<PAGE>

                                                                   EXHIBIT 10.13

                              EXIDE CORPORATION
                      NONQUALIFIED STOCK OPTION AGREEMENT

     This Nonqualified Stock Option Agreement (this "Agreement"), is made as of
May 22, 2000 by Exide Corporation, a Delaware corporation (the "Company"), in
favor of Kevin R. Morano (the "Optionee") Executive Vice President and Chief
Financial Officer.

     As a material inducement to the Optionee's agreement to become employed by
the Company, on May 22, 2000 (the "Grant Date") the Company granted to the
Optionee an option (the "Option") to acquire 150,000 shares of the Company's
common stock, par value $.01 per share (the "Option Shares").

     The Option was not granted pursuant to a stock option plan, however, the
option is subject to the administrative provisions of the Company's 1999 Stock
Incentive Plan (the "Plan").  Certain terms used herein are defined in paragraph
7 below.

     The parties hereto hereby agree as follows:

          1.   Option.  Subject to the terms and conditions set forth herein and
               ------
               in the Plan, the Optionee has been granted an Option to purchase
               the Option Shares at a price per share of $8.25 (the "Exercise
               Price"), payable upon exercise as set forth in Section 7(c) of
               the Plan. The Option shall expire at the close of business on the
               tenth anniversary of the Grant Date (the "Expiration Date"),
               subject to earlier expiration as provided in section 7(b)(2) of
               the Plan. The Exercise Price and the number and kind of shares of
               the Company's common stock or other property for which the Option
               may be exercised shall be subject to adjustment as provided in
               Section 9 of the Plan. The Option is not intended to qualify as
               an "incentive stock option" within the meaning of Section 422 of
               the Code.

          2.   Exercisability/Vesting
               ----------------------


                    (a)  Normal Vesting.  The Option granted hereunder may be
                         --------------
                         exercised only to the extent it has become vested. The
                         Option shall vest in four equal installments on each of
                         the first four anniversaries of the Grant Date for so
                         long as the Optionee is an officer or employee of the
                         Company and shall become fully vested on the fourth
                         anniversary of the Grant Date.

                                       1
<PAGE>

                    (b)  Vesting Under Certain Circumstances.  Notwithstanding
                         -----------------------------------
                         paragraph 2(a) above, under certain circumstances the
                         vesting rules of Section 7(b)(2) of the Plan shall
                         apply.


          3.   Procedure for Exercise.  Subject to the terms of this Agreement
               ----------------------
               and the Plan, the Optionee may exercise all or any portion
               of the Option by delivering written notice to the Company in
               the form attached hereto as Exhibit A together with payment
                                           ----------
               of the Exercise Price in accordance with the provisions of
               Section 7(c) of the Plan. The Option may not be exercised for a
               fraction of an Option Share.

          4.   Conformity with the Plan.  The Option is not granted pursuant
               ------------------------
               to a stock option plan, however, the Option is intended to
               conform in all respects with, and is subject to the
               administrative provisions of the Plan (which is incorporated
               herein by reference). Inconsistencies between the Agreement and
               the Plan shall be resolved in accordance with the terms of the
               Plan.

          5.   Rights of the Optionee.  Nothing in this Agreement shall
               ----------------------
               interfere with or limit in any way the right of the Company to
               terminate the Optionee's employment at any time (with or without
               cause), nor confer upon the Optionee any right to continue in the
               employ of the Company for any period of time or to continue his
               or her present (or any other) rate of compensation.

          6.   Withholding of Taxes.  Withholding of taxes in connection
               --------------------
               with the exercise of the Option shall occur in accordance
               with Section 13 of the Plan.

          7.   Certain Definitions
               -------------------

               "Code"  shall mean the Internal Revenue Code of 1986, as amended,
                ----
               and any successor statute.

               "Common Stock"  shall mean the Company's common stock, par value
                ------------
               $.01 per share.

               "Company"  shall mean Exide Corporation, a Delaware corporation,
                -------
               and (except to the extent the context requires
               otherwise) any subsidiary corporation of the Company as such term
               is defined in Section 424(f) of the Code.

               "Option Shares" shall mean (i) all shares of the common stock
                -------------
               issued or issuable upon the exercise of the Option and (ii) all

                                       2
<PAGE>

               shares of common stock issued with respect to the common stock
               referred to in clause (i) above by way of stock dividend or stock
               split in connection with any conversion, merger, consolidation or
               recapitalization or other reorganization affecting the common
               stock.



                             *    *    *    *    *

                                       3