<PAGE>

                                                                    EXHIBIT 4.02

                          CALCULATION AGENCY AGREEMENT

         CALCULATION AGENCY AGREEMENT, dated as of April 30, 2002 (the
"Agreement"), between Lehman Brothers Holdings Inc. (the "Company") and Lehman
Brothers Inc., as Calculation Agent.

         WHEREAS, the Company has authorized the issuance of up to $19,550,000
aggregate principal amount of S&P 500(R) Index SUNS(R), Stock Upside Note
Securities(R) Due April 30, 2005 (the "Securities")*;

         WHEREAS, the Securities will be issued under an Indenture, dated as of
September 1, 1987, between the Company and Citibank, N.A., as Trustee (the
"Trustee"), as supplemented and amended by supplemental indentures dated as of
November 25, 1987, November 27, 1990, September 13, 1991, October 4, 1993,
October 1, 1995, and June 26, 1997, and incorporating Standard Multiple Series
Indenture Provisions dated July 30, 1987, as amended November 16, 1987
(collectively, the "Indenture"); and

         WHEREAS, the Company requests the Calculation Agent to perform certain
services described herein in connection with the Securities;

         NOW THEREFORE, the Company and the Calculation Agent agree as follows:

         1. Appointment of Agent. The Company hereby appoints Lehman Brothers
Inc. as Calculation Agent and Lehman Brothers Inc. hereby accepts such
appointment as the Company's agent for the purpose of performing the services
hereinafter described upon the terms and subject to the conditions hereinafter
mentioned.

         2. Calculations and Information Provided. In response to a request made
by the Trustee for a determination of the Maturity Payment Amount due at Stated
Maturity of the Securities, the Calculation Agent shall determine such Maturity
Payment Amount and notify the Trustee of its determination. The Calculation
Agent shall also be responsible for (a) the determination of the Maturity
Payment Amount, (b) whether adjustments to the Equity Return should be made, (c)
the Successor Index if publication of the Index is discontinued and (d) whether
a Market Disruption Event has occurred. The Calculation Agent shall notify the
Trustee of any such adjustment or any such Successor Index, or if a Market
Disruption Event has occurred. Annex A hereto sets forth the procedures the
Calculation Agent will use to determine the information described in this
Section 2.

--------
*    "Standard & Poor's(R)," "S&P(R)," "S&P 500(R)," "Standard & Poor's 500,"
     and "500" are trademarks of McGraw-Hill, Inc. and have been licensed for
     use by Lehman Brothers Holdings Inc. The notes, based on the performance of
     the S&P 500(R) Index, are not sponsored, endorsed, sold or promoted by
     Standard & Poor's and Standard & Poor's makes no representation regarding
     the advisability of investing in the notes.

     "Stock Upside Note Securities" and "SUNS" are trademarks of Lehman Brothers
     Inc.

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                                                                               2

         3. Calculations. Any calculation or determination by the Calculation
Agent pursuant hereto shall (in the absence of manifest error) be final and
binding. Any calculation made by the Calculation Agent hereunder shall, at the
Trustee's request, be made available at the Corporate Trust Office.

         4. Fees and Expenses. The Calculation Agent shall be entitled to
reasonable compensation for all services rendered by it as agreed to between the
Calculation Agent and the Company.

         5. Terms and Conditions. The Calculation Agent accepts its obligations
herein set out upon the terms and conditions hereof, including the following, to
all of which the Company agrees:

         (a) in acting under this Agreement, the Calculation Agent is acting
     solely as an independent expert of the Company and does not assume any
     obligation toward, or any relationship of agency or trust for or with, any
     of the holders of the Securities;

         (b) unless otherwise specifically provided herein, any order,
     certificate, notice, request, direction or other communication from the
     Company or the Trustee made or given under any provision of this Agreement
     shall be sufficient if signed by any person who the Calculation Agent
     reasonably believes to be a duly authorized officer or attorney-in-fact of
     the Company or the Trustee, as the case may be;

         (c) the Calculation Agent shall be obliged to perform only such duties
     as are set out specifically herein and any duties necessarily incidental
     thereto;

         (d) the Calculation Agent, whether acting for itself or in any other
     capacity, may become the owner or pledgee of Securities with the same
     rights as it would have had if it were not acting hereunder as Calculation
     Agent; and

         (e) the Calculation Agent shall incur no liability hereunder except for
     loss sustained by reason of its gross negligence or wilful misconduct.

         6. Resignation; Removal; Successor. (a) The Calculation Agent may at
any time resign by giving written notice to the Company of such intention on its
part, specifying the date on which its desired resignation shall become
effective, subject to the appointment of a successor Calculation Agent and
acceptance of such appointment by such successor Calculation Agent, as
hereinafter provided. The Calculation Agent hereunder may be removed at any time
by the filing with it of an instrument in writing signed by or on behalf of the
Company and specifying such removal and the date when it shall become effective.
Such resignation or removal shall take effect upon the appointment by the
Company, as hereinafter provided, of a successor Calculation Agent and the
acceptance of such appointment by such successor Calculation Agent. In the event
a successor Calculation Agent has not been appointed and has not accepted its
duties within 90 days of the Calculation Agent's notice of resignation, the
Calculation Agent may apply to any court of competent jurisdiction for the
designation of a successor Calculation Agent.

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                                                                               3

         (b) In case at any time the Calculation Agent shall resign, or shall be
removed, or shall become incapable of acting, or shall be adjudged bankrupt or
insolvent, or make an assignment for the benefit of its creditors or consent to
the appointment of a receiver or custodian of all or any substantial part of its
property, or shall admit in writing its inability to pay or meet its debts as
they mature, or if a receiver or custodian of it or all or any substantial part
of its property shall be appointed, or if any public officer shall have taken
charge or control of the Calculation Agent or of its property or affairs, for
the purpose of rehabilitation, conservation or liquidation, a successor
Calculation Agent shall be appointed by the Company by an instrument in writing,
filed with the successor Calculation Agent. Upon the appointment as aforesaid of
a successor Calculation Agent and acceptance by the latter of such appointment,
the Calculation Agent so superseded shall cease to be Calculation Agent
hereunder.

         (c) Any successor Calculation Agent appointed hereunder shall execute,
acknowledge and deliver to its predecessor, to the Company and to the Trustee an
instrument accepting such appointment hereunder and agreeing to be bound by the
terms hereof, and thereupon such successor Calculation Agent, without any
further act, deed or conveyance, shall become vested with all the authority,
rights, powers, trusts, immunities, duties and obligations of such predecessor
with like effect as if originally named as Calculation Agent hereunder, and such
predecessor, upon payment of its charges and disbursements then unpaid, shall
thereupon become obligated to transfer, deliver and pay over, and such successor
Calculation Agent shall be entitled to receive, all moneys, securities and other
property on deposit with or held by such predecessor, as Calculation Agent
hereunder.

         (d) Any corporation into which the Calculation Agent hereunder may be
merged or converted or any corporation with which the Calculation Agent may be
consolidated, or any corporation resulting from any merger, conversion or
consolidation to which the Calculation Agent shall be a party, or any
corporation to which the Calculation Agent shall sell or otherwise transfer all
or substantially all of the assets and business of the Calculation Agent shall
be the successor Calculation 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.

         7. Certain Definitions. Terms not otherwise defined herein or in Annex
A hereto are used herein as defined in the Indenture or the Securities.

         8. Indemnification. The Company will indemnify the Calculation Agent
against any losses or liability which it may incur or sustain in connection with
its appointment or the exercise of its powers and duties hereunder except such
as may result from the gross negligence or wilful misconduct of the Calculation
Agent or any of its agents or employees. The Calculation Agent shall incur no
liability and shall be indemnified and held harmless by the Company for or in
respect of any action taken or suffered to be taken in good faith by the
Calculation Agent in reliance upon written instructions from the Company.

         9. Notices. Any notice required to be given hereunder shall be
delivered in person, sent (unless otherwise specified in this Agreement) by
letter, telex or facsimile transmission or communicated by telephone (confirmed
in a writing dispatched within two Business Days), (a) in the case of the
Company, to it at 745 Seventh Avenue, New York, New York 10019 (facsimile: (646)
758-3204) (telephone: (212) 526-7000), Attention: Treasurer, with a copy to 399
Park Avenue, New York, New York 10022 (facsimile: (212) 526-0357)

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                                                                               4

(telephone: (212) 526-7000), Attention: Corporate Secretary, (b) in the case of
the Calculation Agent, to it at 745 Seventh Avenue, New York, New York 10019
(facsimile: (646) 758-4942) (telephone: (212) 526-7000), Attention: Equity
Derivatives Trading and (c) in the case of the Trustee, to it at 111 Wall
Street, 5th Floor, New York, New York 10043 (facsimile: (212) 657-3836)
(telephone: (212) 657-7805), Attention: Corporate Trust Department or, in any
case, to any other address or number of which the party receiving notice shall
have notified the party giving such notice in writing. Any notice hereunder
given by telex, facsimile or letter shall be deemed to be served when in the
ordinary course of transmission or post, as the case may be, it would be
received.

         10. Governing Law. This Agreement shall be governed by and continued in
accordance with the laws of the State of New York.

         11. Counterparts. This Agreement may be executed in any number of
counterparts, each of which when so executed shall be deemed to be an original
and all of which taken together shall constitute one and the same agreement.

         12. Benefit of Agreement. This Agreement is solely for the benefit of
the parties hereto and their successors and assigns, and no other person shall
acquire or have any rights under or by virtue hereof.

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                                                                               5

         IN WITNESS WHEREOF, this Agreement has been entered into as of the day
and year first above written.

                                      LEHMAN BROTHERS HOLDINGS INC.

                                      By:
                                         ---------------------------------------
                                         Name:  Barrett S. DiPaolo
                                         Title: Vice President


                                      LEHMAN BROTHERS INC.,
                                        as Calculation Agent

                                      By:
                                         ---------------------------------------
                                         Name:  Barrett S. DiPaolo
                                         Title: Vice President


<PAGE>

                                     ANNEX A
                                     -------

         1. The Index.

         The Index is the S&P 500(R) Index, as calculated by S&P (the "Index").

         2. Determination of the Maturity Payment Amount.

         The Calculation Agent shall determine the amount payable at Stated
Maturity for each $1,000 principal amount of Securities (the "Maturity Payment
Amount"). The Maturity Payment Amount shall equal the greater of (a) $1,000 and
(b) the Alternative Redemption Amount.

         3. Discontinuance of the Index.

         (a) If S&P discontinues publication of the Index and S&P or another
entity publishes a successor or substitute index (the "Successor Index") that
the Calculation Agent determines, in its sole discretion, to be comparable to
the discontinued Index, then the Calculation Agent shall calculate the Maturity
Payment Amount pursuant to Section 2 hereof by reference to the index level of
such Successor Index at the Close of Trading on the NYSE, AMEX, Nasdaq or the
relevant exchange or market for the Successor Index on the date that any
subsequent Closing Level is to be determined.

         (b) Upon any selection by the Calculation Agent of a Successor Index,
the Company shall promptly give notice to the holders of the Securities.

         (c) If S&P discontinues publication of the Index prior to, and such
discontinuance is continuing on, any date that a Closing Level is to be
determined and the Calculation Agent determines that no Successor Index is
available at such time, then, on such date, the Calculation Agent shall
determine each subsequent Closing Level to be used in computing the Maturity
Payment Amount. Each such Closing Level shall be computed by the Calculation
Agent in accordance with the formula for and method of calculating the Index
last in effect prior to such discontinuance, using the Closing Level (or, if
trading in the relevant securities has been materially suspended or materially
limited, its good faith estimate of the Closing Level that would have prevailed
but for such suspension or limitation) at the close of the principal trading
session on such date of each security most recently comprising the Index on the
primary organized U.S. exchange or trading system.

         4. Alteration of Method of Calculation.

         If at any time the method of calculating the Index or a Successor
Index, or the Closing Level thereof, is changed in a material respect, or if the
Index or a Successor Index is in any other way modified so that such Index does
not, in the opinion of the Calculation Agent, fairly represent the value of the
Index or such Successor Index had such changes or modifications not been made,
then, from and after such time, the Calculation Agent will, at the Close of
Trading in New York City on each date that any Closing Level is to be
determined, make such calculations and adjustments as, in the good faith
judgment of the Calculation Agent, may be necessary in order to arrive at a
level of a stock index comparable to the Index or such Successor Index, as the
case may be, as if such changes or modifications had not been made, and
calculate the Closing Level and the Maturity Payment Amount with reference to
the Index or

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                                                                               2

such Successor Index, as adjusted. Accordingly, if the method of calculating the
Index or a Successor Index is modified so that the level of such index is a
fraction of what it would have been if it had not been modified (for example,
due to a split in the index), then the Calculation Agent shall adjust such index
in order to arrive at a level of the Index or such Successor Index as if it had
not been modified (for example, if such split had not occurred).

         5. Definitions.

         Set forth below are the terms used in the Agreement and in this Annex
A.

         "Agreement" shall have the meaning set forth in the preamble to this
Agreement.

         "AMEX" shall mean the American Stock Exchange.

         "Alternative Redemption Amount" shall mean, with respect to each $1,000
principal amount of Securities, the product of:

         (i)  $1,000; and

                               (   Average Closing                   ).
         (ii)  1  +  0.95  x   (     Index Level     --    1,091.48  )
                               ---------------------------------------
                                              1,091.48

         "Average Closing Index Level" shall mean the arithmetic average of the
Closing Levels of the Index on the 27th day of each of the 36 months after April
2002, starting from and including May 27, 2002 and ending at and including April
27, 2005; provided, that if any such day is not a Business Day, the Closing
Level of the next following Business Day will be used; provided further, that if
a Market Disruption Event occurs on any such date, the Calculation Agent will
determine the Closing Level for such date by reference to the Closing Level on
the next following Business Day on which no Market Disruption Event occurs.

         "Business Day", notwithstanding any provision in the Indenture, shall
mean any day that is not a Saturday, a Sunday or a day on which the NYSE, Nasdaq
or AMEX is not open for trading or banking institutions or trust companies in
the City of New York are authorized or obligated by law or executive order to
close.

         "Calculation Agent" shall mean the person that has entered into an
agreement with the Company providing for, among other things, the determination
of the Maturity Payment Amount, which term shall, unless the context otherwise
requires, include its successors and assigns. The initial Calculation Agent
shall be Lehman Brothers Inc.

         "Close of Trading" shall mean 4:00 p.m., New York City time.

         "Closing Level" shall mean the last reported level of the Index, the
Successor Index or any security which is a component of either such index, as
the case may be, at 4:00 p.m., New York City time, as reported by S&P, the
publisher of the Successor Index or the primary exchange on which any such
security then trades, as the case may be.

         "Company" shall have the meaning set forth in the preamble to this
Agreement.

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         "Indenture" shall have the meaning set forth in the preamble to this
Agreement.

         "Index" shall have the meaning set forth in Section 1 of this Annex A.

         "Market Disruption Event", on any day, shall mean any of the following
events as determined by the Calculation Agent:

         (i) A suspension, absence or material limitation of trading in 20% or
     more of the underlying stocks which then comprise the Index or any
     Successor Index, as the case may be, has occurred on that day, in each
     case, for more than two hours of trading or during the one-half hour period
     preceding the Close of Trading on the primary organized U.S. exchange or
     trading system on which such stocks are traded or, in the case of a common
     stock not listed or quoted in the United States, on the primary exchange,
     trading system or market for that security. Limitations on trading during
     significant market fluctuations imposed pursuant to NYSE Rule 80B or any
     applicable rule or regulation enacted or promulgated by the NYSE, any other
     exchange, trading system or market, any other self regulatory organization
     or the Securities and Exchange Commission of similar scope or as a
     replacement for Rule 80B, may be considered material. Notwithstanding the
     first sentence of this paragraph, a Market Disruption Event for a security
     traded on a bulletin board means a suspension, absence or material
     limitation of trading of that security for more than two hours or during
     the one hour period preceding 4:00 p.m., New York City time.

         (ii) A suspension, absence or material limitation has occurred on that
     day, in each case, for more than two hours of trading or during the
     one-half hour period preceding the Close of Trading in options contracts
     related to the Index or any Successor Index, as the case may be, whether by
     reason of movements in price exceeding levels permitted by an exchange,
     trading system or market on which such options contracts are traded or
     otherwise.

         (iii) Information is unavailable on that date, through a recognized
     system of public dissemination of transaction information, for more than
     two hours of trading or during the one-half hour period preceding the Close
     of Trading, of accurate price, volume or related information in respect of
     20% or more of the underlying stocks which then comprise the Index or any
     Successor Index, as the case may be, or in respect of options contracts
     related to the Index or any Successor Index, as the case may be, in each
     case traded on any major U.S. exchange or trading system or in the case of
     securities of a non-U.S. issuer, traded on the primary non-U.S. exchange,
     trading system or market.

     For purposes of determining whether a Market Disruption Event has occurred:

         (i) a limitation on the hours or number of days of trading shall not
     constitute a Market Disruption Event if it results from an announced change
     in the regular business hours of the relevant exchange, trading system or
     market;

         (ii) any suspension in trading in an options contract on the Index or
     any Successor Index, as the case may be, by a major securities exchange,
     trading system or market by reason of (a) a price change violating limits
     set by such securities market, (b) an imbalance of orders relating to those
     contracts, or (c) a disparity in bid and ask quotes

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                                                                               4

     relating to those contracts, shall constitute a Market Disruption Event
     notwithstanding that the suspension or material limitation is less than two
     hours;

         (iii) a suspension or material limitation on an exchange, trading
     system or in a market shall include a suspension or material limitation of
     trading by one class of investors provided that the suspension continues
     for more than two hours of trading or during the last one-half hour period
     preceding the Close of Trading on the relevant exchange, trading system or
     market but shall not include any time when the relevant exchange, trading
     system or market is closed for trading as part of that exchange's, trading
     system's or market's regularly scheduled business hours; and

         (iv) "Trading systems" include bulletin board services.

         "Maturity Payment Amount" shall have the meaning set forth in Section 2
of this Annex A.

         "Nasdaq" shall mean The Nasdaq Stock Market, Inc.

         "NYSE" shall mean the New York Stock Exchange.

         "S&P" shall mean Standard & Poor's, a division of McGraw-Hill, Inc.

         "Stated Maturity" shall mean April 30, 2005; provided, that if a Market
Disruption Event occurs on April 27, 2005 (or if April 27, 2005 is not a
Business Day, on the next Business Day), the Stated Maturity shall be the third
Business Day following the date that the Closing Level for April 2005 is
determined.

         "Successor Index" shall have the meaning set forth in Section 3(a) of
this Annex A.

         "Trustee" shall have the meaning set forth in the preamble to this
Agreement.