
<PAGE>
 
                                                                    EXHIBIT 99.1

                             STOCK OPTION AGREEMENT


     STOCK OPTION AGREEMENT, dated as of May 26, 1998 (the "Agreement"), between
MAY & SPEH, INC., a Delaware corporation ("Issuer"), and Acxiom Corporation, a
Delaware corporation ("Grantee").


                                   RECITALS


     a.        Issuer and Grantee have entered into an Agreement and Plan of
          Merger, dated as of the date hereof (the "Merger Agreement"; defined
          terms used but not defined herein have the meanings set forth in the
          Merger Agreement), providing for, among other things, the merger of
          Sub with and into Issuer pursuant to the terms of the Merger; and

     b.        As a condition and inducement to Grantee's willingness to enter
          into the Merger Agreement, Grantee has requested that Issuer agree,
          and Issuer has agreed, to grant Grantee the Option (as defined below).

     NOW, THEREFORE, in consideration of the foregoing and the respective
representations, warranties, covenants and agreements set forth herein, Issuer
and Grantee agree as follows:

          i.        Grant of Option. Subject to the terms and conditions set
               forth herein, Issuer hereby grants to Grantee an irrevocable
               option (the "Option") to purchase up to 19.9% of the number of
               shares (the "Option Shares") of common stock, par value $0.01 per
               share ("Issuer Common Stock"), of Issuer issued and outstanding
               immediately prior to the grant of the Option at a purchase price
               of $14.96 (as adjusted as set forth herein) per Option Share (the
               "Purchase Price").

          ii.       Exercise of Option. Grantee may exercise the Option, with
               respect to any or all of the Option Shares at any one time,
               subject to the provisions of Section 2(c), upon the occurrence of
               a Purchase Event (as defined in Section 7(c)), except that (i)
               subject to the last sentence of this Section 2(a), the Option
               will terminate and be of no further force and effect upon the
               earliest to occur of (A) the Effective Time, (B) six months after
               the date on which a Purchase Event (as defined herein) occurs,
               and (C) termination of the Merger Agreement in accordance with
               its terms prior to the occurrence of a Purchase Event, unless, in
               the case of clause (C), the Grantee has the right to receive the
               Company Termination Fee following such termination upon the
               occurrence of certain events, in which case the Option will not
               terminate until
<PAGE>
 
               the later of (x) six months following the time such Company
               Termination Fee becomes payable and (y) the expiration of the
               period in which the Grantee has such right to receive the Company
               Termination Fee, and (ii) any purchase of Option Shares upon
               exercise of the Option will be subject to compliance with the HSR
               Act and the obtaining or making of any consents, approvals,
               orders, notifications or authorizations, the failure of which to
               have obtained or made would have the effect of making the
               issuance of Option Shares illegal (the "Regulatory Approvals")
               and no preliminary or permanent injunction or other order by any
               court of competent jurisdiction prohibiting or otherwise
               restraining such issuance shall be in effect. Notwithstanding the
               termination of the Option, Grantee will be entitled to purchase
               the Option Shares if it has exercised the Option in accordance
               with the terms hereof prior to the termination of the Option, and
               the termination of the Option will not affect any rights
               hereunder which by their terms do not terminate or expire prior
               to or as of such termination.

                         (i)       In the event that Grantee wishes to exercise
                              the Option, it will send to Issuer a written
                              notice (an "Exercise Notice"; the date of which
                              being herein referred to as the "Notice Date") to
                              that effect which Exercise Notice also specifies
                              the number of Option Shares, if any, Grantee
                              wishes to purchase pursuant to this Section 2(b),
                              the number of Option Shares, if any, with respect
                              to which Grantee wishes to exercise its Cash-Out
                              Right (as defined herein) pursuant to Section
                              7(c), the denominations of the certificate or
                              certificates evidencing the Option Shares which
                              Grantee wishes to purchase pursuant to this
                              Section 2(b) and a date not earlier than 20
                              business days nor later than 30 business days from
                              the Notice Date for the closing (an "Option
                              Closing") of such purchase (an "Option Closing
                              Date"). Any Option Closing will be at an agreed
                              location and time in New York, New York on the
                              applicable Option Closing Date or at such later
                              date as may be necessary so as to comply with
                              clause (ii) of Section 2(a).

                         (ii)      Notwithstanding anything to the contrary
                              contained herein, any exercise of the Option and
                              purchase of Option Shares shall be subject to
                              compliance with applicable laws and regulations,
                              which may prohibit the purchase of all the Option
                              Shares specified in the Exercise Notice without
                              first

                                    99.1-2
<PAGE>
 
                              obtaining or making certain Regulatory Approvals.
                              In such event, if the Option is otherwise
                              exercisable and Grantee wishes to exercise the
                              Option, the Option may be exercised in accordance
                              with Section 2(b) and Grantee shall acquire the
                              maximum number of Option Shares specified in the
                              Exercise Notice that Grantee is then permitted to
                              acquire under the applicable laws and regulations,
                              and if Grantee thereafter obtains the Regulatory
                              Approvals to acquire the remaining balance of the
                              Option Shares specified in the Exercise Notice,
                              then Grantee shall be entitled to acquire such
                              remaining balance. Issuer agrees to use its
                              reasonable best efforts to assist Grantee in
                              seeking the Regulatory Approvals.

     In the event (i) Grantee receives official notice that a Regulatory
Approval required for the purchase of any Option Shares will not be issued or
granted or (ii) such Regulatory Approval has not been issued or granted within
six months of the date of the Exercise Notice, Grantee shall have the right to
exercise its Cash-Out Right (as defined herein) pursuant to Section 7(c) with
respect to the Option Shares for which such Regulatory Approval will not be
issued or granted or has not been issued or granted.

          iii.      Payment and Delivery of Certificates. At any Option Closing,
               Grantee will pay to Issuer in same day funds by wire transfer to
               a bank account designated in writing by Issuer an amount equal to
               the Purchase Price multiplied by the number of Option Shares to
               be purchased at such Option Closing.

                         (i)       At any Option Closing, simultaneously with
                              the delivery of same day funds as provided in
                              Section 3(a), Issuer will deliver to Grantee a
                              certificate or certificates representing the
                              Option Shares to be purchased at such Option
                              Closing, which Option Shares will be free and
                              clear of all liens, claims, charges and
                              encumbrances of any kind whatsoever. If at the
                              time of issuance of Option Shares pursuant to an
                              exercise of the Option hereunder, Issuer shall not
                              have issued any securities similar to rights under
                              a shareholder rights plan, then each Option Share
                              issued pursuant to such exercise will also
                              represent such a corresponding right with terms
                              substantially the same as and at least as
                              favorable to Grantee as are provided

                                    99.1-3
<PAGE>
 
                              under any Issuer shareholder rights agreement or
                              any similar agreement then in effect.

                         (ii)      Certificates for the Option Shares delivered
                              at an Option Closing will have typed or printed
                              thereon a restrictive legend which will read
                              substantially as follows:

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
     UNDER THE SECURITIES ACT OF 1993, AND MAY BE OFFERED, SOLD, PLEDGED OR
     OTHERWISE TRANSFERRED ONLY IF SO REGISTERED OR IF ANY EXEMPTION FROM SUCH
     REGISTRATION IS AVAILABLE. SUCH SECURITIES ARE ALSO SUBJECT TO ADDITIONAL
     RESTRICTIONS ON TRANSFER AS SET FORTH IN THE STOCK OPTION AGREEMENT, DATED
     AS OF MAY 26, 1998, A COPY OF WHICH MAY BE OBTAINED FROM THE SECRETARY OF
     MAY & SPEH, INC. AT ITS PRINCIPAL EXECUTIVE OFFICES."

It is understood and agreed that (i) the reference to restrictions arising under
the Securities Act in the above legend will be removed by delivery of substitute
certificate(s) without such reference if such Option Shares have been sold in
compliance with the registration and prospectus delivery requirements of the
Securities Act, such Option Shares have been sold in reliance on and in
accordance with Rule 144 under the Securities Act or Grantee has delivered to
Issuer a copy of a letter from the staff of the SEC, or an opinion of counsel in
form and substance reasonably satisfactory to Issuer and its counsel, to the
effect that such legend is not required for purposes of the Securities Act and
(ii) the reference to restrictions pursuant to this Agreement in the above
legend will be removed by delivery of substitute certificate(s) without such
reference if the Option Shares evidenced by certificate(s) containing such
reference have been sold or transferred in compliance with the provisions of
this Agreement under circumstances that do not require the retention of such
reference.

          iv.       Incorporation of Representations and Warranties of Issuer.
               The representations and warranties of Issuer contained in Article
               V of the Merger Agreement are hereby incorporated by reference
               herein with the same force and effect as though made pursuant to
               this Agreement.

          v.        Representations and Warranties of Issuer. Issuer hereby
               represents and warrants to Grantee as follows:

                    (i)       Corporate Authorization. Issuer has the corporate
                         power and authority to enter into this Agreement and to
                         carry out its obligations hereunder. The execution and
                         delivery of this Agreement and the consummation of the
                         transactions contemplated hereby have been duly and
                         validly authorized

                                    99.1-4
<PAGE>
 
                              by the Board of Directors of Issuer, and no other
                              corporate proceedings on the part of Issuer are
                              necessary to authorize this Agreement and the
                              transactions contemplated hereby. This Agreement
                              has been duly and validly executed and delivered
                              by Issuer, and assuming this Agreement constitutes
                              a valid and binding agreement of Grantee, this
                              Agreement constitutes a valid and binding
                              agreement of Issuer, enforceable against Issuer in
                              accordance with its terms (except insofar as
                              enforceability may be limited by applicable
                              bankruptcy, insolvency, reorganization, moratorium
                              or similar laws affecting creditors' rights
                              generally, or by principles governing the
                              availability of equitable remedies).

                         (ii)      Authorized Stock. Issuer has taken all
                              necessary corporate and other action to authorize
                              and reserve and, subject to the expiration or
                              termination of any required waiting period under
                              the HSR Act, to permit it to issue, and, at all
                              times from the date hereof until the obligation to
                              deliver Option Shares upon the exercise of the
                              Option terminates, shall have reserved for
                              issuance, upon exercise of the Option, shares of
                              Issuer Common Stock necessary for Grantee to
                              exercise the Option, and Issuer will take all
                              necessary corporate action to authorize and
                              reserve for issuance all additional shares of
                              Issuer Common Stock or other securities which may
                              be issued pursuant to Section 7 upon exercise of
                              the Option. The shares of Issuer Common Stock to
                              be issued upon due exercise of the Option,
                              including all additional shares of Issuer Common
                              Stock or other securities which may be issuable
                              upon exercise of the Option or any other
                              securities which may be issued pursuant to Section
                              7, upon issuance pursuant hereto, will be duly and
                              validly issued, fully paid and nonassessable, and
                              will be delivered free and clear of all liens,
                              claims, charges and encumbrances of any kind or
                              nature whatsoever, including without limitation
                              any preemptive rights of any stockholder of
                              Issuer.

          vi.       Representations and Warranties of Grantee. Grantee hereby
               represents and warrants to Issuer that:

                         (i)       Corporate Authorization. Grantee has the
                              corporate power and authority to enter into this
                              Agreement and to carry out its obligations
                              hereunder. The execution and delivery of this
                              Agreement and the consummation of the transactions

                                    99.1-5
<PAGE>
 
                              contemplated hereby have been duly and validly
                              authorized by the Board of Directors of Grantee,
                              and no other corporate proceedings on the part of
                              Grantee are necessary to authorize this Agreement
                              and the transactions contemplated hereby. This
                              Agreement has been duly and validly executed and
                              delivered by Grantee, and assuming this Agreement
                              constitutes a valid and binding agreement of
                              Issuer, this Agreement constitutes a valid and
                              binding agreement of Grantee, enforceable against
                              Grantee in accordance with its terms (except
                              insofar as enforceability may be limited by
                              applicable bankruptcy, insolvency, reorganization,
                              moratorium or similar laws affecting creditors'
                              rights generally, or by principles governing the
                              availability of equitable remedies).

                         (ii)      Purchase Not For Distribution. Any Option
                              Shares or other securities acquired by Grantee
                              upon exercise of the Option will not be, and the
                              Option is not being, acquired by Grantee with a
                              view to the public distribution thereof. Neither
                              the Option nor any of the Option Shares will be
                              offered, sold, pledged or otherwise transferred
                              except in compliance with, or pursuant to an
                              exemption from, the registration requirements of
                              the Securities Act.

               vii.      Adjustment upon Changes in Capitalization, Etc. In the
                    event of any changes in Issuer Common Stock by reason of a
                    stock dividend, reverse stock split, merger,
                    recapitalization, combination, exchange of shares, or
                    similar transaction, the type and number of shares or
                    securities subject to the Option, and the Purchase Price
                    therefor, will be adjusted appropriately, and proper
                    provision will be made in the agreements governing such
                    transaction, so that Grantee will receive upon exercise of
                    the Option the number and class of shares or other
                    securities or property that Grantee would have received with
                    respect to Issuer Common Stock if the Option had been
                    exercised immediately prior to such event or the record date
                    therefor, as applicable.

                         (i)       Without limiting the parties' relative rights
                              and obligations under the Merger Agreement, in the
                              event that the Issuer enters into an agreement (i)
                              to consolidate with or merge into any person,
                              other than Grantee or one of its subsidiaries, and
                              Issuer will not be the continuing or surviving
                              corporation in such consolidation or merger, (ii)
                              to permit any person, other than Grantee or one of
                              its subsidiaries, to merge into Issuer and Issuer
                              will be the continuing or surviving

                                    99.1-6
<PAGE>
 
                              corporation, but in connection with such merger,
                              the shares of Issuer Common Stock outstanding
                              immediately prior to the consummation of such
                              merger will be changed into or exchanged for stock
                              or other securities of Issuer or any other person
                              or cash or any other property, or the shares of
                              Issuer Common Stock outstanding immediately prior
                              to the consummation of such merger will, after
                              such merger represent less than 50% of the
                              outstanding voting securities of the merged
                              company, or (iii) to sell or otherwise transfer
                              all or substantially all of its assets to any
                              person, other than Grantee or one of its
                              subsidiaries, then, and in each such case, the
                              agreement governing such transaction will make
                              proper provision so that the Option will, upon the
                              consummation of any such transaction and upon the
                              terms and condition set forth herein, be converted
                              into, or exchanged for, an option with identical
                              terms appropriately adjusted to acquire the number
                              and class of shares or other securities or
                              property that Grantee would have received in
                              respect of Issuer Common Stock if the Option had
                              been exercised immediately prior to such
                              consolidation, merger, sale, or transfer, or the
                              record date therefor, as applicable and make any
                              other necessary adjustments.

                         (ii)      If, at any time during the period commencing
                              on the occurrence of an event as a result of which
                              Grantee is entitled to receive the Company
                              Termination Fee pursuant to Section 7.12 of the
                              Merger Agreement (the "Purchase Event") and ending
                              on the termination of the Option in accordance
                              with Section 2, Grantee sends to Issuer an
                              Exercise Notice indicating Grantee's election to
                              exercise its right (the "Cash-Out-Right") pursuant
                              to this Section 7(c), then Issuer shall pay to
                              Grantee, on the Option Closing Date, in exchange
                              for the cancellation of the Option with respect to
                              such number of Option Shares as Grantee specifies
                              in the Exercise Notice, an amount in cash equal to
                              such number of Option Shares multiplied by the
                              difference between (i) the average closing price
                              for the 10 trading days commencing on the 12th
                              Nasdaq trading day immediately preceding the
                              Notice Date, per share of Issuer Common Stock as
                              reported on the Nasdaq National Market (or, if not
                              listed on the Nasdaq, as reported on any other
                              national securities exchange or national
                              securities quotation system on which the Issuer
                              Common Stock is listed or quoted, as reported in
                              The Wall Street Journal (Northeast

                                    99.1-7
<PAGE>
 
                              edition), or, if not reported thereby, any other
                              authoritative source) (the "Closing Price") and
                              (ii) the Purchase Price, except that in no event
                              shall the Issuer be required to pay to the Grantee
                              pursuant to this Section 7(c) an amount exceeding
                              the product of (x) $2.00 and (y) such number of
                              Option Shares. Notwithstanding the termination of
                              the Option, Grantee will be entitled to exercise
                              its rights under this Section 7(c) if it has
                              exercised such rights in accordance with the terms
                              hereof prior to the termination of the Option.

          viii.     Repurchase Option. In the event that Grantee notifies Issuer
               of its intention to exercise the Option pursuant to Section 2(a),
               Issuer may require Grantee upon the delivery to Grantee of
               written notice during the period beginning on the Notice Date and
               ending two days prior to the Option Closing Date, to sell to
               Issuer the Option Shares acquired by Grantee pursuant to such
               exercise of the Option at a purchase price per share for such
               sale equal to the Purchase Price plus $2.00. The Closing of any
               repurchase of Option Shares pursuant to this Section 8 shall take
               place immediately following consummation of the sale of the
               Option Shares to Grantee on the Option Closing Date at the
               location and time agreed upon with respect to such Option Closing
               Date.

          ix.       Registration Rights.

          (a) Grantee may by written notice (a "Registration Notice") to Issuer
request Issuer to register under the Securities Act all or any part of the
Option Shares or other securities acquired by Grantee pursuant to this Agreement
(collectively, the "Registrable Securities") in order to permit the sale or
other disposition of such securities pursuant to a bona fide, firm commitment
underwritten public offering in which Grantee and the underwriters shall effect
as wide a distribution of such Registrable Securities as is reasonably
practicable and shall use reasonable efforts to prevent any person or group from
purchasing through such offering shares representing more than 3% of the shares
of Issuer Common Stock then outstanding on a fully-diluted basis; provided,
however, that any such Registration Notice must relate to a number of shares
equal to at least 2% of the shares of Issuer Common Stock then outstanding on a
fully-diluted basis and that any rights to require registration hereunder shall
terminate with respect to any shares that may be sold pursuant to Rule 144(k)
under the Securities Act.

          (b) Issuer shall use reasonable best efforts to effect, as promptly as
practicable, the registration under the Securities Act of the Registrable
Securities requested to be registered in the Registration Notice; provided,
however, that (i) Grantee shall not be entitled to more than an aggregate of two
effective registration statements hereunder and (ii) Issuer will not be required
to file any such registration statement during any period of time (not to exceed
40 days after a Registration Notice in the case of clause (A) below or 90 days
after a Registration Notice in the case of clauses (B) and (C) below) when (A)
Issuer is in possession of material non-public

                                    99.1-8
<PAGE>
 
information which it reasonably believes would be detrimental to be disclosed at
such time and, based upon the advice of outside securities counsel to Issuer,
such information would have to be disclosed if a registration statement were
filed at that time; (B) Issuer would be required under the Securities Act to
include audited financial statements for any period in such registration
statement and such financial statements are not yet available for inclusion in
such registration statement; or (C) Issuer determines, in its reasonable
judgment, that such registration would interfere with any financing, acquisition
or other material transaction involving Issuer. If the consummation of the sale
of any Registrable Securities pursuant to a registration hereunder does not
occur within 180 days after the filing with the SEC of the initial registration
statement therefor, the provisions of this Section shall again be applicable to
any proposed registration, it being understood that Grantee shall not be
entitled to more than an aggregate of two effective registration statements
hereunder. Issuer will use reasonable efforts to cause each such registration
statement to become effective, to obtain all consents or waivers of other
parties which are required therefor, and to keep such registration statement
effective for such period not in excess of 180 calendar days from the day such
registration statement first becomes effective as may be reasonably necessary to
effect such sale or other disposition. Issuer shall use reasonable best efforts
to cause any Registrable Securities registered pursuant to this Section to be
qualified for sale under the securities or blue sky laws of such jurisdictions
as Grantee may reasonably request and shall continue such registration or
qualification in effect in such jurisdictions; provided, however, that Issuer
shall not be required to qualify to do business in, or consent to general
service of process in, any jurisdiction.

          (c) If Issuer effects a registration under the Securities Act of
Issuer Common Stock for its own account or for any other stockholders of Issuer
(other than on Form S-4 or Form S-8, or any successor form), it will allow
Grantee the right to participate in such registration, and such participation
will not affect the obligation of Issuer to effect demand registration
statements for Grantee under this Section 9, except that, if the managing
underwriters of such offering advise Issuer in writing that in their opinion the
number of shares of Issuer Common Stock requested to be included in such
registration exceeds the number which can be sold in such offering, Issuer will
include the shares requested to be included therein by Grantee pro rata with the
shares intended to be included therein by Issuer.

          (d) The registration rights set forth in this Section are subject to
the condition that Grantee shall provide Issuer with such information with
respect to Grantee Registrable Securities, the plan for distribution thereof,
and such other information with respect to Grantee as, in the reasonable
judgment of counsel for Issuer, is necessary to enable Issuer to include in a
registration statement all material facts required to be disclosed with respect
to a registration hereunder.

          (e) A registration effected under this Section shall be effected at
Issuer's expense, except for underwriting discounts and commissions and the fees
and expenses of Grantee's counsel, and Issuer shall provide to the underwriters
such documentation (including certificates, opinions of counsel and "comfort"
letters from auditors) as are customary in connection with

                                    99.1-9
<PAGE>
 
underwritten public offerings and as such underwriters may reasonably require.
In connection with any registration, Grantee and Issuer agree to enter into an
underwriting agreement reasonably acceptable to each such party, in form and
substance customary for transactions of this type.

          x.        Transfers. The Option Shares may not be sold, assigned,
               transferred, or otherwise disposed of except (i) pursuant to
               Section 8 hereof, (ii) in an underwritten public offering as
               provided in Section 9 or (iii) to any purchaser or transferee who
               would not, to the knowledge of the Grantee after reasonable
               inquiry, immediately following such sale, assignment, transfer or
               disposal beneficially own more than 4.9% of the then-outstanding
               voting power of the Issuer, except that Grantee shall be
               permitted to sell any Option Shares if such sale is made pursuant
               to a tender or exchange offer that has been approved or
               recommended by a majority of the members of the Board of
               Directors of Issuer (which majority shall include a majority of
               directors who were directors as of the date hereof).

          xi.       Listing. If Issuer Common Stock or any other securities to
               be acquired upon exercise of the Option are then listed on the
               Nasdaq (or any other national securities exchange or national
               securities quotation system), Issuer, upon the request of
               Grantee, will promptly file an application to list the shares of
               Issuer Common Stock or other securities to be acquired upon
               exercise of the Option on the Nasdaq (and any such other national
               securities exchange or national securities quotation system) and
               will use reasonable efforts to obtain approval of such listing as
               promptly as practicable.

          xii.      Miscellaneous. Expenses. Except as otherwise provided in the
               Merger Agreement, each of the parties hereto will pay all costs
               and expenses incurred by it or on its behalf in connection with
               the transactions contemplated hereunder, including fees and
               expenses of its own financial consultants, investment bankers,
               accountants and counsel.

                         (i)       Amendment. This Agreement may not be amended,
                              except by an instrument in writing signed on
                              behalf of each of the parties.

                         (ii)      Extension; Waiver. Any agreement on the part
                              of a party to waive any provision of this
                              Agreement, or to extend the time for performance,
                              will be valid only if set forth in an instrument
                              in writing signed on behalf of such party. The
                              failure of any party to this Agreement to assert
                              any of its rights under this Agreement or
                              otherwise will not constitute a waiver of such
                              rights.

                                    99.1-10
<PAGE>
 
                         (iii)      Entire Agreement; No Third-Party
                              Beneficiaries. This Agreement, the Merger
                              Agreement (including the documents and instruments
                              attached thereto as exhibits or schedules or
                              delivered in connection therewith) and the
                              Confidentiality Agreement (i) constitute the
                              entire agreement, and supersede all prior
                              agreements and under standings, both written and
                              oral, between the parties with respect to the
                              subject matter of this Agreement, and (ii) are not
                              intended to confer upon any person other than the
                              parties any rights or remedies.

                         (iv)      Governing Law. This Agreement will be
                              governed by, and construed in accordance with, the
                              laws of the State of Delaware, regardless of the
                              laws that might otherwise govern under applicable
                              principles of conflict of laws thereof.

                         (v)       Notices. All notices, requests, claims,
                              demands, and other communications under this
                              Agreement must be in writing and will be deemed
                              given if delivered personally, telecopied (which
                              is confirmed), or sent by overnight courier
                              (providing

proof of delivery) to the parties at the following addresses (or at such other
address for a party as shall be specified by like notice):

     If to Issuer to:

        May & Speh, Inc.
        1501 Opus Place
        Downers Grove, IL 60515
        Fax: (630) 719-0525
        Attention: Chief Executive Officer
 
     with a copy to:

        Winston & Strawn
        35 West Wacker Drive
        Chicago, IL 60601
        Fax: (312) 558-5700
        Attention:  Bruce  A. Toth

     If to Grantee to:

                                    99.1-11
<PAGE>
 
        Acxiom Corporation
        P.O. Box 2000
        301 Industrial Boulevard
        Conway, AR 72033-2000
        Fax: (501) 336-3913
        Attention: President

     with a copy to:

        Skadden, Arps, Slate, Meagher & Flom LLP
        919 Third Avenue
        New York, New York 10022
        Attention:  J. Michael Schell
        Telecopy: (212) 735-2000


                         (vi)      Assignment. Neither this Agreement, the
                              Option nor any of the rights, interests, or
                              obligations under this Agreement may be assigned,
                              transferred or delegated, in whole or in part, by
                              operation of law or otherwise, by Issuer or
                              Grantee without the prior written consent of the
                              other. Any assignment, transfer or delegation in
                              violation of the preceding sentence will be void.
                              Subject to the first and second sentences of this
                              Section 12(g), this Agreement will be binding
                              upon, inure to the benefit of, and be enforceable
                              by, the parties and their respective successors
                              and assigns.

                         (vii)     Further Assurances. In the event of any
                              exercise of the Option by Grantee, Issuer and
                              Grantee will execute and deliver all other
                              documents and instruments and take all other
                              action that may be reasonably necessary in order
                              to consummate the transactions provided for by
                              such exercise.

                         (viii)    Enforcement. The parties agree that
                              irreparable damage would occur and that the
                              parties would not have any adequate remedy at law
                              in the event that any of the provisions of this
                              Agreement were not performed in accordance with
                              their specific terms or were otherwise breached.
                              It is accordingly agreed that the parties will be
                              entitled to an injunction or injunctions to
                              prevent breaches of this Agreement and to enforce
                              specifically the terms

                                    99.1-12
<PAGE>
 
                              and provisions of this Agreement in any Federal
                              court located in the State of Delaware or in
                              Delaware state court, the foregoing being in
                              addition to any other remedy to which they are
                              entitled at law or in equity. In addition, each of
                              the parties hereto (i) consents to submit itself
                              to the personal jurisdiction of any Federal court
                              located in the State of Delaware or any Delaware
                              state court in the event any dispute arises out of
                              this Agreement or any of the transactions
                              contemplated by this Agreement, (ii) agrees that
                              it will not attempt to deny or defeat such
                              personal jurisdiction by motion or other request
                              for leave from any such court, and (iii) agrees
                              that it will not bring any action relating to this
                              Agreement or any of the transactions contemplated
                              by this Agreement in any court other than a
                              Federal court sitting in the State of Delaware or
                              a Delaware state court.

                                    99.1-13
<PAGE>
 
     IN WITNESS WHEREOF, Issuer and Grantee have caused this Agreement to be
signed by their respective officers thereunto duly authorized as of the day and
year first written above.


                                       MAY & SPEH, INC.


                                       By: /s/ Peter I. Mason
                                           --------------------------------
                                           Name:  Peter I. Mason
                                           Title: Chairman, President and 
                                                    Chief Executive Officer


                                       ACXIOM CORPORATION


                                       By: /s/ Charles D. Morgan, Jr.
                                           --------------------------------
                                           Name:  Charles D. Morgan, Jr.
                                           Title: CEO and President

