EXHIBIT 99.2

ARGONAUT GROUP, INC.

NON-EMPLOYEE DIRECTOR STOCK OPTION PLAN

(as amended 3/26/2004)

1. Purpose.

The purpose of this Non-Employee Director Stock Option Plan (the “Plan”) of Argonaut Group, Inc., a Delaware corporation (the “Company”), is to attract and retain qualified and competent persons to serve as members of the board of directors of the Company by providing a means whereby such persons may acquire stock ownership in the Company. The Plan will provide a means whereby such directors may purchase shares of the Common Stock of the Company pursuant to options which are not “incentive stock options” under Section 422 of the Internal Revenue Code, as amended (the “Code”).

2. Administration.

The Plan shall be administered by the Board of Directors of the Company (the “Board of Directors”) or by a Committee selected by the Board of Directors consisting of two or more persons, to whom administration of the Plan has been duly delegated (the “Committee”). Any action of the Board of Directors or the Committee with respect to administration of the Plan shall be taken by a majority vote or written consent of its members.

Subject to the provisions of the Plan, the Board of Directors or Committee shall have authority (i) to construe and interpret the Plan, (ii) to define the terms used therein, (iii) to prescribe, amend and rescind rules and regulations relating to the Plan, and (iv) to make all other determinations necessary or advisable for the administration of the Plan. All determinations and interpretations made by the Board of Directors or Committee shall be binding and conclusive on all participants in the Plan and their legal representatives and beneficiaries.

The Board of Directors and the Committee shall have no discretion with respect to the selection of directors to receive options, the number of shares subject to the Plan or to each option granted hereunder, or the purchase price for shares subject to option grants hereunder. The Board of Directors and the Committee shall have no authority (absent stockholder approval) to materially increase benefits under the Plan.

3. Shares Subject to the Plan.

Subject to adjustment as provided in paragraph 15 hereof, the shares to be offered under the Plan shall consist of the Company’s authorized but unissued Common Stock, and the aggregate amount of such stock which may be issued upon exercise of all options under the Plan shall not exceed 250,000 of such shares. If any option granted under the Plan shall expire or terminate for any reason, without having been exercised in full, the unpurchased shares subject thereto shall again be available for options to be granted under the Plan.

4. Eligibility and Participation.

Only Directors of the Company who are not regular employees of the Company (“Non-Employee Directors”) are eligible to participate in the Plan.

5. Schedule of Option Grants.

Subject to paragraph 15, grants under the Plan shall be made in accordance with the following schedule:

(a) Initial Grants. Each Non-Employee Director who is serving on the date on which the stockholders of this Company approve this Plan shall receive an option to purchase 5,000 shares of Common Stock on such date.

(b) Annual Grants. Immediately after each annual meeting of stockholders of the Company (beginning with the Company’s 2004 annual meeting), each Non-Employee Director who is in office at such time shall be granted an option to purchase 5,000 shares of Common Stock.

(c) Grants to New Non-Employee Directors. Upon the appointment or election to the Board of Directors of a Non-Employee Director who was not previously a member of the Board of Directors, such Non-Employee Director shall be granted an option to purchase 5,000 shares of Common Stock on the date of appointment or election; provided, however, a Non-Employee Director who is first made a member of the Board of Directors in connection with the vote of stockholders of the Company at its annual meeting shall not be entitled to receive the grant described in this subparagraph (c).

6. Duration of Options.

Each option and all rights associated therewith shall expire six (6) years after the date on which such option is granted, and shall be subject to earlier termination as provided herein.

7. Purchase Price.

The purchase price of the stock covered by each option shall be equal to one hundred percent (100%) of the fair market value of such stock on the date the option is granted as determined in paragraph 9. The purchase price of the shares upon exercise of an option shall be paid in full at the time of exercise (i) in cash or by certified, cashier’s or personal check payable to the order of the Company or (ii) by delivery of shares of Common Stock of the Company already owned by, and in the possession of the option holder (subject to any required holding period imposed by the Board of Directors or the Committee), or any combination thereof. Shares of Common Stock used to satisfy the exercise price of an option shall be valued at their fair market value determined (in accordance with paragraph 9 hereof) as of the close of business on the date of exercise (or if such date is not a business day, as of the close of the business day immediately preceding such date).

8. Exercise of Options.

Subject to the other provisions of this Plan, the option granted under this Plan shall become vested in one of two ways: (1) one year after the date of grant if granted at other than the annual meeting or, (2) one day prior to the next scheduled annual meeting if granted at the previous annual meeting; provided, however, upon the occurrence of a Change of Control (as defined below), each option shall become immediately vested and exercisable. No option may be exercised for a fraction of a share and no partial exercise of any option may be for less than one hundred (100) shares.

For purposes of this Plan, “Change of Control” shall mean the occurrence of any of the following:

(i) Any “Person” or “Group” (as such terms are defined in Section 13(d) of the Securities Exchange Act of 1934 (the “Exchange Act”) and the rules and regulations promulgated thereunder) is or becomes the “Beneficial Owner” (within the meaning of Rule 13d-3 under the Exchange Act), directly or indirectly, of securities of the Company, or of any entity resulting from a merger or consolidation involving the Company, representing more than fifty percent (50%) of the combined voting power of the then outstanding securities of the Company or such entity.

(ii) The individuals who, as of the date that this Plan is approved by the stockholders of the Company, are members of the Board of Directors (the “Existing Directors”), cease, for any reason, to constitute more than fifty percent (50%) of the number of authorized directors of the Company as determined in the manner prescribed in the Company’s Certificate of Incorporation and Bylaws; provided, however, that if the election, or nomination for election, by the Company’s stockholders of any new director was approved by a vote of at least fifty percent (50%) of the Existing Directors, such new director shall be considered an Existing Director; provided further, however, that no individual shall be considered an Existing Director if such individual initially assumed office as a result of either an actual or threatened “Election Contest” (as described in Rule 14a-11 promulgated under the Exchange Act) or other actual or threatened solicitation of proxies by or on behalf of anyone other than the Board (a “Proxy Contest”), including by reason of any agreement intended to avoid or settle any Election Contest or Proxy Contest.

(iii) The consummation of (x) a merger, consolidation or reorganization to which the Company is a party, whether or not the Company is the Person surviving or resulting therefrom, or (y) a sale, assignment, lease, conveyance or other disposition of all or substantially all of the assets of the Company, in one transaction or a series of related transactions, to any Person other than the Company, where any such transaction or series of related transactions as is referred to in clause (x) or clause (y) above in this subparagraph (iii) (a “Transaction”) does not otherwise result in a “Change in Control” pursuant to subparagraph (i) of this definition of “Change in Control”; provided, however, that no such Transaction shall constitute a “Change in Control” under this subparagraph

(iii) if the Persons who were the stockholders of the Company immediately before the consummation of such Transaction are

2

the Beneficial Owners, immediately following the consummation of such Transaction, of fifty percent (50%) or more of the combined voting power of the then outstanding voting securities of the Person surviving or resulting from any merger, consolidation or reorganization referred to in clause (x) above in this subparagraph (iii) or the Person to whom the assets of the Company are sold, assigned, leased, conveyed or disposed of in any transaction or series of related transactions referred in clause (y) above in this subparagraph (iii).

9. Fair Market Value of Common Stock.

The fair market value of a share of Common Stock of the Company shall be determined for purposes of the Plan by reference to the closing price on the principal stock exchange on which such shares are then listed or, if such shares are not then listed on an exchange, by reference to the closing price (if a National Market Issue) or the mean between the bid and asked price (if other over-the-counter issue) of a share as supplied by the National Association of Securities Dealers through NASDAQ (or its successor in function), in each case as reported by The Wall Street Journal, for the date on which the option is granted or exercised, or if such date is not a business day, for the business day immediately preceding such date (or, if for any reason no such price is available, in such other manner as the Board of Directors or the Committee may deem appropriate to reflect the then fair market value thereof).

10. Withholding Tax.

Upon the exercise of options, the Company shall have the right to require the participant to pay the Company the amount of any taxes which the Company may be required to withhold (if any) with respect to such shares.

11. Nontransferability.

An option granted under the Plan shall, by its terms, be non-transferable by the option holder, either voluntarily or by operation of law, otherwise than by will or the laws of descent and distribution, and shall be exercisable during option holder’s lifetime only by the option holder, regardless of any community property interest therein of the spouse of the option holder, or such spouse’s successors in interest. If the spouse of the option holder shall have acquired a community property interest in such option, the option holder, or the option holder’s permitted successors in interest, may exercise the option on behalf of the spouse of the option holder or such spouse’s successors in interest.

12. Holding of Stock After Exercise of Option.

At the discretion of the Board of Directors or Committee, any option may provide that the option holder, by accepting such option, represents and agrees, for the option holder and the option holder’s permitted transferees (by will or the laws of descent and distribution), that none of the shares purchased upon exercise of the option will be acquired with a view to any sale, transfer or distribution of said shares in violation of the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder, or any applicable state “blue sky” laws, and the person entitled to exercise the same shall furnish evidence satisfactory to the Company (including a written and signed representation) to that effect in form and substance satisfactory to the Company, including an indemnification of the Company in the event of any violation of the Securities Act of 1933 or state blue sky law by such person.

13. Termination of Status as Non-Employee Director.

If an option holder ceases to be a Non-Employee Director for any reason any unvested options held by such option holder shall immediately become void and of no further force or effect. Any options which are vested as of the date of cessation (“Termination Date”) shall be exercisable for a period of three (3) months after the Termination Date to the extent exercisable on the Termination Date and shall thereafter expire and be void and of no further force or effect; provided, however, where such cessation occurs as a result of the option holder’s death or permanent and total disability (within the meaning of Section 22(e)(3) of the Code), the vested portion of the option shall be exercisable for one year following the Termination Date; provided, further, in no event shall any options be exercisable after the scheduled expiration date of such options.

14. Privileges of Stock Ownership.

No person entitled to exercise any option granted under the Plan shall have any of the rights or privileges of a stockholder of the Company in respect of any shares of stock issuable upon exercise of such option until certificates representing such shares shall have been issued and delivered. No shares shall be issued and delivered upon the exercise of any option unless and until there shall have been full compliance with all applicable requirements of the Securities Act of 1933 (whether by registration or satisfaction of exemption conditions), all applicable listing requirements of any national securities exchange on which shares of the same class are then listed and any other requirements of law or of any regulatory bodies having jurisdiction over such issuance and delivery.

3

15. Adjustments.

If the outstanding shares of the Common Stock of the Company are increased, decreased, changed into or exchanged for a different number or kind of shares or securities of the Company through reorganization, recapitalization, reclassification, stock dividend, stock split, reverse stock split or other similar transaction, an appropriate and proportionate adjustment shall be made in the maximum number and kind of shares as to which options may be granted under this Plan pursuant to paragraph 3 and the numbers of options to be granted pursuant to paragraph 5. A corresponding adjustment changing the number or kind of shares allocated to unexercised options or portions thereof, which shall have been granted prior to any such change, shall likewise be made. Any such adjustment in the outstanding options shall be made without change in the aggregate purchase price applicable to the unexercised portion of the option but with a corresponding adjustment in the price for each shares or other unit of any security covered by the option.

Upon the dissolution or liquidation of the Company, or upon a reorganization, merger or consolidation of the Company with one or more corporations as a result of which the Company is not the surviving corporation, or upon a sale of substantially all the property or more than eighty percent (80%) of the then outstanding stock of the Company to another corporation, the Plan shall terminate, and all options theretofore granted hereunder shall terminate.

Notwithstanding the foregoing, the Board of Directors or the Committee may provide in writing in connection with such transaction for any or all of the following alternatives (separately or in combinations): (i) for the options theretofore granted to become immediately exercisable notwithstanding the provisions of paragraph 8; (ii) for the assumption by the successor corporation of the options theretofore granted or the substitution by such corporation for such options of new options covering the stock of the successor corporation, or a parent or subsidiary thereof, with appropriate adjustments as to the number and kind of shares and prices; (iii) for the continuance of the Plan by such successor corporation in which event the Plan and the options theretofore granted shall continue in the manner and under the terms so provided; or (iv) for the payment in cash or stock in lieu of and in complete satisfaction of such options.

Adjustments under this paragraph 15 shall be made by the Board of Directors or Committee, whose determination as to what adjustments shall be made, and the extent thereof, shall be final, binding and conclusive. No fractional shares of stock shall be issued under the Plan on any such adjustment.

16. Amendment and Termination of Plan.

The Board of Directors or the Committee may at any time suspend or terminate the Plan. The Board of Directors or the Committee may also at any time amend or revise the terms of the Plan, provided that no such amendment or revision shall, unless permitted under the provisions of paragraph 15 or unless appropriate stockholder approval of such amendment or revision is obtained, (i) increase the maximum number of shares in the aggregate which may be sold pursuant to options granted under the Plan pursuant to paragraph 3, (ii) permit the granting of options to anyone other than as provided in paragraph 4, (iii) increase the number of options to be granted pursuant to paragraph 5, (iv) increase the maximum term of stock options provided for in paragraph 6, or (v) change the purchase price of stock options set forth in paragraph 7.

17. Effective Date of Plan.

Effectiveness of the Plan is subject to approval by the holders of the outstanding voting stock of the Company. The Plan shall be deemed approved by the holders of the outstanding voting stock of the Company by the affirmative vote of the holders of a majority of the voting shares of the Company represented and voting at a duly held meeting at which a quorum is present.

4