NONQUALIFIED STOCK OPTION CERTIFICATE (Optionee: James E. Rogers

Exhibit 10.4

NONQUALIFIED STOCK OPTION CERTIFICATE

(Optionee: James E. Rogers

April 4, 2006 Grant Date)

THIS CERTIFIES THAT on the above-specified Grant Date, James E. Rogers (“Optionee”) has been awarded an OPTION to purchase an aggregate of one million, eight hundred seventy-seven thousand, six hundred forty six (1,877,646) shares of DUKE ENERGY CORPORATION Common Stock, no par value, at a price per share of $29.14, subject to the terms and conditions of this Certificate and the related Nonqualified Stock Option Agreement specifying the same Optionee and Grant Date as this Certificate (the “Agreement”).

THE OPTION shall expire ten (10) years from the Grant Date of this Certificate. Except as may be otherwise provided in the Agreement, the right to exercise THE OPTION shall vest as to a portion of the aggregate number of shares set forth above in accordance with the following schedule:

THE OPTION, shall not be exercisable unless and until, and then only to the extent it is vested and shall not be exercisable as to less than twenty-five (25) shares, or, if less, all remaining shares then exercisable. Except as otherwise provided in the Agreement, no shares acquired upon exercise of the Option shall be sold, transferred, exchanged, assigned, pledged, hypothecated, alienated or otherwise encumbered until April 3, 2009 or, if earlier, the termination of the Optionee’s continuous employment by Duke Energy Corporation (including its subsidiaries).

IN WITNESS OF its agreement to be bound by the provisions of this Certificate and the Agreement, DUKE ENERGY CORPORATION has caused this Certificate to be signed on its behalf by its duly authorized officer this      day of April 2006 in duplicate.

IN WITNESS OF Optionee’s acceptance of THE OPTION and Optionee’s agreement to be bound by the provisions of this Certificate, the Agreement (including, but not limited to, Section 12 thereof, entitled “Optionee Confidentiality Obligations”) and the Plan, Optionee has signed this Certificate this 5th day of April 2006.

NONQUALIFIED STOCK OPTION AGREEMENT

(Optionee: James E. Rogers

April 4, 2006 Grant Date)

THIS AGREEMENT is made as of the Grant Date specified above (the “Grant Date”), between Duke Energy Corporation, a Delaware corporation (the “Corporation”), and the Optionee specified above (the “Optionee”).

RECITALS

The Corporation has entered into an employment agreement with the Optionee dated April 4, 2006 (the “Employment Agreement”), pursuant to which it has agreed to make certain equity-based awards to the Optionee, including the award memorialized by this Agreement. The Corporation has assumed the 1998 Long-Term Incentive Plan that, prior to the consummation of the transactions contemplated by the Agreement and Plan of Merger dated May 8, 2005, by and among the Corporation, Duke Energy Corporation, a North Carolina corporation (“Old Duke”), Cinergy Corp., Deer Acquisition Corp. and Cougar Acquisition Corp., was maintained by Old Duke (the “Company Plan”). The grant memorialized by this Agreement is not made pursuant to the Company Plan; however, for convenience, it shall be deemed to be made pursuant to a plan document with terms substantially identical to the Company Plan (such deemed plan document, the “Plan”). The applicable terms/provisions of the Plan are incorporated in this Agreement by reference, including the definitions of terms contained in the Plan (except to the extent a term is otherwise defined herein).

1. Grant and Designation of Option. Pursuant to the provisions of the Employment Agreement, the Corporation hereby grants to the Optionee, subject to the terms and conditions of the Employment Agreement, this Agreement, and the related Nonqualified

Stock Option Certificate specifying the same Optionee and Grant Date as this Agreement, which certificate is incorporated herein by reference (the “Certificate”), the right and option to purchase from the Corporation the aggregate number of shares of common stock, 1,877,646 par value, of the Company (“Common Stock”) set forth on the Certificate at the per share price set forth on the Certificate (the “Option Price”), subject to any adjustment as provided in this Agreement or the Plan (collectively, the “Option”). The Option is not an incentive stock option within the meaning of Code Section 422A. This Agreement, together with the Certificate, shall constitute an “Award Agreement” under the Plan.

2. Term of Option and Vesting. Subject to earlier forfeiture, termination, acceleration or cancellation of the Option as provided in this Agreement or the Certificate, the term of the Option shall be for a period of ten (10) years from the Grant Date. Subject to the provisions of this Agreement, the Option shall vest at such times and as to such number of shares as determined on the basis of the schedule set forth on the Certificate.

3. Method of Exercise. To the extent that the right to purchase shares has become vested, the Option, or any part thereof, may be exercised by giving signed, written notice of exercise to the Corporation (the “Exercise Notice”) specifying the number of shares to be purchased, subject to Section 10. The date of exercise shall be the date the properly completed Exercise Notice is delivered to the Corporation. The Exercise Notice shall be accompanied by payment of the aggregate Option Price for the shares to be purchased, in the following manner:

For purposes of paragraph (a) above, if, and in such manner, as the Optionee is permitted by the Corporation’s Executive Compensation and Benefits Department, and which is not contrary to federal or state securities or other laws, rules and regulations, the Optionee may provide for the payment of the aggregate Option Price for the shares to be purchased by delivering a properly executed Exercise Notice together with irrevocable instructions to a broker to promptly deliver to the Corporation the amount of such aggregate Option Price. The Corporation, acting through its Executive Compensation and Benefits Department, may comply with applicable law by restricting the manner by which the Optionee may pay the Option Price or permitting an alternate method therefore.

Subject to Section 4 and the other applicable provisions of this Agreement and the Plan, in the event of the exercise of the Option, the Corporation shall deliver to the Optionee or, if applicable, to a broker designated by the Optionee, a certificate representing the shares of Common Stock purchased as a result of the exercise.

No partial exercise of the Option may be for fewer than twenty-five (25) shares or the full number of shares as to which the Option is exercisable at the time of such partial exercise, if less than twenty-five (25) shares.

4. Tax Withholding. Shares of Common Stock shall not be issued upon the exercise of the Option unless all federal, state and other governmental withholding tax requirements arising from such exercise have been satisfied by the Optionee or provision therefor has been made to the satisfaction of the Executive Compensation and Benefits Department. Notwithstanding the foregoing, to the extent that Optionee fails to timely tender to the Corporation sufficient cash to satisfy withholding for tax requirements, such withholding shall be applied to reduce the number of shares of Common Stock that would otherwise be deliverable upon exercise of the Option.

5. Nonalienation. The Option granted hereunder is not assignable or transferable by the Optionee otherwise than by will or the laws of descent and distribution, and is exercisable, during the Optionee’s lifetime, only by the Optionee. Upon any attempt to transfer, assign, pledge, hypothecate or otherwise dispose of the Option, or of any right or privilege conferred hereby, contrary to the provisions hereof, or upon the levy of any attachment or similar process upon, or other voluntary or involuntary attempted alienation of, the Option, or any right or privilege conferred hereby, the Option and the right and privilege conferred hereby shall immediately become null and void. Notwithstanding the foregoing provisions of this Section 5, in accordance with Section 6.5 of the Plan, the Optionee may, with the advance approval of the Committee, transfer or assign some or all of the Option granted hereunder to members of the Optionee’s immediate family (as determined by the Committee) or to trusts, partnerships or corporations whose beneficiaries,

members or owners are members of the Optionee’s immediate family. Any such transfer or assignment shall be subject to the terms and conditions specified by the Committee as described in an Option Transfer Agreement to be executed by the Corporation, the Optionee and the assignee or transferee. Except to the extent provided in Sections 3 or 4 above or the foregoing provisions of this Section 5, in no event may shares of Common Stock subject to the Option be sold, transferred, exchanged, assigned, pledged, hypothecated, alienated or otherwise encumbered until April 3, 2009 or, if earlier, the termination of the Optionee’s continuous employment by the Corporation (including its subsidiaries).

6. Rights as a Stockholder. The Optionee shall have no rights as a stockholder with respect to any shares of Common Stock subject to the Option prior to the date of issuance to Optionee of a certificate or certificates for such shares.

7. Effect of Termination of Employment. Except as otherwise provided in Section 7(a) or 7(b), below, the Option shall be forfeited in the event of the termination of the Optionee’s continuous employment by the Corporation (including its subsidiaries). The Committee may make such provision as it deems appropriate if the Optionee is on approved leave of absence from such employment. The Option shall be subject to the following provisions in the case of the cessation of the Optionee’s employment during the term of the Option:

Subject to the limitations described in the foregoing provisions of this Section 7, the Option may be exercised, to the extent vested, at any time within ten (10) years from the Grant Date; provided that, if the Optionee’s employment terminates by reason of “Cause” within the meaning of Exhibit B to the Employment Agreement, the Option may be exercised, to the extent vested, at any time within ninety (90) days from the date of termination (provided that in no event may the Option be exercised more than ten (10) years from the Grant Date), after which time the Option shall expire.

9. Notices. Except as otherwise provided in this Agreement, any notice to be given to the Corporation under this Agreement shall be addressed to the Executive Compensation and Benefits Department—Stock Option (PB04A), Duke Energy Corporation at P. O. Box 1244, Charlotte, North Carolina ###-###-####, and any notice to be given to the Optionee under this Agreement shall be addressed to the Optionee at the address for the Optionee obtained from the records of the Corporation’s Executive Compensation and Benefits Department; provided, however, that either party may substitute a different address by notice in writing to the other. Except as otherwise provided in this Agreement, any such notice shall be deemed to have been duly given if and when enclosed in a properly sealed envelope addressed as aforesaid and deposited, postage prepaid, in a post office or branch post office regularly maintained by the United States Government.

10. No Employment Rights. Nothing in the Plan, this Agreement or the Certificate shall confer upon the Optionee the right to continue in the employment or the service of the Company or any Subsidiary, or affect the right of the Corporation or any Subsidiary to terminate the employment or service of the Optionee at any time for any, or no, reason.

11. Successors and Assigns. This Agreement shall bind and inure to the benefit of, and be enforceable by, the Corporation, and its successors and assigns, and the Optionee, and the Optionee’s successors and assigns expressly permitted by Section 5.

12. Optionee Confidentiality Obligations. In accepting the Option, Optionee acknowledges that Optionee is obligated under company policy, and under federal/state law to protect and safeguard the confidentiality of trade secrets and other proprietary and confidential information belonging to the Corporation and the Subsidiaries that are acquired by Optionee during Optionee’s employment with the Corporation and the Subsidiaries, and

that such obligations continue beyond the termination of such employment. Optionee agrees to notify any subsequent employer of such obligations and that the Corporation and the Subsidiaries, in order to enforce such obligations, may pursue legal recourse not only against Optionee, but against a subsequent employer of Optionee.

13. Governing Law. This Agreement shall be governed by, construed and enforced in accordance with the laws of the State of Delaware applicable to transactions that take place entirely within the State of Delaware and, where applicable, the laws of the United States.

14. Determinations. Determinations by the Committee, or its delegatee, shall be final and conclusive with respect to the interpretation of the Plan, the Certificate or this Agreement.

15. Conflicts with Plan and Correction of Errors. In the event that, due to administrative error, the Certificate and this Agreement do not accurately reflect an option properly granted to the Optionee pursuant to the Employment Agreement, the Corporation, acting through its Executive Compensation and Benefits Department, reserves the right to cancel any erroneous document and, if appropriate, to replace the cancelled document with a corrected document.

By their execution of the Certificate, the Corporation and Optionee enter into this Agreement and agree to be bound by its provisions.