<PAGE>



================================================================================





                                WARRANT AGREEMENT



                                     between



                                  eSpeed, Inc.



                                       and



                        Exchange Brokerage Systems Corp.










                         Dated as of September 13, 2001






================================================================================


<PAGE>



                                WARRANT AGREEMENT


       This Warrant Agreement (this "Agreement") is entered into as of September
13, 2001 between eSpeed, Inc., a Delaware corporation ("eSpeed"), and Exchange
Brokerage Systems Corp., a New York corporation ("EBS").


                               W I T N E S S E T H
                               -------------------

       WHEREAS eSpeed has entered into a Purchase Agreement, dated as ofAugust
7, 2001, with EBS (the "Purchase Agreement"), providing for the purchase by
eSpeed of certain intellectual property rights owned by EBS;

       WHEREAS the Purchase Agreement provides that eSpeed will issue to EBS
15,000 warrants (the "Warrants"), each Warrant entitling the holder to purchase
initially one share of eSpeed Class A Common Stock (as hereinafter defined)
subject to adjustment, upon the terms and subject to the conditions hereinafter
set forth; and

       WHEREAS eSpeed is duly authorized to create and issue the Warrants as
herein provided;

       NOW, THEREFORE, in consideration of the premises and the mutual
agreements hereinafter set forth, the parties hereby agree as follows:

       Section 1. Certain Definitions

       For purposes of this Agreement, the following terms have the meanings
indicated.

       (a) "Affiliate" of any Person means any other Person directly or
indirectly controlling, controlled by or under common control with such Person
at the time at which the determination of affiliation is made.

       (b) "Business Day" means any day other than a Saturday, Sunday or a day
on which banks are generally not open for business in the City of New York.

       (c) "Close of Business" on any given date shall mean 5:00 P.M., New York
City time, on such date; provided, however, that if such date is not a Business
Day, it shall mean 5:00 P.M., New York City time, on the next succeeding
Business Day.

       (d) "Closing Date" means the date hereof.

       (e) "Closing Price" with respect to a share of eSpeed Class A Common
Stock on any day means the last reported sale price on that day during regular
trading hours or, in case no reported sale takes place on such day, the average
of the last reported bid and asked prices, regular way, on that day during
regular trading hours, in either case, as reported in the consolidated
transaction reporting system with respect to securities reported on Nasdaq or,
if the


                                                                               2
<PAGE>

shares of eSpeed Class A Common Stock are not then quoted on Nasdaq, as reported
in the principal consolidated transaction reporting system with respect to
securities listed on the principal national securities exchange on which the
shares of eSpeed Class A Common Stock are then listed or admitted to trading or,
if the shares of eSpeed Class A Common Stock are not quoted on Nasdaq and then
not listed or admitted to trading on any national securities exchange, the last
quoted price or, if not so quoted, the average of the high bid and low asked
prices during regular trading hours on such other nationally recognized
quotation system then in use, or, if on any such day the shares of eSpeed Class
A Common Stock are not quoted on any such quotation system, the average of the
closing bid and asked prices as furnished by a professional market maker
selected by the Board of Directors of eSpeed making a market in the shares of
eSpeed Class A Common Stock. If the shares of eSpeed Class A Common Stock are
not then publicly held or so listed, quoted or publicly traded, the term
"Closing Price" means the fair market value of a share of eSpeed Class A Common
Stock, as determined in good faith by the Board of Directors of eSpeed.

       (f) "Current Market Price" has the meaning set forth in Section 10(a).

       (g) "Dollars" and "$" mean U.S. dollars.

       (h) "eSpeed Class A Common Stock" means the Class A common stock, par
value $0.01 per share, of eSpeed.

       (i) "Exercise Period" means the period at any time after the Closing Date
and ending at the Close of Business on the 10 year anniversary of the Closing
Date.

       (j) "Purchase Agreement" has the meaning set forth in the recitals
hereto.

       (k) "Nasdaq" means The Nasdaq Stock Market.

       (l) "Person" means any corporation (including a limited or unlimited
liability company), general or limited partnership, joint venture, estate,
trust, association, organization or other entity or governmental or regulatory
authority or agency.

       (m) "Securities Act" means the U.S. Securities Act of 1933 or any
successor U.S. federal statute, and the rules and regulations of the U.S.
Securities Exchange Commission or any successor authority promulgated
thereunder, all as the same shall be in effect from time to time.

       (n) "Share Rate" has the meaning set forth in Section 2(a).

       (o) "Trading Day " means any day on which Nasdaq is open for the
transaction of business.

       (p) "Warrant Certificate" has the meaning set forth in Section 2(b).

       (q) "Warrantholder" means a holder of a Warrant Certificate.

       (r) "Warrants" has the meaning set forth in the recitals hereto.


                                                                               3

<PAGE>

       Section 2. Issue of Warrants and Form of Warrant Certificates

       (a) A total of 15,000 Warrants are hereby created and authorized to be
issued hereunder upon the terms and conditions herein set forth, and shall be
executed by eSpeed, each Warrant entitling the registered holder thereof to
acquire a number of shares of eSpeed Class A Common Stock for each such Warrant
(the "Share Rate"), subject to adjustment as provided herein, at an initial
Share Rate of one share of eSpeed Class A Common Stock for each Warrant.

       (b) The certificate representing the Warrants, including the form of
election to purchase eSpeed Class A Common Stock (the "Warrant Certificate"),
shall be substantially in the form of Exhibit I hereto and may have such marks
of identification or designation and such legends, summaries or endorsements
printed thereon as eSpeed may deem appropriate 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 to conform to usage.
Subject to the provisions of Section 14, the Warrant Certificate, when issued,
shall be dated the Closing Date and on its face shall entitle the holders
thereof to purchase such number of shares of eSpeed Class A Common Stock at an
initial price per share of $10.83 (the "Exercise Price"), payable in cash;
provided that such number of shares and the Exercise Price shall be subject to
the adjustments provided in this Agreement.

       Section 3. Signature and Registration

       The Warrant Certificate shall be executed on behalf of eSpeed by its
Chief Executive Officer, Vice Chairman or President, either manually or by
facsimile signature, and have affixed thereto eSpeed's seal or a facsimile
thereof which shall be attested by the Secretary or an Assistant Secretary of
eSpeed, either manually or by facsimile signature.

       Section 4. Transfer; Mutilated, Destroyed, Lost or Stolen Warrant
Certificate

       (a) EBS shall not sell, transfer, assign, hypothecate, pledge, hedge or
otherwise convey the Warrants or any portion thereof issued, whether by
dividend, distribution or otherwise, except in accordance with the terms hereof.

       (b) Upon receipt by eSpeed of evidence reasonably satisfactory to it of
the loss, theft, destruction or mutilation of a Warrant Certificate, and, in
case of loss, theft or destruction, of indemnity or security satisfactory to
eSpeed, and reimbursement to eSpeed of all reasonable expenses incidental
thereto, and upon surrender to eSpeed and cancellation of the Warrant
Certificate if mutilated, eSpeed shall make and deliver a new Warrant
Certificate of like tenor to the registered holder in lieu of the Warrant
Certificate so lost, stolen, destroyed or mutilated.

       Section 5. Exercise of Warrants; Exercise Price; Expiration Date of
Warrants

       (a) On the Closing Date, 15,000 Warrants represented by a Warrant
Certificate will be issued and registered in the name of EBS.

       (b) A Warrant may be exercised only during the Exercise Period.


                                                                               4

<PAGE>

       (c) During the Exercise Period and subject to paragraph (d) below, the
registered holder of any Warrant Certificate may exercise the Warrants evidenced
thereby in whole or in part upon surrender of the Warrant Certificate, with the
form of election to purchase thereof duly executed, to eSpeed at its principal
office, together with payment of the Exercise Price in immediately available
funds for each share of eSpeed Class A Common Stock for which the Warrants are
exercised. Each Warrant not exercised during the Exercise Period shall become
void, and all rights under the applicable unexercised Warrant Certificates and
all rights under this Agreement shall cease as of such time.

       (d) Upon receipt of a Warrant Certificate, with the form of election to
purchase duly executed, accompanied by payment of the Exercise Price for the
shares of eSpeed Class A Common Stock to be purchased and an amount equal to any
applicable tax or governmental charges referred to in Section 16 in cash, or by
certified check or bank draft payable to the order of eSpeed, eSpeed shall
thereupon promptly (i) requisition from any transfer agent of the eSpeed Class A
Common Stock certificates for the number of whole shares of eSpeed Class A
Common Stock to be purchased, (ii) pay an amount of cash required to be paid in
lieu of the issuance of fractional shares and (iii) after receipt of such
certificates, cause the same to be delivered to or upon the order of the
registered Warrantholder, registered in such name or names as may be designated
by such Warrantholder, and when appropriate, after receipt promptly deliver such
cash to or upon the order of the registered Warrantholder.

       (e) In case any registered Warrantholder exercises less than all Warrants
evidenced by a Warrant Certificate, a new Warrant Certificate evidencing the
Warrants equivalent to the Warrants remaining unexercised shall be issued by
eSpeed to such registered Warrantholder or to his or her duly authorized
assigns, subject to the provisions of Section 10.

       Section 6. eSpeed Class A Common Stock Record Date

       Each Person in whose name any certificate for shares of eSpeed Class A
Common Stock is issued upon the exercise of Warrants shall for all purposes be
deemed to have become the holder of record for the eSpeed Class A Common Stock
represented thereby on, and such certificate shall be dated the date upon which
the Warrant Certificate evidencing such Warrants was duly surrendered and
payment of the Exercise Price (and any applicable transfer taxes) was made;
provided, however, that if the date of such surrender and payment is a date upon
which the eSpeed Class A Common Stock transfer books of eSpeed are closed, such
Person shall be deemed to have become the record holder of such shares on, and
such certificate shall be dated, the next succeeding Business Day on which the
eSpeed Class A Common Stock transfer books of eSpeed are open.

       Section 7. Adjustments

       The number and kind of securities purchasable upon the exercise of the
Warrants and the Exercise Price thereof shall be subject to adjustment from time
to time after the date hereof as follows:

       (a) Stock Dividends. In case shares of eSpeed Class A Common Stock are
issued as a dividend or other distribution on the eSpeed Class A Common Stock
(or such



                                                                               5
<PAGE>


dividend is declared), then the Exercise Price shall be adjusted, as of the date
a record is taken of the holders of eSpeed Class A Common Stock for the purpose
of receiving such dividend or distribution (or if no such record is taken, as at
the earliest of the date of such declaration, payment or other distribution), to
that price determined by multiplying the per share Exercise Price in effect
immediately prior to such declaration, payment or other distribution by a
fraction of which (i) the numerator shall be the number of shares of eSpeed
Class A Common Stock outstanding immediately prior to the declaration or payment
of such dividend or other distribution, and (ii) the denominator shall be the
total number of shares of eSpeed Class A Common Stock outstanding immediately
after the declaration or payment of such dividend or other distribution.

       (b) Adjustment of Aggregate Number of Shares Issuable. Upon each
adjustment of the per share Exercise Price under the provisions of this Section
7, the Share Rate shall be adjusted to the nearest whole number to an amount
determined by multiplying the number of eSpeed Class A Common Stock issuable
prior to such adjustment by a fraction (i) the numerator of which is the per
share Exercise Price in effect immediately prior to the event causing such
adjustment and (ii) the denominator of which is the adjusted per share Exercise
Price.

       (c) For purposes of this Section 7, the number of shares of Class A
Common Stock at any time outstanding shall not include any shares thereof then
directly or indirectly owned or held by or for the account of eSpeed.

       (d) Notwithstanding anything in this Section 7 to the contrary, no
adjustment in the Exercise Price or number of shares of eSpeed Class A Common
Stock issuable upon exercise of a Warrant shall be required unless such
adjustment would require an increase or decrease in the Exercise Price then in
effect of at least 1%; provided, however, that any such amount shall be carried
forward and an adjustment in respect thereof shall be made at the time of and
together with any subsequent adjustment which, together with such amount and any
other amounts so carried forward, shall aggregate an increase or decrease of 1%
or more.

       (e) All Warrants originally issued by eSpeed prior to any adjustment made
to the Exercise Price pursuant to this Section 7 shall evidence the right to
purchase, at the adjusted Exercise Price, the number of shares of eSpeed Class A
Common Stock purchasable from time to time hereunder upon exercise of the
Warrants, all subject to further adjustment as provided herein.

       (f) Irrespective of any adjustment or change in the Exercise Price or the
number of shares of eSpeed Class A Common Stock issuable upon the exercise of
the Warrants, the Warrant Certificates theretofore issued may continue to
express the Exercise Price per share and the number of shares which were
expressed upon the initial Warrant Certificates issued under this Agreement.

       (g) In any case in which this Section 7 shall require that an adjustment
in the Exercise Price be made effective as of a record date for a specified
event, eSpeed may elect to defer until the occurrence of such event the issuance
to the holder of any Warrant exercised after such record date of the shares of
eSpeed Class A Common Stock; provided, however, that


                                                                               6
<PAGE>


eSpeed shall deliver to such holder a due bill or other appropriate instrument
evidencing such holder's right to receive such additional shares upon the
occurrence of the event requiring such adjustment.

       (h) eSpeed shall be entitled, but not required, to make such reductions
in the Exercise Price, in addition to those expressly required by this Section
7, as and to the extent that it in its sole discretion may determine to be
advisable in order that any event treated for Federal income tax purposes as a
distribution of stock or stock rights shall not be taxable to the recipients.

       (i) eSpeed shall be entitled, but not required, to make such reductions
in the Exercise Price, in addition to those expressly required by this Section
7, as and to the extent that it in its sole discretion shall determine to be
advisable, including, without limitation, in order that any dividend in or
distribution of shares of eSpeed Class A Common Stock or shares of capital stock
of any class other than eSpeed Class A Common Stock, subdivision,
reclassification or combination of shares of eSpeed Class A Common Stock,
issuance of rights or warrants, or any other transaction having a similar
effect, shall not be treated as a distribution of property by eSpeed to its
stockholders under Section 305 of the Internal Revenue Code of 1986, as amended,
or any successor provision and shall not be taxable to them.

       Section 8. Adjusted Exercise Price or Share Rate

       With respect to adjustments in the Exercise Price or the Share Rate as
provided in Section 7 or 9:

       (a) eSpeed shall (i) prepare a certificate setting forth the Exercise
Price as so adjusted or the number of shares of eSpeed Class A Common Stock
issuable upon exercise of each Warrant as so adjusted, and a brief statement of
the facts accounting for such adjustment and (ii) mail a brief summary thereof
to each holder of Warrants.

       (b) The adjustments shall, in the case of any adjustment to the Share
Rate, be computed to the nearest one one-hundredth of a share of eSpeed Class A
Common Stock, and in the case of any adjustments in the Share Rate and/or
Exercise Price, apply cumulatively to successive subdivisions, consolidations,
distributions, issuances or other events resulting in any adjustment.

       (c) In the event of any question arising with respect to adjustments to
the number and kind of securities purchasable upon the exercise of the Warrants
or the Exercise Price, or any other adjustments applicable to the Warrants
contemplated by the Warrant Agreement, such question shall be conclusively
determined by eSpeed's auditors or, if they are unable or unwilling to act, by
such firm of chartered accountants as is appointed by eSpeed and acceptable to
EBS. Such accountants shall have access to all necessary records of eSpeed and
such determination shall be binding upon eSpeed and the Warrantholders absent
manifest error.

       (d) If and whenever eSpeed shall take any action affecting or relating to
the eSpeed Class A Common Stock, other than any action described in Section 7 or
Section 9, which in the opinion of the directors would prejudicially affect the
rights of any holders of Warrants,


                                                                               7
<PAGE>

the Share Rate and/or Exercise Price will be adjusted by the Board of Directors
in such manner, if any, and at such time, as the Board of Directors may in its
sole discretion determine to be equitable in the circumstances to such holders.

       Section 9. Reclassification, Consolidation, Merger, Combination, Sale or
Conveyance

       (a) In the event of a reorganization, share exchange or reclassification
in which the holders of eSpeed Class A Common Stock are entitled to receive
stock, securities or property with respect to or in exchange of eSpeed Class A
Common Stock, other than a change in the par value, or from par value to no par
value, or from no par value to par value of eSpeed Class A Common Stock or a
transaction described in subsection (b) or (c) below, the Warrants shall
thereafter be exercisable into the kind and number of shares of stock or other
securities or other property of eSpeed which EBS would have been entitled to
receive if EBS had held the eSpeed Class A Common Stock issuable upon the
exercise of the Warrants immediately prior to such reorganization, share
exchange or reclassification. The provisions of this Section 9 shall similarly
apply to successive reorganizations and reclassifications.

       (b) In the event of a merger or consolidation to which eSpeed is a party
or the sale of all or substantially all of the assets of eSpeed, the Warrants
shall, after such merger, consolidation or sale, be exercisable for the kind and
number of shares of stock and/or other securities, cash or other property which
EBS would have been entitled to receive if EBS had held the eSpeed Class A
Common Stock issuable upon exercise of the Warrants immediately prior to such
merger, consolidation or sale. The provisions of this Section 9 shall similarly
apply to successive mergers and transfers.

       (c) In case outstanding shares of eSpeed Class A Common Stock shall be
subdivided, the per share warrant price shall be proportionately reduced as of
the effective date of such subdivision, or as of the date a record is taken of
the holders of eSpeed Class A Common Stock for the purpose of so subdividing,
whichever is earlier. In case outstanding shares of eSpeed Class A Common Stock
shall be combined, the per share warrant price shall be proportionately
increased as of the effective date of such combination, or as of the date a
record is taken of the holders of eSpeed Class A Common Stock for the purpose of
so combining, whichever is earlier.

       Section 10. Fractional Warrants and Fractional Shares of eSpeed Class A
Common Stock

       (a) eSpeed shall not be required to issue fractions of Warrants or to
distribute Warrant Certificates which evidence fractional Warrants. In lieu of
such fractional Warrants, there shall be paid to the Persons to whom Warrant
Certificates representing such fractional Warrants would otherwise be issuable
an amount in cash (without interest) equal to the product of such fraction of a
Warrant multiplied by the Current Market Price per whole Warrant. The "Current
Market Price" per share of eSpeed Class A Common Stock (or per Warrant) on any
date shall be deemed to be the average of the daily Closing Prices per share of
eSpeed Class A Common Stock for the 10 consecutive Trading Days immediately
prior to such date.


                                                                               8
<PAGE>


       (b) eSpeed shall not be required to issue fractions of shares of eSpeed
Class A Common Stock upon exercise of Warrants or to distribute stock
certificates that evidence fractional shares of eSpeed Class A Common Stock. In
lieu of fractional shares, there shall be paid to the registered holders of
Warrant Certificates at the time such Warrant Certificates are exercised as
herein provided an amount in cash (without interest) equal to the product of
such fractional part of a share of eSpeed Class A Common Stock multiplied by the
Current Market Price per share of eSpeed Class A Common Stock.

       (c) Each holder of a Warrant Certificate, by accepting the same, shall be
deemed to waive his or her right to receive any fractional Warrant or any
fractional share of eSpeed Class A Common Stock upon exercise of a Warrant.

       Section 11. Right of Action

       Rights of action in respect of this Agreement are vested in any
registered Warrantholder, and any registered Warrantholder may enforce, and may
institute and maintain any suit, action or proceeding against eSpeed to enforce,
or otherwise act in respect of, such rights of such Warrantholder.

       Section 12. Agreement of Warrant Certificate Holders

       The holder of the Warrant Certificate, by accepting the same, shall be
deemed to consent and agree with eSpeed that:

       (a) the Warrant Certificate is not transferable without the consent of
eSpeed; the Warrant Certificate is transferable only on the registry books of
eSpeed if surrendered at the principal office of eSpeed, duly endorsed or
accompanied by a proper instrument of transfer, and only in accordance with this
Agreement; and

       (b) eSpeed may deem and treat the Person in whose name the Warrant
Certificate is registered as the absolute owner thereof and of the Warrants
evidenced thereby (notwithstanding any notations of ownership or writing on the
Warrant Certificate made by anyone other than eSpeed) for all purposes
whatsoever, and eSpeed shall not be affected by any notice to the contrary.

       Section 13. Warrant Certificate Holder Not Deemed a Stockholder

       No holder, as such, of the Warrant Certificate shall be entitled to vote,
receive dividends or distributions on, or be deemed for any purpose the holder
of, eSpeed Class A Common Stock or any other securities of eSpeed which may at
any time be issuable on the exercise or conversion of the Warrants represented
thereby, nor shall anything contained in this Agreement or in the Warrant
Certificate be construed to confer upon the holder of the Warrant Certificate,
as such, any of the rights of a stockholder of eSpeed or any right to vote for
the election of directors or upon any matter submitted to stockholders at any
meeting thereof, or to give or withhold consent to any corporate action, or to
receive notice of meetings or other actions affecting stockholders (except as
provided in Section 15), or to receive dividends or distributions



                                                                               9
<PAGE>


or subscription rights, or otherwise, until the Warrant or Warrants evidenced by
the Warrant Certificate shall have been exercised in accordance with the
provisions of this Agreement.

       Section 14. Issuance of New Warrant Certificates

       Notwithstanding any of the provisions of this Agreement or of the
Warrants to the contrary, eSpeed may, at its option, issue a new Warrant
Certificate or Warrant Certificates evidencing Warrants in such form as may be
approved by its Board of Directors to reflect any adjustment or change in the
Exercise Price in accordance with this Agreement and the number or kind or class
of shares of stock or other securities or property purchasable under the Warrant
Certificate made in accordance with the provisions of this Agreement.

       Section 15. Notice of Proposed Actions

       If at any time, (i) eSpeed shall declare a stock dividend (or any other
distribution except for cash dividends) on eSpeed Class A Common Stock; (ii)
there shall be any capital reorganization or reclassification of eSpeed Class A
Common Stock, or any consolidation or merger to which eSpeed is a party, or any
sale or transfer of all or substantially all of the assets of eSpeed; or (iii)
there shall be a voluntary or involuntary dissolution, liquidation or winding-up
of eSpeed; then in any one or more of such cases, eSpeed shall give written
notice to EBS, not less than 10 days before any record date or other date set
for definitive action, or of the date on which such reorganization,
reclassification, sale, consolidation, merger, dissolution, liquidation or
winding up shall take place, as the case may be. Such notice shall also set
forth such facts as shall indicate the effect of such action (to the extent such
effect may be known at the date of such notice) on the current per share warrant
price and the kind and amount of eSpeed Class A Common Stock and other
securities and property deliverable upon exercise of the Warrants. Such notice
shall also specify the date (to the extent known) as of which the holders of
eSpeed Class A Common Stock or record shall be entitiled to exchange their
eSpeed Class A Common Stock for securities or the property deliverable upon such
reorganization, reclassification, sale, consolidation, merger, dissolution,
liquidation or winding up, as the case may be.

       Section 16. Reservation and Availability of Shares of eSpeed Class A
Common Stock or Cash; Taxes

       (a) eSpeed hereby covenants and agrees that, from and after the Closing
Date until the termination of the Exercise Period, it shall cause to be reserved
and kept available out of its authorized and unissued shares of eSpeed Class A
Common Stock or its authorized and issued shares of eSpeed Class A Common Stock
held in its treasury, free from preemptive rights, the number of shares of
eSpeed Class A Common Stock that will be sufficient to permit the exercise in
full of all outstanding Warrants.

       (b) eSpeed shall not be responsible for any tax or governmental charge
that may be payable in connection with the issuance or delivery of the Warrant
Certificate, the transfer of the Warrant Certificate or the issuance or delivery
of certificates for eSpeed Class A Common Stock to a Warrantholder. In addition,
eSpeed shall not be required to issue or deliver any certificate for shares of
eSpeed Class A Common Stock upon the exercise of any Warrant until any such tax
or governmental charge shall have been paid (any such tax or governmental


                                                                              10
<PAGE>


charge being payable by the holder of such Warrant Certificate at the time of
surrender) or until it has been established to eSpeed's satisfaction that no
such tax or governmental charge is due.

       Section 17. Notices

       Notices or demands authorized by this Agreement to be given or made by
either party to this Agreement shall be deemed given (x) on the date delivered,
if delivered personally, (y) on the second Trading Day following the deposit
thereof with Federal Express or another recognized overnight courier, if sent by
Federal Express or another recognized overnight courier, and (z) on the sixth
Trading Day following the mailing thereof with postage prepaid, if mailed by
registered or certified mail (return receipt requested), in each case to the
parties at the following addresses (or at such other address for a party as
shall be specified by like notice):

       (i)  If to eSpeed, to:

            eSpeed, Inc. 135 East 57th Street
            New York, NY 10022

            Attention: President
            fax: (212) 829-4708

            and to

            Attention: General Counsel
            fax: (212) 829-4708

       (ii) If to EBS, to the address of EBS as shown on the registry books of
            eSpeed.

       Section 18. Supplements and Amendments

       (a) eSpeed may from time to time supplement or amend this Agreement
without the approval of EBS in order to cure any ambiguity, to correct or
supplement any provision contained herein which may be defective or inconsistent
with any other provisions herein, or to make any other provisions with regard to
matters or questions arising hereunder which eSpeed may deem necessary or
desirable, all of which shall not adversely affect the interests of EBS.

       (b) Except as otherwise provided herein, the provisions of this Agreement
may be amended and eSpeed may take any action herein prohibited, or omit to
perform any act herein required to be performed by it, only if eSpeed has
obtained the prior written consent of EBS.

       Section 19. Successors

       All covenants and provisions of this Agreement by or for the benefit of
eSpeed shall bind and inure to the benefit of its respective successors and
assigns.


                                                                              11
<PAGE>

       Section 20. Benefits of this Agreement

       Nothing in this Agreement shall be construed to give any Person other
than eSpeed and the registered Warrantholder any legal or equitable right,
remedy or claim under this Agreement.

       Section 21. Governing Law

       This Agreement and the Warrant Certificate issued hereunder shall be
governed by, and construed in accordance with, the laws of the State of New
York; provided, however, that any matters herein within the purview of the
General Corporation Law of the State of Delaware shall be governed by, and
construed in accordance with, that law.

       Section 22. Captions

       The captions of the sections of this Agreement have been inserted for
convenience only and shall not control or affect the meaning or construction of
any of the provisions hereof.

       Section 23. Termination

       This Agreement shall terminate on the fifteenth day following the earlier
to occur of (i) the end of the Exercise Period and (ii) the date on which there
remains no Warrant outstanding.

       Section 24. Counterparts

       This Agreement may be executed in counterparts and each of such
counterparts shall for all purposes be deemed to be an original, and all such
counterparts shall together constitute one and the same instrument.

       IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed as of the day and year first above written.

                                            ESPEED, INC.


                                            By: /s/ Howard W. Lutnick
                                                --------------------------------
                                                Authorized Officer



                                            EXCHANGE BROKERAGE SYSTEMS CORP.


                                            By: /s/ David Lawrence
                                                --------------------------------
                                                Authorized Officer





                                                                              12

<PAGE>


                                    Exhibit I

                           FORM OF WARRANT CERTIFICATE



Certificate No.  1                                              15,000  Warrants
                ---                                             ------


                    NOT EXERCISABLE AFTER September 13, 2011

                               Warrant Certificate

                                  eSPEED, INC.

NEITHER THESE WARRANTS NOR THE SHARES OF CLASS A COMMON STOCK ISSUABLE UPON
EXERCISE OF THESE WARRANTS HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF
1933, AND NEITHER THESE WARRANTS NOR SUCH SHARES MAY BE SOLD, ENCUMBERED OR
OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT
UNDER SUCH ACT OR AN EXEMPTION FROM SUCH REGISTRATION REQUIREMENT, AND, IF AN
EXEMPTION SHALL BE APPLICABLE, THE HOLDER SHALL HAVE DELIVERED AN OPINION OF
COUNSEL ACCEPTABLE TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED.

       This certifies that Exchange Brokerage Systems Corp. ("EBS") or its
registered assigns, is the registered owner of the number of Warrants set forth
above, each of which entitles the owner thereof, subject to the terms,
provisions and conditions of the Warrant Agreement, dated as of September 13,
2001 (the "Warrant Agreement"), between eSpeed, Inc., a Delaware corporation
("eSpeed"), and EBS to purchase from eSpeed during the Exercise Period at the
principal office of eSpeed in New York City, during regular business hours, the
number of shares of Class A common stock, par value $0.01 per share, of eSpeed
("eSpeed Class A Common Stock") represented hereby at a price per share of
eSpeed Class A Common Stock, payable in cash only, equal to Ten Dollars and
Eighty Three Cents (US $10.83) (the "Exercise Price"), in each case upon
presentation and surrender of this Warrant Certificate with the Form of Election
to Purchase duly executed. The number of Warrants evidenced by this Warrant
Certificate (and the number of shares of eSpeed Class A Common Stock which may
be purchased upon exercise thereof) set forth above and the Exercise Price set
forth above are the number and Exercise Price based on the shares of eSpeed
Class A Common Stock as constituted at such date. As provided in the Warrant
Agreement, the Exercise Price and the number of shares of eSpeed Class A Common
Stock which may be purchased upon the exercise of the Warrants evidenced by this
Warrant Certificate are subject to modification and adjustment upon the
occurrence of certain events.

       Terms defined in the Warrant Agreement, and not otherwise defined herein,
shall have, for the purposes of this Warrant Certificate, the meanings ascribed
to them in the Warrant Agreement. This Warrant Certificate is subject to all of
the terms, provisions and conditions of



                                                                              13
<PAGE>


the Warrant Agreement, which terms, provisions and conditions are hereby
incorporated herein by reference and made a part hereof and to which Warrant
Agreement reference is hereby made for a full description of the rights,
limitations of rights, obligations, duties and immunities hereunder of eSpeed
and the holders of the Warrant Certificates. Copies of the Warrant Agreement are
on file at the above-mentioned office of eSpeed. After 5:00 P.M., New York City
time, on the last Business Day of the Exercise Period, all Warrants evidenced by
this Warrant Certificate shall become null and void and of no value.

       Neither this Warrant Certificate nor any of the Warrants represented by
this Warrant Certificate may be sold, transferred, assigned, hypothecated,
pledged or otherwise conveyed by EBS or its registered assigns, except as
expressly permitted in the Warrant Agreement.

       If this Warrant Certificate shall be exercised in part, the holder hereof
shall be entitled to receive upon surrender hereof another Warrant Certificate
or Warrant Certificates for the number of Warrants not exercised.

       eSpeed shall make a cash payment in lieu of issuing fractional Warrants
or fractional shares of eSpeed Class A Common Stock, as provided in the Warrant
Agreement.

       No holder of this Warrant Certificate, as such, shall be entitled to
vote, receive dividends or distributions on, or be deemed for any purpose the
holder of eSpeed Class A Common Stock or of any other securities of eSpeed which
may at any time be issuable on the exercise hereof, nor shall anything contained
in the Warrant Agreement or herein be construed to confer upon the holder
hereof, as such, any of the rights of a stockholder of eSpeed or any right to
vote for the election of directors or upon any matter submitted to stockholders
at any meeting thereof, or to give or withhold consent to any corporate action,
or to receive notice of meetings or other actions affecting stockholders (except
as expressly provided in the Warrant Agreement), or to receive dividends or
subscription rights, or otherwise, until the Warrant or Warrants evidenced by
this Warrant Certificate shall have been exercised as provided in the Warrant
Agreement.

       WITNESS the facsimile signatures of the proper officers of eSpeed. Dated
as of September 13, 2001.


ATTEST:                                     ESPEED, INC.


                                            By:
--------------------------------                --------------------------------
Secretary                                       President




                                                                              14
<PAGE>


                                   Exhibit II

                          FORM OF ELECTION TO PURCHASE

                      (To be executed if holder desires to
                       exercise the Warrant Certificate.)


To: eSpeed, Inc.,

       The undersigned hereby irrevocably elects to exercise __________________
Warrants represented by this Warrant Certificate to purchase the shares of
eSpeed Class A Common Stock issuable upon the exercise of such Warrants and
requests that Certificates for such shares of eSpeed Class A Common Stock be
issued in the name of and delivered to:

Please insert Social Security
or other identifying number



-------------------------------------------------
        (Please print name and address)


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


If such number of Warrants shall not be all the Warrants evidenced by this
Warrant Certificate, a new Warrant Certificate for the balance remaining of such
Warrants shall be registered in the name of and delivered to:



-------------------------------------------------
        (Please print name and address)


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


Dated:
       ------------------------------           --------------------------------
                                                Signature
                                                (Signature must conform in all
                                                respects to name of holder as
                                                specified on the face of this
                                                Warrant Certificate)
Signature Guaranteed: