<PAGE>

EXHIBIT 10.2                  THE BISYS GROUP, INC.

                      Non-Qualified Stock Option Agreement

Officer/Optionee:

Number of Option Shares:

Pursuant to The BISYS Group, Inc. 1999 Stock Option Plan (the "Plan"), the
Option Committee (the "Committee") of the Board of Directors of The BISYS Group,
Inc. (the "Company") has granted to you on this date an option (the "Option") to
purchase the number of shares of the Company's Common Stock, $.02 par value
("Common Stock"), set forth above. Such number of shares (as such may be
adjusted as described in Section 10 below) is herein referred to as the "Option
Shares". This Option shall constitute and be treated as a "non-qualified stock
option" as described in Treasury Regulation Section 1.83-7 for federal income
tax purposes. The terms and conditions of this Option are set out below.

1.  Date of Grant. This Option is granted to you on the Grant Date of [DATE], as
    set forth on the attached Grant Detail Report.

2.  Termination of Option. Your right to exercise this Option (and to purchase
    the Option Shares) shall expire and terminate in all events on the earliest
    to occur of:

    (a) the Expiration Date set forth on the attached Grant Detail Report [10
        YEARS FROM DATE OF GRANT];

    (b) the date provided in Sections 8(a), 8(b), 8(c) or 8(d) below in the
        event you cease to be employed by the Company or any Subsidiary of the
        Company (as defined in the Plan); or

    (c) the date provided in Section 8(e) below in the event you violate any
        provisions of the Restrictive Covenants Agreement (as defined in Section
        8(e) below).

3.  Option Price. The purchase price to be paid upon the exercise of this Option
    shall be the Option Price set forth on the Grant Detail Report, the fair
    market value of a share of Common Stock (as determined by the Committee) on
    the close of business on the business day preceding the date of grant of
    this Option.

4.  Vesting Provisions. This option shall vest and become exercisable in
    accordance with the schedule set forth under the caption Options Becoming
    Exercisable on the attached Grant Detail Report. [20% OF THE OPTIONS VEST ON
    EACH OF THE FIRST FIVE ANNIVERSARIES OF THE DATE OF GRANT]

5.  Additional Provisions Relating to Exercise.

    (a) Once you become entitled to exercise this Option (and to purchase Option
        Shares) as provided in Section 4 hereof, such right will continue until
        the date on which this Option expires and terminates pursuant to Section
        2 hereof.

    (b) i. The Committee, in its sole discretion, may at any time accelerate the
           time at which this Option may be exercised by you with respect to any
           Option Shares.

       ii. In the event of a "change in control" of the Company (as defined
           below), all Option Shares granted hereunder shall be automatically
           vested (to the extent not previously

                                     1 of 4

<PAGE>

            vested) as of the effective date of such change in control event and
            exercisable by you. For the purposes hereof, "change in control" of
            the Company shall mean (x) a sale or other disposition of more than
            50% of the outstanding Common Stock of the Company to an unrelated
            and unaffiliated third party purchaser, other than in connection
            with an underwritten public offering by the Company registered under
            the Securities Act of 1933, as amended, or (y) a sale of
            substantially all of the assets of the Company (as determined by the
            Board of Directors of the Company) to an unrelated and unaffiliated
            third party purchase (an "Asset Sale").

6.  Exercise of Option.

    (a) To exercise the Option, you must deliver a completed copy of the
        attached Option Exercise Form to the address indicated on the Form,
        specifying the number of Option Shares being purchased as a result of
        such exercise, together with payment of the full option price for the
        Option Shares being purchased. Payment of the option price must be made
        in cash or by check or by use of any cashless stock option exercise
        program offered by the Company through a brokerage firm.

    (b) At the time of exercise, you will recognize as taxable ordinary income
        (compensation income), an amount equal to the excess of the fair market
        value of the exercised option shares on the date of exercise over the
        exercise price.

7.  Transferability of Option. This Option may not be transferred by you (other
    than by will or the laws of descent and distribution) and may be exercised
    during your lifetime only by you.

8.  Termination of Employment.

    (a) In the event that you cease to be employed by the Company or any
        Subsidiary for any reason other than because of your "retirement" (as
        defined below), death, or "disability" (within the meaning of Section
        22(e)(3) of the Code), this Option may only be exercised within one
        month after you cease to be so employed, and only to the same extent
        that you were entitled to exercise this Option on the date you ceased to
        be so employed and had not previously done so.

    (b) In the event that you cease to be employed by the Company or any
        Subsidiary by reason of "disability" (as defined in paragraph (a)
        above), this Option may only be exercised within one year after the date
        you cease to be so employed, and only to the same extent that you were
        entitled to exercise this Option on the date you ceased to be so
        employed by reason of such disability and had not previously done so.

    (c) In the event that you die while employed by the Company or any
        Subsidiary (or within a period of one month after ceasing to be employed
        by the Company or any Subsidiary for any reason other than "retirement"
        or "disability" [as defined in paragraph (a) above] or within a period
        of one year after ceasing to be employed by the Company by reason of
        such "retirement" or "disability"), this Option may only be exercised
        within one year after your death. In such event, this Option may be
        exercised during such one year period by the executor or administrator
        of your estate or by any person who shall have acquired the Option
        through bequest or inheritance, but only to the same extent that you
        were entitled to exercise this Option immediately prior to the time of
        your death and you had not previously done so.

    (d) In the event that you "retire" from employment with the Company or any
        Subsidiary, this Option may only be exercised within one year after the
        date you cease to be so employed,

                                     2 of 4

<PAGE>

        and only to the same extent that you were entitled to exercise this
        Option on the date you ceased to be so employed and had not previously
        done so. For purposes hereof, you are eligible for this one-year
        "retirement" exercise period, rather than the one-month exercise period
        provided for in paragraph (a) above, where you "retire" after attaining
        the age of 55 and serving at least ten years with the Company or any
        Subsidiary (including any service bridging afforded in connection with
        an acquisition). Accordingly, the one-year post-retirement exercise
        period shall expire early in the event of, and upon, your subsequent
        employment or other engagement for services that would result in taxable
        income to you for services performed.

    (e) Reference is made to a certain restrictive covenants agreement between
        you and the Company previously entered into or entered into
        simultaneously herewith (the "Restrictive Covenants Agreement"). You
        hereby reaffirm the contents of your Restrictive Covenants Agreement and
        you acknowledge and agree that the grant of the Option Shares hereby
        constitutes consideration for your undertakings and agreements set forth
        in the Restrictive Covenants Agreement. Notwithstanding anything to the
        contrary expressly set forth or implied herein, in the event that you at
        any time violate any of the provisions of the Restrictive Covenants
        Agreement, then your right to exercise this Option with respect to all
        or any portion of the Option Shares (including, without limitation, any
        Option Shares which you were entitled to purchase hereunder but had not
        previously done so) shall thereupon terminate.

    (f) Notwithstanding any provisions contained in this Section 8 to the
        contrary, in no event may this Option be exercised to any extent by
        anyone after the Expiration Date.

9.  Representations. You further represent and warrant that you understand the
    Federal, state and local income tax consequences of the granting of this
    Option to you, the exercise of this Option and purchase of Option Shares,
    and the subsequent sale or other disposition of any Option Shares. In
    addition, you understand that the Company may be required to withhold
    Federal, state or local taxes in respect of any compensation income realized
    by you as result of any Option Shares acquired upon exercise of the option
    granted hereunder. In the event that the Company is required to withhold any
    such taxes, you hereby agree to provide the Company with cash funds equal to
    the total Federal, state and local taxes required to be so withheld, or make
    other arrangements satisfactory to the Company regarding such payment. It is
    understood that all matters with respect to the total amount of taxes to be
    withheld in respect of any such compensation income shall be determined by
    the Committee in its sole discretion.

10. Adjustments.

    (a) Subject to paragraph (b) below, if the total outstanding shares of
        Common Stock of the Company shall be increased or decreased or changed
        into or exchanged for a different number or kind of shares of stock or
        other securities of the Company or of another corporation through
        reorganization, combination or exchange or shares or declaration of any
        dividends payable in stock, then the Committee shall appropriately
        adjust the number of Option Shares (and price per share) subject to the
        unexercised portion of this Option (to the nearest possible full share)
        subject in all cases to the limitations of Section 425 of the Code.

    (b) Notwithstanding the foregoing, in the event of:

        i.  any offer to holders of Common Stock generally relating to the
            acquisition of their shares including, without limitation, through
            purchase, merger, consolidation or otherwise, or

                                     3 of 4

<PAGE>

        ii. any transaction generally relating to the acquisition of
            substantially all of the assets or business of the Company,

        subject to Section 5(b) (ii), the Board of Directors may make such
        adjustment as it deems equitable in respect of this Option including,
        without limitation, the revision or cancellation of this Option. Any
        such determination by the Board of Directors shall be effective and
        binding for all purposes of this Agreement.

11. Continuation of Employment. Neither the Plan nor this Option shall confer
    upon you any right to continue in the employ of the Company or any
    Subsidiary or limit in any respect the right of the Company or any
    Subsidiary to terminate your employment at any time.

12. Plan Documents. This Option Agreement is qualified in its entirety by
    reference to the provisions of the Plan applicable to "non-qualified stock
    options", which are hereby incorporated herein by reference.

13. Governing Law. This Agreement shall be governed by and construed in
    accordance with the laws of the State of Delaware. If any one or more
    provisions of this Agreement shall be found to be illegal or unenforceable
    in any respect, the validity and enforceability of the remaining provisions
    hereof shall not be in any way be affected or impaired thereby.

Please acknowledge receipt of this Option Agreement by signing the enclosed copy
of this Non-Qualified Stock Option Agreement in the space provided below and
returning it promptly to the Chief Executive Officer of the Company.

                                                           THE BISYS GROUP, INC.

                                                           By:   _______________
                                                                 Name:
                                                                 Title:

ACCEPTED AND AGREED TO
AS OF [GRANT DATE]

_______________________
Officer/Optionee

                                     4 of 4