PARALLEL PETROLEUM CORPORATION

Exhibit 10.2

PARALLEL PETROLEUM CORPORATION

1998 STOCK OPTION PLAN

I. Purpose of the Plan

The Parallel Petroleum Corporation 1998 Stock Option Plan (the “Plan”) is intended to provide a means whereby certain employees of Parallel Petroleum Corporation, a Delaware corporation (the “Company”), and its subsidiaries may develop a sense of proprietorship and personal involvement in the development and financial success of the Company, and to encourage them to remain with and devote their best efforts to the business of the Company, thereby advancing the interests of the Company and its stockholders. Accordingly, the Plan provides for granting certain employees the option (“Option”) to purchase shares of the common stock of the Company (“Stock”), as hereinafter set forth. Options granted under the Plan to employees may be either incentive stock options, within the meaning of Section 422 of the Internal Revenue Code of 1986, as amended (the “Code”), (“Incentive Stock Options”) or options which do not constitute Incentive Stock Options.

II. Administration

The Plan shall be administered by the Board of Directors of the Company (the “Board”) or by a committee (the “Committee”) of two or more directors of the Company appointed by the Board. If a Committee is not appointed by the Board, the Board shall act as and be deemed to be the Committee for all purposes of the Plan. The Committee shall have sole authority (within the limitations described herein) to select the employees who are to be granted Options hereunder and to establish the number of shares which may be issued to employees under each Option and to prescribe the form of the agreement embodying awards of Options. The Committee is authorized to interpret the Plan and may from time to time adopt such rules and regulations, consistent with the provisions of the Plan, as it may deem advisable to carry out the Plan. All decisions made by the Committee in selecting the employees to whom Options shall be granted, in establishing the number of shares which may be issued to employees under each Option and in construing the provisions of the Plan shall be final. No member of the Board shall be liable for anything done or omitted to be done by such member or by any other member of the Board in connection with the Plan, except for such member’s own willful misconduct or as expressly provided by statute.

III. Option Agreements; Terms and Conditions

Each Option granted under the Plan shall be evidenced by an agreement and shall contain such terms and conditions, and may be exercisable for such periods, as the Committee shall prescribe from time to time in accordance with this Plan, and shall comply with the following terms and conditions:

(a) The Option exercise price shall be the fair market value of the Stock subject to the Option on the date the Option is granted. For all purposes under the Plan, the fair market of a share of Stock on a particular date shall be equal to the average of the high and low sales prices of the Stock on the date of grant as reported on the Nasdaq National Market tier of The Nasdaq Stock Market (“NMS”), or on the stock exchange composite tape if the Stock is traded on a national stock exchange on that date, or if no prices are reported on that date, on the last preceding date on which such prices of the Stock are so reported. If the Stock is not traded on the NMS or other stock exchange on that date, but is otherwise traded over the counter at the time a determination of its fair market value is required to be made hereunder, its fair market value shall be deemed to be equal to the average between the reported high and low or closing bid and asked prices of the Stock on the most recent date on which the Stock was publicly traded. If the Stock is not publicly traded at the time a determination of its value is required to be made hereunder, the determination of its fair market value shall be made by the Committee in such manner as it deems appropriate.

(b) The Option shall not be transferable otherwise than by will or the laws of descent and distribution, and may be exercised only by the employee during the employee’s lifetime and while the employee remains employed by the Company, except that: (i) if the employee ceases to be an employee of the Company because of disability, the Option may be exercised in full by the employee (or the employee’s estate or the person who acquires the Option by will or the laws of descent and distribution or otherwise by reason of the death of the employee) at any time during the period of one year following such termination; (ii) if the employee dies while he is an employee of the Company, the employee’s estate, or the person who acquires the Option by will or the laws of descent and distribution or otherwise by reason of the death of the employee, may exercise the Option in full at any time during the period of one year following the date of the employee’s death; and (iii) if the employee ceases to be an employee of the Company for any reason other than as described in clause (i) or (ii) above, unless the employee is removed for cause, the Option may be exercised by the employee at any time during the period of three months following the date the employee ceases to be an employee of the Company, or by the employee’s estate (or the person who acquires the Option by will or the laws of descent and distribution or otherwise by reason of the death of the employee) during a period of one year following the employee’s death if the employee dies during such three-month period, but in each case only as to the number of shares the employee was entitled to purchase hereunder upon exercise of the Option as of the date the employee ceases to be an employee.

(c) The Option shall not be exercisable in any event after the expiration of ten years from the date of grant.

(d) The purchase price of shares as to which the Option is exercised shall be paid in full at the time of exercise (a) in cash, (b) by delivering to the Company shares of Stock having a fair market value equal to the purchase price, or (c) any combination of cash or Stock, as shall be established by the Committee. Unless and until a certificate or certificates representing such shares shall have been issued by the Company to the employee, the employee (or the person permitted to exercise the Option in the event of the employee’s death) shall not be or have any of the rights or privileges of a stockholder of the Company with respect to shares acquirable upon an exercise of the Option.

(e) The terms and conditions of the respective employee stock option agreements need not be identical.

IV. Eligibility of Optionee

(a) Subject to the provisions of paragraph (b) below, Options may be granted only to individuals who are employees (including officers and directors who are also employees) of the Company or any parent or subsidiary corporation (as defined in Section 424 of the Code) of the Company at the time the Option is granted. Options may be granted to the same employee on more than one occasion.

(b) No Incentive Stock Option shall be granted to an individual if, at the time the Option is granted, such individual owns stock possessing more than 10% of the total combined voting power of all classes of stock of the Company or of its parent or subsidiary corporation, within the meaning of Section 422(b)(6) of the Code, unless (i) at the time such Option is granted the option price is at least 110% of the fair market value of the Stock subject to the Option and (ii) such Option by its terms is not exercisable after the expiration of five years from the date of grant. To the extent that the aggregate fair market value (determined at the time the respective Incentive Stock Option is granted) of stock with respect to which Incentive Stock Options are exercisable for the first time by an individual during any calendar year under all incentive stock option plans of the Company and its parent and subsidiary corporations exceeds $100,000, such Incentive Stock Options shall be treated as options which do not constitute Incentive Stock Options. The Committee shall determine, in accordance with applicable provisions of the Code, Treasury Regulations and other administrative pronouncements, which of an employee optionee’s Incentive Stock Options will not constitute Incentive Stock Options because of such limitation and shall notify the employee optionee of such determination as soon as practicable after such determination.

V. Shares Subject to the Plan

The aggregate number of shares which may be issued under Options granted under the Plan shall not exceed 850,000 shares of Stock. Such shares may consist of authorized but unissued shares of Stock or previously issued shares of Stock reacquired by the Company. Any of such shares which remain unissued and which are not subject to outstanding Options at the termination of the Plan shall cease to be subject to the Plan, but, until termination of the Plan, the Company shall at all times make available a sufficient number of shares to meet the requirements of the Plan. Should any Option hereunder expire or terminate prior to its exercise in full, the shares theretofore subject to such Option may again be subject to an Option granted under the Plan. The aggregate number of shares which may be issued under the Plan shall be subject to adjustment in the same manner as provided in Article VII hereof with respect to shares of Stock subject to Options then outstanding. Exercise of an Option in any manner shall result in a decrease in the number of shares of Stock which may thereafter be available, both for purposes of the Plan and for sale to any one individual, by the number of shares as to which the Option is exercised. Separate stock certificates shall be issued by the Company for those shares acquired pursuant to the exercise of an Incentive Stock Option and for those shares acquired pursuant to the exercise of any Option which does not constitute an Incentive Stock Option.

VI. Term of Plan

The Plan shall be effective upon the date of its approval and adoption by the stockholders of the Company. Except with respect to Options then outstanding, if not sooner terminated under the provisions of Article VIII, the Plan shall terminate upon and no further Options shall be granted after the expiration of ten years from the date of its adoption by the Board.

VII. Recapitalization or Reorganization

(a) The existence of the Plan and the Options granted hereunder shall not affect in any way the right or power of the Board or the stockholders of the Company to make or authorize any adjustment, recapitalization, reorganization or other change in the Company’s capital structure or its business, any merger or consolidation of the Company, any issue of debt or equity securities ahead of or affecting the Stock or the rights thereof, the dissolution or liquidation of the Company or any sale, lease, exchange or other disposition of all or any part of its assets or business or any other corporate act or proceeding.

(b) The shares with respect to which Options may be granted are shares of Stock as presently constituted, but if, and whenever, prior to the expiration of an Option theretofore granted, the Company shall effect a subdivision or consolidation of shares of Stock or the payment of a stock dividend on Stock without receipt of consideration by the Company, the number of shares of Stock with respect to which such Option may thereafter be exercised (i) in the event of an increase in the number of outstanding shares shall be proportionately increased, and the purchase price per share shall be proportionately reduced, and (ii) in the event of a reduction in the number of outstanding shares shall be proportionately reduced, and the purchase price per share shall be proportionately increased.

(c) If the Company recapitalizes or otherwise changes its capital structure, thereafter upon any exercise of an Option theretofore granted the optionee shall be entitled to purchase under such Option, in lieu of the number of shares of Stock as to which such Option shall then be exercisable, the number and class of shares of stock and securities to which the optionee would have been entitled pursuant to the terms of the recapitalization if, immediately prior to such recapitalization, the optionee had been the holder of record of the number of shares of Stock as to which such Option is then exercisable. If (i) the Company shall not be the surviving entity in any merger or consolidation (or survives only as a subsidiary of an entity other than a previously wholly-owned subsidiary of the Company), (ii) the Company sells, leases or exchanges or agrees to sell, lease or exchange all or substantially all of its assets to any other person or entity (other than a wholly-owned subsidiary of the Company), (iii) the Company is to be dissolved and liquidated, (iv) any person or entity, including a “group” as contemplated by Section 13(d)(3) of the Securities Exchange Act of 1934, as amended, acquires or gains ownership or control (including, without limitation, power to vote) of more than 50% of the outstanding shares of Stock, or (v) as a result of or in connection with a contested election of directors, the persons who were directors of the Company before such election shall cease to constitute a majority of the Board (each such event is referred to herein as a “Corporate Change”), then upon the occurrence of any such Corporate Change, any outstanding Options held by employees shall become fully exercisable and upon any exercise of an Option theretofore granted the employee shall be entitled to purchase under such Option, in lieu of the number of shares of Stock as to which such Option shall then be exercisable, the number and class of shares of stock or other securities or property to which the employee would have been entitled pursuant to the terms of the Corporate Change if, immediately prior to such Corporate Change, the employee had been the holder of record of the number of shares of Stock as to which such Option is then exercisable. Notwithstanding any of the foregoing provisions of this paragraph (c) to the contrary, any Option referred to herein shall be adjusted, where necessary, so that the fair value of the Option immediately after the transaction or event referred to herein is equal to the fair value of the Option immediately prior to such transaction or event by adjusting the number and type of shares of Stock and/or the purchase price per share, and/or making such other adjustments as may be appropriate, in order to comply with the requirements of Section 409A of the Code and the final regulations and other guidance issued thereunder.

(d) Any adjustment provided for in paragraphs (b) or (c) above shall be subject to any required stockholder action.

(e) Except as hereinbefore expressly provided, the issuance by the Company of shares of stock of any class or securities convertible into shares of stock of any class, for cash, property, labor or services, upon direct sale, upon the exercise of rights or warrants to subscribe therefor, or upon conversion of shares or obligations of the Company convertible into such shares or other securities, and in any case whether or not for fair value, shall not affect, and no adjustment by reason thereof shall be made with respect to, the number of shares of Stock subject to Options theretofore granted or the purchase price per share.

VIII. Amendment or Termination of the Plan

The Board in its discretion may terminate the Plan at any time with respect to any shares for which Options have not theretofore been granted. The Board shall have the right to alter or amend the Plan or any part thereof from time to time, provided, that no change in any Option theretofore granted may be made which would impair the rights of the optionee without the consent of such optionee.

IX. Miscellaneous Provisions

(a) Neither the Plan nor any action taken hereunder shall be construed as giving any employee any right to be retained in the service of the Company.

(b) An optionee’s rights and interest under the Plan may not be assigned or transferred in whole or in part either directly or by operation of law or otherwise (except in the event of an optionee’s death or disability, by will or the laws of descent and distribution, all as provided in Article III), including, but not by way of limitation, execution, levy, garnishment, attachment, pledge, bankruptcy, or in any other manner, and no such right or interest of any participant in the Plan shall be subject to any obligation or liability of such participant.

(c) No shares of Stock shall be issued hereunder unless counsel for the Company shall be satisfied that such issuance will be in compliance with applicable Federal, state, and other securities laws and regulations.

(d) It shall be a condition to the obligation of the Company to issue shares of Stock upon exercise of an Option, that the optionee (or any beneficiary or person entitled to act under or through Optionee as provided herein) pay to the Company, upon its demand, such amount as may be requested by the Company for the purpose of satisfying any liability to withhold Federal, state, local, or foreign income or other taxes. If the amount requested is not paid, the Company may refuse to issue shares of Stock.

(e) By accepting any Option under the Plan, each optionee and each person claiming under or through such person shall be conclusively deemed to have indicated his or her acceptance and ratification of, and consent to, any action taken under the Plan by the Company, the Board of Directors or the Committee.