<PAGE>

                                                                    EXHIBIT 10.2

                              DELTA AIR LINES, INC.

                                    AMENDMENT
                                       TO
                            PILOTS STOCK OPTION PLAN

      THIS AMENDMENT ("Amendment") to the Delta Air Lines, Inc. Pilots Stock
Option Plan, as amended, (the "Plan") amends the Plan effective as of such time
as this Amendment is both approved by the shareowners of the Company and agreed
to by the Association. Capitalized terms not otherwise defined herein will have
the meaning ascribed to such terms in the Plan.

      1. Section 2.17 of the Plan is amended and restated to read in its
entirety as follows:

            "2.17 "Stock" means the Common Stock, $1.50 par value, of the
      Company."

      2. Section 4.1 of the Plan is amended and restated to read in its entirety
as follows:

            "4.1 Stock Reserved. The total number of shares of Stock reserved
      and available for distribution under the Plan shall be 20,000,000, which
      number reflects the two-for-one split of the Common Stock of the Company
      effective in 1998. Stock issued under the Plan may be either authorized
      and unissued shares or treasury shares. Notwithstanding the foregoing,
      such number of shares of Stock as are subject to Stock Options that are
      cancelled pursuant to the Stock Option Exchange Program (as defined in
      Article 9 hereof) and as are necessary to grant Replacement Options (as
      defined in Article 9 hereof) in exchange for such cancelled Stock Options
      will again be available for distribution pursuant to such Replacement
      Options and, otherwise, shares of Stock subject to such cancelled Stock
      Options will not be available for distribution under the Plan."

      3. The Plan is amended to add the following Article 9, which reads in its
entirety as follows:

                    "ARTICLE 9. STOCK OPTION EXCHANGE PROGRAM

            9.1 In General. At such time as the Committee determines advisable,
      the Company will be permitted (but not required) to offer each Eligible
      Participant (as defined below) who holds Eligible Options (as defined
      below) a one-time opportunity to elect to surrender all of such Eligible
      Participant's Eligible Options for cancellation ("Surrendered Options") in
      exchange for the grant of replacement options to purchase shares of Stock
      to be granted under the Plan ("Replacement Options") on a date to be
      determined by the Committee that is no less than six months and one day
      following the cancellation of such Surrendered Options (such exchange, the
      "Stock Option Exchange Program"). The Stock Option Exchange
<PAGE>
      Program and the Replacement Options shall have the terms and conditions
      set forth or provided for in this Article 9. Except to the extent
      otherwise determined by the Committee, the Stock Option Exchange Program
      will be structured so that the Company avoids incurring financial
      accounting charges as a result thereof.

            To participate in the Stock Option Exchange Program and receive any
      grant of Replacement Options, an Eligible Participant must be an Eligible
      Participant on each of the following dates: (i) the date the Stock Option
      Exchange Program commences, (ii) the date the period during which
      Surrendered Options may be surrendered for cancellation pursuant to the
      Stock Option Exchange Program expires and (iii) the date of grant of the
      Replacement Options.

            9.2 Eligible Participants. For purposes of the Stock Option Exchange
      Program, the term "Eligible Participant" shall mean an employee of the
      Company whose name appears on the Delta Air Lines Pilots' System Seniority
      List and who is not on (i) Retirement, (ii) Furlough, (iii) long-term
      Disability or (iv) Leave of Absence other than Leave of Absence due to
      military service or due to any other reason as determined by the
      Committee.

            9.3 Eligible Options. For purposes of the Stock Option Exchange
      Program, the term "Eligible Option" shall mean an outstanding Stock Option
      granted under the Plan.

            9.4 Exchange Ratio. In exchange for three shares of Stock subject to
      Surrendered Options, a Replacement Option to purchase one share of Stock
      will be granted, subject to any adjustments for transactions or events
      specified in Section 4.2 of the Plan. Notwithstanding the foregoing, if
      the number of shares subject to a Replacement Option determined by
      application of the foregoing exchange ratio is a fractional number, such
      fractional number will be rounded up to the nearest whole number for the
      purposes of determining the number of such shares. In determining the
      number of Replacement Options to be granted in exchange for Surrendered
      Options, the foregoing exchange ratio shall be applied separately to
      Surrendered Options having the same grant date and the resulting number of
      Replacement Options shall then be rounded in accordance with the
      foregoing.

            9.5 Terms of Replacement Options. Notwithstanding any other
      provision of the Plan, Replacement Options shall have the terms set forth
      in this Section 9.5 and such other terms and conditions as may be
      determined by the Committee in accordance with the provisions hereof.

                  9.5.1. Exercise Price. The price at which a share of Stock
      covered by a Replacement Option may be purchased shall be the closing
      price of the Stock on the New York Stock Exchange on the date of grant, if
      the date is a trading day, and, if not, on the previous trading day.

                                       2
<PAGE>
                  9.5.2. Option Exercise Period and Term. Each Replacement
      Option will become exercisable on the first anniversary of its date of
      grant and immediately exercisable, vested and nonforfeitable upon a change
      in control of the Company. For the purpose of the foregoing, a "change in
      control of the Company" shall have such meaning as may be determined by
      the Committee in accordance with the provisions hereof. Subject to Article
      7 of the Plan, each Replacement Option, once exercisable, will be
      exercisable for the remaining term of the Surrendered Options in exchange
      for which it is granted and for an additional period of time beyond such
      remaining term equal to the period of time from the date of cancellation
      of such Surrendered Options through and including the date of grant of
      such Replacement Option. Following such period for which a Replacement
      Option is exercisable, such Replacement Option shall expire and no shares
      of Stock may be purchased thereunder.

                  9.5.3. Non-Qualified Options. All Replacement Options shall be
      deemed "non-qualified" for purposes of Section 422 of the Internal Revenue
      Code of 1986, as amended from time to time, and any successor thereto.

            9.6 Administration. In addition to the authority of the Committee
      set forth in Section 3.2 of the Plan, which authority the Committee shall
      have with respect to the Stock Option Exchange Program and the Replacement
      Options, the Committee shall have full discretionary authority to
      establish conditions for the commencement, continuation and/or
      consummation of the Stock Option Exchange Program, to determine the extent
      to which the Stock Option Exchange Program will result in the Company
      incurring financial accounting charges and to adopt such further terms and
      conditions relating to the Stock Option Exchange Program that are
      consistent with the provisions set forth in this Article 9. Without
      limiting the generality of Section 3.2 or of the foregoing, the Committee
      will have total and exclusive responsibility to control, operate, manage
      and administer the Stock Option Exchange Program in accordance with its
      terms and conditions and all the authority that may be necessary or
      helpful to enable it to discharge its responsibilities with respect to the
      Stock Option Exchange Program."

      4. All references in the Plan and this Amendment to the "Plan" shall be
deemed to be references to the Plan as amended hereby. Unless the context
requires otherwise, references in Sections 3.2, 4.2, 6.2, 6.5, 6.6, 6.7, 7.1,
7.2, 7.3, 8.4, 8.6 of the Plan to "Stock Options," "Participants" and "Option
Price" shall, in addition, be deemed to be references to "Replacement Options,"
"Eligible Participants" and "the price at which a share of Stock covered by a
Replacement Option may be purchased" (as described in Section 9.5.1 hereof),
respectively.

      5. This Amendment does not supersede the terms and conditions of the Plan,
except to the extent expressly described herein and the Plan, as amended hereby,
shall remain in full force and effect as so amended.

                                       3
<PAGE>
      IN WITNESS WHEREOF, this Amendment is executed as of April 14,
2003.

FOR DELTA AIR LINES, INC.               FOR THE AIR LINE PILOTS
                                        ASSOCIATION, INTERNATIONAL

By: /s/ Terry M. Erskine                By: /s/ Duane E. Woerth
    --------------------------              --------------------------
Terry M. Erskine                        Captain Duane E. Woerth
Vice-President-Labor Relations          President

                                        By: /s/ William C. Buergey
                                            --------------------------
                                        Captain William C. Buergey
                                        Chairman, Delta MEC

                                       4