THIRD AMENDMENT TO THE NOBLE CORPORATION 1991 STOCK OPTION AND RESTRICTED STOCK PLAN

Exhibit 10.2

THIRD AMENDMENT TO THE

NOBLE CORPORATION 1991 STOCK OPTION AND RESTRICTED STOCK PLAN

Pursuant to the provisions of Section 15 thereof, Section 2(e) of the Noble Corporation 1991 Stock Option and Restricted Stock Plan, as amended and restated effective as of October 29, 2009, and as thereafter amended (the “Plan”), is hereby amended in its entirety to read as follows, effective as of February 3, 2012:

“(e) ‘Change in Control’ means:

(i) the acquisition by any individual, entity or group (within the meaning of Section 13(d)(3) or 14(d)(2) of the Exchange Act) (a ‘Person’) of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Exchange Act) of 25% or more of either (A) the then outstanding Registered Shares of the Company (the ‘Outstanding Parent Shares’) or (B) the combined voting power of the then outstanding voting securities of the Company entitled to vote generally in the election of directors (the ‘Outstanding Parent Voting Securities’); provided, however, that for purposes of this subparagraph (e)(i) the following acquisitions shall not constitute a Change of Control: (w) any acquisition directly from the Company (excluding an acquisition by virtue of the exercise of a conversion privilege), (x) any acquisition by the Company, (y) any acquisition by any employee benefit plan (or related trust) sponsored or maintained by the Company or any company controlled by the Company, or (z) any acquisition by any corporation pursuant to a reorganization, merger, amalgamation or consolidation, if, following such reorganization, merger, amalgamation or consolidation, the conditions described in clauses (A), (B) and (C) of subparagraph (iii) of this Section 2(e) are satisfied; or

(ii) individuals who, as of the date of this Agreement, constitute the Board (the ‘Incumbent Board’) cease for any reason to constitute a majority of such Board; provided, however, that any individual becoming a director of the Company subsequent to the date hereof whose election, or nomination for election by the Company’s shareholders, was approved by a vote of a majority of the directors of the Company then comprising the Incumbent Board shall be considered as though such individual were a member of the Incumbent Board, but excluding, for this purpose, any such individual whose initial assumption of office occurs as a result of either an actual or threatened election contest or other actual or threatened solicitation of proxies or consents by or on behalf of a Person other than the Board; or

(iii) consummation of a reorganization, merger, amalgamation or consolidation of the Company, with or without approval by the shareholders of the Company, in each case, unless, following such reorganization, merger, amalgamation or consolidation, (A) more than 50% of, respectively, the then

outstanding shares of common stock (or equivalent security) of the company resulting from such reorganization, merger, amalgamation or consolidation and the combined voting power of the then outstanding voting securities of such company entitled to vote generally in the election of directors is then beneficially owned, directly or indirectly, by all or substantially all of the individuals and entities who were the beneficial owners, respectively, of the Outstanding Parent Shares and Outstanding Parent Voting Securities immediately prior to such reorganization, merger, amalgamation or consolidation in substantially the same proportions as their ownership, immediately prior to such reorganization, merger, amalgamation or consolidation, of the Outstanding Parent Shares and Outstanding Parent Voting Securities, as the case may be, (B) no Person (excluding the Company, any employee benefit plan (or related trust) of the Company or such company resulting from such reorganization, merger, amalgamation or consolidation, and any Person beneficially owning, immediately prior to such reorganization, merger, amalgamation or consolidation, directly or indirectly, 25% or more of the Outstanding Parent Shares or Outstanding Parent Voting Securities, as the case may be) beneficially owns, directly or indirectly, 25% or more of, respectively, the then outstanding shares of common stock (or equivalent security) of the company resulting from such reorganization, merger, amalgamation or consolidation or the combined voting power of the then outstanding voting securities of such company entitled to vote generally in the election of directors, and (C) a majority of the members of the board of directors of the company resulting from such reorganization, merger, amalgamation or consolidation were members of the Incumbent Board at the time of the execution of the initial agreement providing for such reorganization, merger, amalgamation or consolidation; or

(iv) consummation of a sale or other disposition of all or substantially all the assets of the Company, with or without approval by the shareholders of the Company, other than to a corporation, with respect to which following such sale or other disposition, (A) more than 50% of, respectively, the then outstanding shares of common stock (or equivalent security) of such corporation and the combined voting power of the then outstanding voting securities of such corporation entitled to vote generally in the election of directors is then beneficially owned, directly or indirectly, by all or substantially all the individuals and entities who were the beneficial owners, respectively, of the Outstanding Parent Shares and Outstanding Parent Voting Securities immediately prior to such sale or other disposition in substantially the same proportion as their ownership, immediately prior to such sale or other disposition, of the Outstanding Parent Shares and Outstanding Parent Voting Securities, as the case may be, (B) no Person (excluding the Company, any employee benefit plan (or related trust) of the Company or such corporation, and any Person beneficially owning, immediately prior to such sale or other disposition, directly or indirectly, 25% or more of the Outstanding Parent Shares or Outstanding Parent Voting Securities, as the case may be) beneficially owns, directly or indirectly, 25% or more of, respectively, the then outstanding shares of common stock (or equivalent security) of such corporation or the combined voting power of the then outstanding voting securities of such corporation entitled to vote generally in the election of directors,

-2-

and (C) a majority of the members of the board of directors of such corporation were members of the Incumbent Board at the time of the execution of the initial agreement or action of the Board providing for such sale or other disposition of assets of the Company; or

(v) approval by the shareholders of the Company of a complete liquidation or dissolution of the Company.

Notwithstanding the foregoing, or anything to the contrary set forth herein, a transaction or series of related transactions will not be considered to be a Change of Control if (i) the Company becomes a direct or indirect wholly owned subsidiary of a holding company and (ii) (A) immediately following such transaction(s), the then outstanding shares of common stock (or equivalent security) of such holding company and the combined voting power of the then outstanding voting securities of such holding company entitled to vote generally in the election of directors is then beneficially owned, directly or indirectly, by all or substantially all the individuals and entities who were the beneficial owners, respectively, of the Outstanding Parent Shares and Outstanding Parent Voting Securities immediately prior to such transaction(s) in substantially the same proportion as their ownership immediately prior to such transaction(s) of the Outstanding Parent Shares and Outstanding Parent Voting Securities, as the case may be, or (B) the shares of Outstanding Parent Voting Securities outstanding immediately prior to such transaction(s) constitute, or are converted into or exchanged for, a majority of the outstanding voting securities of such holding company immediately after giving effect to such transaction(s).”

IN WITNESS WHEREOF, this Amendment has been executed on this 6th day of February, 2012, but effective as of February 3, 2012.

-3-