer is involved, the Company shall not be required to issue or deliver
any Warrant Security until such tax or other charge shall have been paid or it
has been established to the Company's satisfaction that no such tax or other
charge is due.



                                       5
<PAGE>

                                   ARTICLE 3
            OTHER PROVISIONS RELATING TO RIGHTS OF HOLDERS OF WARRANT

         SECTION 3.01. No Rights as Warrant Securityholder Conferred by Warrants
                       or Warrant Certificates.

         No Warrant Certificate or Warrant evidenced thereby shall entitle the
Holder or any beneficial owner thereof to any of the rights of a holder or
beneficial owner of Warrant Securities, including, without limitation, [the
right to receive the payment of principal of (premium, if any) or interest, if
any, on Warrant Securities or to enforce any of the covenants in the Indenture]
[the right to receive dividend payments on the Warrant Securities or any voting
rights].

         SECTION  3.02. Lost, Mutilated, Stolen or Destroyed Warrant
                        Certificates.

         Upon receipt by the Warrant Agent of evidence reasonably satisfactory
to it and the Company of the ownership of and the loss, mutilation, theft or
destruction of any Warrant Certificate and of such security or indemnity as may
be required by the Company and the Warrant Agent to hold each of them and any
agent of them harmless and, in the case of mutilation of a Warrant Certificate,
upon surrender thereof to the Warrant Agent for cancellation, then, in the
absence of notice to the Company or the Warrant Agent that such Warrant
Certificate has been acquired by a bona fide purchaser, the Company shall
execute, and an authorized officer of the Warrant Agent shall manually
countersign and deliver, in exchange for or in lieu of the lost, mutilated,
stolen or destroyed Warrant Certificate, a new Warrant Certificate of the same
tenor and evidencing a like number of Warrants. Upon the issuance of any new
Warrant Certificate under this Section, the Company may require the payment of a
sum sufficient to cover any stamp or other tax or other governmental charge that
may be imposed in relation thereto and any other expenses (including the fees
and expenses of the Warrant Agent) in connection therewith. Every substitute
Warrant Certificate executed and delivered pursuant to this Section in lieu of
any lost, mutilated, stolen or destroyed Warrant Certificate shall represent an
additional contractual obligation of the Company, whether or not the lost,
stolen or destroyed Warrant Certificate shall be at any time enforceable by
anyone, and shall be entitled to the benefits of this Agreement equally and
proportionately with any and all other Warrant Certificates duly executed and
delivered hereunder. The provisions of this Section are exclusive and shall
preclude (to the extent lawful) all other rights and remedies with respect to
the replacement of lost, mutilated, stolen or destroyed Warrant Certificates.

         SECTION 3.03. Enforcement of Rights.

         Notwithstanding any of the provisions of this Agreement, any Holder of
a Warrant Certificate, without the consent of the Warrant Agent, the Trustee,
the holder of any Offered Securities or the Holder of any other Warrant
Certificate, may, in its own behalf and for its own benefit, enforce, and may
institute and maintain any suit, action or proceeding against the Company
suitable to enforce, or otherwise in respect of, its right to exercise its
Warrants in the manner provided in its Warrant Certificate and in this
Agreement.



                                       6
<PAGE>

         SECTION 3.04. Merger, Amalgamation, Consolidation, Conveyance or
                       Transfer.

         (a) If at any time there shall be a merger or amalgamation or
consolidation of the Company or a conveyance or transfer of its property and
assets substantially as an entirety [as permitted under the Indenture], then in
any such event the successor or assuming corporation referred to therein shall
succeed to and be substituted for the Company, with the same effect[, subject to
the Indenture,] as if it had been named herein and in the Warrant Certificates
as the Company; the Company shall thereupon, except in the case of a transfer by
way of lease, be relieved of any further obligation hereunder and under the
Warrants and the Warrant Certificates, and the Company as the predecessor
corporation, except in the case of a transfer by way of lease, may thereupon or
at any time thereafter be dissolved, wound up or liquidated. Such successor or
assuming corporation may thereupon cause to be signed, and may issue either in
its own name or in the name of the Company, Warrant Certificates evidencing any
or all of the Warrants issuable hereunder which theretofore shall not have been
signed by the Company, and may execute and deliver Warrant Securities in its own
name [, pursuant to the Indenture], in fulfillment of its obligations to deliver
Warrant Securities upon exercise of the Warrants. All the Warrants so issued
shall in all respects have the same legal rank and benefit under this Agreement
as the Warrants theretofore or thereafter issued in accordance with the terms of
this Agreement as though all of such Warrants had been issued at the date of the
execution hereof. In any case of any such merger, amalgamation, consolidation,
conveyance or transfer, such changes in phraseology and form (but not in
substance) may be made in the Warrant Certificates representing the Warrants
thereafter to be issued as may be appropriate.

         (b) The Warrant Agent may receive a written opinion of legal counsel
(who shall be acceptable to the Warrant Agent) as conclusive evidence that any
such merger, consolidation, conveyance or transfer complies with the provisions
of this Section and the Indentures.

         [Add Anti-Dilution provisions as necessary.]

                                   ARTICLE 4
                              EXCHANGE AND TRANSFER

         SECTION 4.01. Exchange and Transfer.

         (a) Upon surrender at the corporate trust office of the Warrant Agent
at [address] [or ], Warrant Certificates evidencing Warrants may be exchanged
for Warrant Certificates in other authorized denominations evidencing such
Warrants or the transfer thereof may be registered in whole or in part;
provided, however, that such other Warrant Certificates shall evidence the same
aggregate number of Warrants as the Warrant Certificates so surrendered.


                                       7
<PAGE>

         (b) The Warrant Agent shall keep, at its corporate trust office at
[address] [and at ], books in which, subject to such reasonable regulations as
it may prescribe, it shall register Warrant Certificates and exchanges and
transfers of outstanding Warrant Certificates upon surrender of such Warrant
Certificates to the Warrant Agent at its corporate trust office at [address] [or
] for exchange or registration of transfer, properly endorsed [or accompanied by
appropriate instruments of registration of transfer and written instructions for
transfer, all in form satisfactory to the Company and the Warrant Agent.]

         (c) No service charge shall be made for any exchange or registration of
transfer of Warrant Certificates, but the Company may require payment of a sum
sufficient to cover any stamp or other tax or other governmental charge that may
be imposed in connection with any such exchange or registration of transfer.

         (d) Whenever any Warrant Certificates, are so surrendered for exchange
or registration of transfer, an authorized officer of the Warrant Agent shall
manually countersign and deliver to the person or persons entitled thereto a
Warrant Certificate or Warrant Certificates, duly authorized and executed by the
Company, as so requested. The Warrant Agent shall not effect any exchange or
registration of transfer which will result in the issuance of a Warrant
Certificate, evidencing a fraction of a Warrant or a number of full Warrants and
a fraction of a Warrant.

         (e) All Warrant Certificates, issued upon any exchange or registration
of transfer of Warrant Certificates shall be the valid obligations of the
Company, evidencing the same obligations, and entitled to the same benefits
under this Agreement, as the Warrant Certificates surrendered for such exchange
or registration or transfer.

         SECTION 4.02. Treatment of Holders of Warrant Certificates.

         Each Holder of a Warrant Certificate, by accepting the same, consents
and agrees with the Company, the Warrant Agent and every subsequent Holder of
such Warrant Certificate that until the transfer of such Warrant Certificate is
registered on the books of such Warrant Agent, the Company and the Warrant Agent
may treat the registered Holder of such Warrant Certificate as the absolute
owner thereof for any purpose and as the person entitled to exercise the rights
represented by the Warrants evidenced thereby, any notice to the contrary
notwithstanding.

         SECTION 4.03. Cancellation of Warrant Certificates.

         [(a)] Any Warrant Certificate surrendered for exchange or registration
of transfer or exercise of the Warrants evidenced thereby shall, if surrendered
to the Company, be delivered to the Warrant Agent, and all Warrant Certificates
surrendered or so delivered to the Warrant Agent shall be promptly cancelled by
the Warrant Agent and shall not be reissued and, except as expressly permitted
by this Agreement, no Warrant Certificate shall be issued hereunder in exchange
therefor or in lieu thereof. The Warrant Agent shall cause all cancelled Warrant
Certificates to be destroyed and shall deliver a certificate of such destruction
to the Company.



                                       8
<PAGE>

         [(b) If the Company notifies the Trustee of its election to redeem [,
as a whole but not in part,] the Warrant Securities pursuant to the Indenture or
the terms thereof, the Company may elect, and shall give notice to the Warrant
Agent of its election, to cancel the unexercised Warrants, the Warrant
Certificates and the rights evidenced thereby. Promptly after receipt of such
notice by the Warrant Agent, the Company shall, or, at the Company's request,
the Warrant Agent shall in the name of and at the expense of the Company, give
notice of such cancellation to the Holders of the Warrant Certificates, such
notice to be so given not less than 30 nor more than 60 days prior to the date
fixed for the redemption of the Warrant Securities pursuant to the Indenture or
the terms thereof. The unexercised Warrants, the Warrant Certificates and the
rights evidenced thereby shall be cancelled and become void on the 15th day
prior to such date fixed for redemption.]

                                   ARTICLE 5
                          CONCERNING THE WARRANT AGENT

         SECTION 5.01. Warrant Agent.

         The Company hereby appoints [ ] as Warrant Agent of the Company in
respect of the Warrants and the Warrant Certificates upon the terms and subject
to the conditions herein and in the Warrant Certificates set forth; and [ ]
hereby accepts such appointment. The Warrant Agent shall have the powers and
authority granted to and conferred upon it in the Warrant Certificates and
herein and such further powers and authority to act on behalf of the Company as
the Company may hereafter grant to or confer upon it. All of the terms and
provisions with respect to such powers and authority contained in the Warrant
Certificates are subject to and governed by the terms and provisions hereof.

         SECTION 5.02. Conditions of Warrant Agent's Obligations.

         The Warrant Agent accepts its obligations herein set forth upon the
terms and conditions hereof, including the following, to all of which the
Company agrees and to all of which the rights hereunder of the Holders from time
to time of the Warrant Certificates shall be subject:

         (a) Compensation and Indemnification. The Company agrees promptly to
pay the Warrant Agent the compensation to be agreed upon with the Company for
all services rendered by the Warrant Agent and to reimburse the Warrant Agent
for reasonable out-of-pocket expenses (including reasonable attorneys' fees)
incurred by the Warrant Agent without negligence, bad faith or willful
misconduct or breach of this Agreement on its part in connection with the
services rendered hereunder by the Warrant Agent. The Company also agrees to
indemnify the Warrant Agent for, and to hold it harmless against, any loss,
liability or expense incurred without negligence, bad faith or willful
misconduct on the part of the Warrant Agent, arising out of or in connection
with its acting as Warrant Agent hereunder, as well as the reasonable costs and
expenses of defending against any claim of such liability.



                                       9
<PAGE>

         (b) Agent for the Company. In acting under this Agreement and in
connection with the Warrants and the Warrant Certificates, the Warrant Agent is
acting solely as agent of the Company and does not assume any obligation or
relationship of agency or trust for or with any of the Holders of Warrant
Certificates or beneficial owners of Warrants.

         (c) Counsel. The Warrant Agent may consult with counsel satisfactory to
it in its reasonable judgment, and the advice of such counsel shall be full and
complete authorization and protection in respect of any action taken, suffered
or omitted by it hereunder in good faith and in accordance with the advice of
such counsel.

         (d) Documents. The Warrant Agent shall be protected and shall incur no
liability for or in respect of any action taken or thing suffered by it in
reliance upon any Warrant Certificate, notice, direction, consent, certificate,
affidavit, statement or other paper or document reasonably believed by it to be
genuine and to have been presented or signed by the proper parties.

         (e) Certain Transactions. The Warrant Agent, and its officers,
directors and employees, may become the owner of, or acquire any interest in,
Warrants, with the same rights that it or they would have if it were not the
Warrant Agent hereunder, and, to the extent permitted by applicable law, it or
they may engage or be interested in any financial or other transaction with the
Company and may act on, or as depositary, trustee or agent for, any committee or
body of holders of Warrant Securities or other obligations of the Company as
freely as if it were not the Warrant Agent hereunder. [Nothing in this Warrant
Agreement shall be deemed to prevent the Warrant Agent from acting as Trustee
under the Indenture.]

         (f) No Liability for Interest. The Warrant Agent shall have no
liability for interest on any monies at any time received by it pursuant to any
of the provisions of this Agreement or of the Warrant Certificates.

         (g) No Liability for Invalidity. The Warrant Agent shall not be under
any responsibility with respect to the validity or sufficiency of this Agreement
or the execution and delivery hereof (except the due authorization to execute
this Agreement and the due execution and delivery hereof by the Warrant Agent)
or with respect to the validity or execution of any Warrant Certificates (except
its countersignature thereof).

         (h) No Liability for Recitals. The recitals contained herein shall be
taken as the statements of the Company and the Warrant Agent assumes no
liability for the correctness of the same.



                                       10
<PAGE>

         (i) No Implied Obligations. The Warrant Agent shall be obligated to
perform only such duties as are herein and in the Warrant Certificates
specifically set forth and no implied duties or obligations shall be read into
this Agreement or the Warrant Certificates against the Warrant Agent. The
Warrant Agent shall not be under any obligation to take any action hereunder
which may tend to involve it in any expense or liability, the payment of which
within a reasonable time is not, in its reasonable opinion, assured to it. The
Warrant Agent shall not be accountable or under any duty or responsibility for
the use by the Company of any of the Warrant Certificates countersigned by the
Warrant Agent and delivered by it to the Company pursuant to this Agreement or
for the application by the Company of the proceeds of the Warrant Certificates.
The Warrant Agent shall have no duty or responsibility in case of any default by
the Company in the performance of its covenants or agreements contained herein
or in the Warrant Certificates or in the case of the receipt of any written
demand from a Holder of a Warrant Certificate with respect to such default,
including, without limiting the generality of the foregoing, any duty or
responsibility to initiate or attempt to initiate any proceedings at law or
otherwise or, except as provided in Section 6.02, to make any demand upon the
Company.

         SECTION 5.03. Resignation and Appointment of Successor.

         (a) The Company agrees, for the benefit of the Holders from time to
time of the Warrant Certificates, that there shall at all times be a Warrant
Agent hereunder until all the Warrants have been exercised or are no longer
exercisable.

         (b) The Warrant Agent may at any time resign as such by giving written
notice of its resignation to the Company, specifying the desired date on which
its resignation shall become effective; provided, however, that such date shall
be not less than 90 days after the date on which such notice is given unless the
Company agrees to accept shorter notice. Upon receiving such notice of
resignation, the Company shall promptly appoint a successor Warrant Agent (which
shall be a bank or trust company in good standing, authorized under the laws of
the jurisdiction of its organization to exercise corporate trust powers) by
written instrument in duplicate signed on behalf of the Company, one copy of
which shall be delivered to the resigning Warrant Agent and one copy to the
successor Warrant Agent. The Company may, at any time and for any reason, remove
the Warrant Agent and appoint a successor Warrant Agent (qualified as aforesaid)
by written instrument in duplicate signed on behalf of the Company and
specifying such removal and the date when it is intended to become effective,
one copy of which shall be delivered to the Warrant Agent being removed and one
copy to the successor Warrant Agent. Any resignation or removal of the Warrant
Agent and any appointment of a successor Warrant Agent shall become effective
upon acceptance of appointment by the successor Warrant Agent as provided in
this subsection (b). In the event a successor Warrant Agent has not been
appointed and accepted its duties within 90 days of the Warrant Agent's notice
of resignation, the Warrant Agent may apply to any court of competent
jurisdiction for the designation of a successor Warrant Agent. Upon its
resignation or removal, the Warrant Agent shall be entitled to the payment by
the Company of the compensation and to the reimbursement of all reasonable
out-of-pocket expenses (including reasonable attorneys' fees) incurred by it
hereunder as agreed to in Section 5.02(a).



                                       11
<PAGE>

         (c) The Company shall remove the Warrant Agent and appoint a successor
Warrant Agent if the Warrant Agent (i) shall become incapable of acting, (ii)
shall be adjudged bankrupt or insolvent, (iii) shall commence a voluntary case
or other proceeding seeking 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, custodian or other similar official of it or any substantial part of
its property, (iv) shall consent to, or shall have had entered against it a
court order for, any such relief or to the appointment of or taking possession
by any such official in any involuntary case or other proceedings commenced
against it, (v) shall make a general assignment for the benefit of creditors or
(vi) shall fail generally to pay its debts as they become due. Upon the
appointment as aforesaid of a successor Warrant Agent and acceptance by it of
such appointment, the predecessor Warrant Agent shall, if not previously
disqualified by operation of law, cease to be Warrant Agent hereunder.

         (d) Any successor Warrant Agent appointed hereunder shall execute,
acknowledge and deliver to its predecessor and the Company an instrument
accepting such appointment hereunder, and thereupon such successor Warrant
Agent, without any further act, deed or conveyance, shall become vested with all
the authority, rights, powers, immunities, duties and obligations of such
predecessor with like effect as if originally named as Warrant Agent hereunder,
and such predecessor shall thereupon become obligated to transfer, deliver and
pay over, and such successor Warrant Agent shall be entitled to receive, all
monies, securities and other property on deposit with or held by such
predecessor as Warrant Agent hereunder.

         (e) Any corporation into which the Warrant Agent hereunder may be
merged or converted or any corporation with which the Warrant Agent may be
consolidated, or any corporation resulting from any merger, conversion or
consolidation to which the Warrant Agent shall be a party, or any corporation to
which the Warrant Agent shall sell or otherwise transfer all or substantially
all the assets and business of the Warrant Agent, provided that it shall be
qualified as aforesaid, shall be the successor Warrant Agent under this
Agreement without the execution or filing of any paper or any further act on the
part of any of the parties hereto.

                                    ARTICLE 6
                                  MISCELLANEOUS

         SECTION 6.01. Amendment.

         This Agreement and the terms of the Warrants and the Warrant
Certificates may be amended by the parties hereto, without the consent of the
Holder of any Warrant Certificate or the beneficial owner of any Warrant, for
the purpose of curing any ambiguity, or of curing, correcting or supplementing
any defective or inconsistent provision contained herein or in the Warrant
Certificates, or making any other provisions with respect to matters or
questions arising under this Agreement as the Company and the Warrant Agent may
deem necessary or desirable, provided that such action shall not affect
adversely the interests of the Holders of the Warrant Certificates or the
beneficial owners of Warrants in any material respect.


                                       12
<PAGE>

         SECTION 6.02. Notices and Demands to the Company and Warrant Agent.

         If the Warrant Agent shall receive any notice or demand addressed to
the Company by the Holder of a Warrant Certificate pursuant to the provisions of
the Warrant Certificates, the Warrant Agent shall promptly forward such notice
or demand to the Company.

         SECTION 6.03. Addresses.

         Any communication from the Company to the Warrant Agent with respect to
this Agreement shall be addressed to [ ], Attention: [ ], and any communication
from the Warrant Agent to the Company with respect to this Agreement shall be
addressed to Endurance Specialty Holdings Ltd., Wellesley House, 90 Pitts Bay
Road, Pembroke HM 08, Bermuda, Attention: General Counsel (or such other address
as shall be specified in writing by the Warrant Agent or by the Company).

         SECTION 6.04. Applicable Law.

         The validity, interpretation and performance of this Agreement and each
Warrant Certificate issued hereunder and of the respective terms and provisions
hereof and thereof shall be governed by, and construed in accordance with, the
laws of the State of New York.

         SECTION 6.05. Delivery of Prospectus.

         The Company will furnish to the Warrant Agent sufficient copies of a
prospectus relating to the Warrant Securities deliverable upon exercise of
Warrants (the "Prospectus"), and the Warrant Agent agrees that upon the exercise
of any Warrant, the Warrant Agent will deliver to the Holder of the Warrant
Certificate evidencing such Warrant, prior to or concurrently with the delivery
of the Warrant Securities issued upon such exercise, a Prospectus. The Warrant
Agent shall not, by reason of any such delivery, assume any responsibility for
the accuracy or adequacy of such Prospectus.

         SECTION 6.06. Obtaining of Governmental Approval.

         The Company will from time to time take all action which may be
necessary to obtain and keep effective any and all permits, consents and
approvals of governmental agencies and authorities and securities acts filings
under United States federal and state laws (including without limitation a
registration statement in respect of the Warrants and Warrant Securities under
the Securities Act of 1933), which may be or become requisite in connection with
the issuance, sale, transfer and delivery of the Warrant Certificates, the
exercise of the Warrants, the issuance, sale, transfer and delivery of the
Warrant Securities issued upon exercise of the Warrants or upon the expiration
of the period during which the Warrants are exercisable.



                                       13
<PAGE>

         SECTION 6.07. Persons Having Rights Under Warrant Agreement.

         Nothing in this Agreement shall give to any person other than the
Company, the Warrant Agent and the Holders of the Warrant Certificates any
right, remedy or claim under or by reason of this Agreement.

         SECTION 6.08. Headings.

         The descriptive headings of the several Articles and Sections of this
Agreement are inserted for convenience only and shall not control or affect the
meaning or construction of any of the provisions hereof.

         SECTION 6.09. Counterparts.

         This Agreement may be executed in any number of counterparts, each of
which as so executed shall be deemed to be an original, but such counterparts
shall together constitute but one and the Same instrument.

         SECTION 6.10. Inspection of Agreement.

         A copy of this Agreement shall be available at all reasonable times at
the principal corporate trust office of the Warrant Agent for inspection by the
Holder of any Warrant Certificate. The Warrant Agent may require such Holder to
submit his Warrant Certificate for inspection by it.

         SECTION 6.11. Notices to Holders of Warrants.

         Any notice to Holders of Warrants evidenced by Warrant Certificates
which by any provisions of this Warrant Agreement is required or permitted to be
given shall be given by first class mail prepaid at such Holder's address as it
appears on the books of the Warrant Agent.


                                       14
<PAGE>


         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed.


                                              ENDURANCE SPECIALTY HOLDINGS LTD.

                                              By:__________________________
                                                 Name:
                                                 Title:


                                              [WARRANT AGENT]

                                              By:__________________________
                                                 Name:
                                                 Title:



                                       15
<PAGE>

                                                                       EXHIBIT A

                          [FORM OF WARRANT CERTIFICATE]

                                     [Face]


Form of Legend if                               [Prior to ________________,
Warrants are not                                Warrants evidenced by this
immediately exercisable:                        Warrant Certificate cannot be
                                                exercised.]

                EXERCISABLE ONLY IF AUTHENTICATED BY THE WARRANT
                            AGENT AS PROVIDED HEREIN

               VOID AFTER THE CLOSE OF BUSINESS ON _________, ____
                        ENDURANCE SPECIALTY HOLDINGS LTD.

                        Warrant Certificate representing
                              Warrants to purchase
                          [Title of Warrant Securities]
                               as described herein

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

No.
Warrants

         This certifies that [_____________________] or registered assigns is
the registered owner of the above indicated number of Warrants, each Warrant
entitling such registered owner to purchase, at any time [after the close of
business on _________, ____, and] on or before the close of business on
____________, ____, [____ shares of the [Title of Warrant Securities]]
[$________ aggregate principal amount of [Title of Warrant Securities]](the
"Warrant Securities") of Endurance Specialty Holdings Ltd. (the "Company")[,
issued or to be issued under the Indenture (as hereinafter defined),] on the
following basis.(2) [During the period from ________, ____ through and including
___________, ____, each Warrant shall entitle the Holder thereof, subject to the
provisions of this Agreement, to purchase from the Company the [principal]
amount of Warrant Securities stated above in this Warrant Certificate at the
exercise price of [ ] [___% of the principal amount thereof [plus accrued
amortization, if any, of the original issue discount of the Warrant
Securities][plus accrued interest, if any, from the most recent date from which
interest shall have been paid on the Warrant Securities or, if no interest shall
have been paid on the Warrant Securities, from ___________, ____]; [in each
case, the original issue discount ($_______ for each $1,000 principal amount of
Warrant Securities) will be amortized at a ___% annual rate, computed on a[n]
[semi-]annual basis[, using a 360-day year constituting of twelve 30-day
months]] (the "Exercise Price"). The Holder of this Warrant Certificate may
exercise the Warrants evidenced hereby, in whole or in part, by surrendering
this Warrant Certificate, with the purchase form set forth hereon duly
completed, accompanied [by payment in full, in lawful money of the United States
of America, [in cash or by certified check or official bank check in New York
Clearing House funds] [by bank wire transfer in immediately available funds]],
the Exercise Price for each Warrant exercised, to the Warrant Agent (as
hereinafter defined), at the corporate trust office of [name of Warrant Agent],
or its successor as warrant agent (the "Warrant Agent") [or at ____________,] at
the addresses specified on the reverse hereof and upon compliance with and
subject to the conditions set forth herein and in the Warrant Agreement (as
hereinafter defined). This Warrant Certificate may be exercised only for the
purchase of [ shares of] Warrant Securities [in the principal amount of       ]
or any integral multiple thereof. [Cashless Exercise Option].

-------------------
(2) Complete and modify the following provisions as appropriate to reflect the
    terms of the Warrants and the Warrant Securities.



                                       A-1
<PAGE>

         The term "Holder" as used herein shall mean the person in whose name at
the time such Warrant Certificate shall be registered upon the books to be
maintained by the Warrant Agent for that purpose pursuant to Section 3.01 of the
Warrant Agreement.

         Any whole number of Warrants evidenced by this Warrant Certificate may
be exercised to purchase Warrant Securities in registered form. Upon any
exercise of fewer than all of the Warrants evidenced by this Warrant
Certificate, there shall be issued to the registered owner hereof a new Warrant
Certificate evidencing the number of Warrants remaining unexercised.

         This Warrant Certificate is issued under and in accordance with the
Warrant Agreement dated as of __________, ____ (the "Warrant Agreement"),
between the Company and the Warrant Agent and is subject to the terms and
provisions contained in the Warrant Agreement, to all of which terms and
provisions the Holder of this Warrant Certificate consents by acceptance hereof.
Copies of the Warrant Agreement are on file at the above-mentioned office of the
Warrant Agent [and at _______________].

         [The Warrant Securities to be issued and delivered upon the exercise of
Warrants evidenced by this Warrant Certificate will be issued under and in
accordance with an Indenture, dated as of ________________ (the "Indenture"),
between the Company and ________________, a [corporation] [national banking
association] organized under the laws of the State of __________, as trustee
(such trustee, and any successors to such trustee, the "Trustee") and will be
subject to the terms and provisions contained in the Warrant Securities and in
the Indenture. Copies of the Indenture, including the form of the Warrant
Securities, are on file at the corporate trust office of the Trustee [and at
               ].]

         This Warrant Certificate, and all rights hereunder, may be transferred
when surrendered at the corporate trust office of the Warrant Agent [or
_________] by the registered owner or his assigns, in person or by an attorney
duly authorized in writing, in the manner and subject to the limitations
provided in the Warrant Agreement.



                                       A-2
<PAGE>

         After authentication by the Warrant Agent and prior to the expiration
of this Warrant Certificate, this Warrant Certificate may be exchanged at the
corporate trust office of the Warrant Agent [or at _____________] for Warrant
Certificates representing the same aggregate number of Warrants.

         This Warrant Certificate shall not entitle the registered owner hereof
to any of the rights of a registered holder of the Warrant Securities,
including, without limitation, [the right to receive payments of principal of
(and premium, if any) or interest, if any, on the Warrant Securities or to
enforce any of the covenants of the Indenture] [the right to receive dividend
payments on the Warrant Securities or any voting rights].

         Reference is hereby made to the further provisions of this Warrant
Certificate set forth on the reverse hereof, which further provisions shall for
all purposes have the same effect as if set forth at this place.

         This Warrant Certificate shall not be valid or obligatory for any
purpose until authenticated by the Warrant Agent.

         IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be duly executed.

         Dated:
               ---------------

                                       ENDURANCE SPECIALTY HOLDINGS LTD.

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


Attest:

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


                          Certificate of Authentication

         This is one of the Warrant Certificates referred to in the
within-mentioned Warrant Agreement.

-----------------------------------
          As Warrant Agent

By:
   --------------------------------
       Authorized Signature



                                      A-3
<PAGE>



                     [REVERSE] [FORM OF WARRANT CERTIFICATE]
                     (Instructions for Exercise of Warrants)

         To exercise any Warrants evidenced hereby, the Holder of this Warrant
Certificate must pay [in cash or by certified check or official bank check in
New York Clearing House funds or by bank wire transfer in immediately available
funds], the Exercise Price in full for each of the Warrants exercised, to
_________, Corporate Trust Department, _______________, Attn: ___________ [or
________________], which payment should specify the name of the Holder of this
Warrant Certificate and the number of Warrants exercised by such Holder. In
addition, the Holder of this Warrant Certificate should complete the information
required below and present in person or mail by registered mail this Warrant
Certificate to the Warrant Agent at the addresses set forth below.

                               [FORM OF EXERCISE]
                   (To be executed upon exercise of Warrants.)

         The undersigned hereby irrevocably elects to exercise _________
Warrants, represented by this Warrant Certificate, to purchase [_______ shares
of [Title of Equity Securities]] [$_________ aggregate principal amount of the
[Title of Debt Securities]] (the "Warrant Securities") of Endurance Specialty
Holdings Ltd. and represents that he has tendered payment for such Warrant
Securities [in cash or by certified check or official bank check in New York
Clearing House funds or by bank wire transfer in immediately available funds] to
the order of Endurance Specialty Holdings Ltd., c/o [ ] in the amount of
$___________ in accordance with the terms hereof. The undersigned requests that
said [principal] amount of Warrant Securities be in fully registered form, in
the authorized denominations, registered in such names and delivered, all as
specified in accordance with the instructions set forth below.

         If said [principal] amount of Warrant Securities is less than all of
the Warrant Securities purchasable hereunder, the undersigned requests that a
new Warrant Certificate representing the remaining balance of the Warrants
evidenced hereby be issued and delivered to the undersigned unless otherwise
specified in the instructions below.

Dated:
       --------------

Name
    -----------------------------
          (Please Print)

---------------------------------
(Insert Social Security or Other
Identifying Number of Holder)

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



                                       A-4
<PAGE>

Signature
         -----------------------
           (Signed exactly as name appears
           on the other side of this Warrant
           Certificate)

                       This Warrant may be exercised at the following addresses:
                           By hand at
                                          -----------------------------
                                          -----------------------------
                                          -----------------------------
                                          -----------------------------

                           By mail at
                                          -----------------------------
                                          -----------------------------
                                          -----------------------------
                                          -----------------------------

(Instructions as to form and delivery of Warrant Securities and/or Warrant
Certificates):




                                      A-5
<PAGE>



                              [[FORM OF ASSIGNMENT]

              (TO BE EXECUTED TO TRANSFER THE WARRANT CERTIFICATE)

         FOR VALUE RECEIVED __________________ hereby sells, assigns and
transfers unto
                                                        Please insert social
                                                        security or other
                                                        identifying number

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

-----------------------------------
(Please print name and address
including zip code)


________________________________________________________________________________
the right represented by the within Warrant Certificate and does hereby
irrevocably constitute and appoint _________________, Attorney, to transfer said
Warrant Certificate on the books of the Warrant Agent with full power of
substitution.

Dated: _____________


                           --------------------------------------
                                          Signature
                           (Signed exactly as name appears on the
                           other side of this Warrant Certificate)

Signature Guarantee:


-------------------------------------
Participant in a recognized Signature
Guarantee Medallion Program (or other
signature guarantor program reasonably
acceptable to the Warrant Agent)



                                      A-6