FORM OF NON-QUALIFIED STOCK OPTION AGREEMENT

Exhibit 10.2

FORM OF NON-QUALIFIED STOCK OPTION AGREEMENT

THIS AGREEMENT, made this 17th day of February, 2009 (the “Grant Date”), by and between Max Capital Group Ltd. (the “Company”) and W. Marston Becker (the “Optionee”).

W I T N E S S E T H:

WHEREAS, pursuant to the Max Capital Group Ltd. 2008 Stock Incentive Plan, as amended (the “Plan”), the Company desires to afford the Optionee the opportunity to acquire, or enlarge, his ownership of the Company’s common shares, $1.00 par value per share (“Common Shares”), so that he may have a direct proprietary interest in the Company’s success.

NOW, THEREFORE, in consideration of the covenants and agreements herein contained, the parties hereto hereby agree as follows:

1. Grant of Option. Subject to the terms and conditions set forth herein and in the Plan, the Company hereby grants to the Optionee, during the period commencing on the date of this Agreement and ending on the close of business on the day of the tenth anniversary of the date hereof (the “Termination Date”), the right and option (the right to purchase any one Common Share hereunder being an “Option”) to purchase from the Company, at a price of $18.25 per share (the “Option Price”), an aggregate of 108,333 Common Shares (the “Option Shares”).

2. Limitation on Exercise of Option. Subject to the terms and conditions set forth herein and the Plan:

(a) Optionee will become vested in 50% of the Options on January 1, 2010; provided, that, the book value of the underlying Common Shares on December 31, 2009 is at least 12.5% greater than the book value of such Common Shares on December 31, 2008 (the book value of Common Shares on December 31, 2008 calculated by dividing Total Shareholders’ Equity by Common Shares Issued and Outstanding shall be referred to herein as “Baseline 1,” and the amount which is 12.5% greater than Baseline 1 shall be referred to herein as “Baseline 2”); provided, further that, the Optionee is employed by the Company on the relevant vesting date (“Tranche 1 Options”).

(b) Optionee will become vested in 50% of the Options on January 1, 2011; provided, that, the book value of the underlying Common Shares on December 31, 2010 is at least 12.5% greater than Baseline 2 (such amount, “Baseline 3” and such Options, “Tranche 2 Options”), provided, further that, the Optionee is employed by the Company on the relevant vesting date. If Tranche 1 Options do not vest on January 1, 2010, but Baseline 3 is at least 25% greater than Baseline 1, then Tranche 1 Options and Tranche 2 Options shall become vested as of

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January 1, 2011; provided, that, the Optionee is employed by the Company on the relevant vesting date. For the avoidance of doubt, if any tranche of Options is unvested as of January 1, 2011, such tranche shall automatically terminate and cease to be exercisable and shall not be considered outstanding for any purpose.

Notwithstanding the foregoing, if on or prior to January 1, 2011, the Optionee’s employment with the Company is terminated: (i) by the Company without Cause (as defined in the Employment Agreement between the Company and W. Marston Becker effective November 13, 2006, as may be amended from time to time (the “Employment Agreement”)); (ii) by the Optionee for Good Reason (as defined in the Employment Agreement); or (iii) following a Change in Control (as defined in the Employment Agreement), the unvested portion of the Options that are still outstanding shall automatically vest and become exercisable.

For purposes of this Agreement, Total Shareholder’s Equity and Common Shares Issued and Outstanding shall be as set forth in the consolidated balance sheet of the Company’s audited consolidated financial statements for the applicable year ended December 31.

3. Termination of Employment. Any Options held by the Optionee upon termination of employment shall remain exercisable as follows, subject to the conditions set forth in Section 4 hereof:

(a) Except as provided in Section 2 hereof, upon Optionee’s termination of employment for any reason, all unvested Options shall terminate and cease to be exercisable.

(b) If the Optionee’s termination of employment is due to death or Disability (as defined in the Employment Agreement), all unvested Options shall automatically terminate and cease to be exercisable and, to the extent vested, all vested Options shall be exercisable by the Optionee or any prior transferee of the Option or by the Optionee’s designated beneficiary, or, if none, the person(s) to whom such Optionee’s rights under the Option are transferred by will or the laws of descent and distribution for one (1) year following such termination of employment (but in no event beyond the Termination Date), and shall thereafter terminate; and

(c) If the Optionee’s termination of employment is for any other reason, all unvested Options shall terminate and cease to be exercisable on the date of termination; and all vested Options, shall be exercisable for a period of 90 days following such termination of employment (but in no event beyond the Termination Date), and shall thereafter terminate. An Optionee’s status as an employee shall not be considered terminated in the case of a leave of absence agreed to in writing by the Company (including, but not limited to, military and sick leave); provided, that, such leave is for a period of not more than 90 days or re-employment upon expiration of such leave is guaranteed by contract or statute.

4. Method of Exercising Option.

(a) Payment of Option Price. Options, to the extent vested, may be exercised, in whole or in part, by giving written notice of exercise to the Company specifying the number of Common Shares to be purchased. Such notice shall be accompanied by the payment in full of the Option Price. Such payment shall be made: (i) in cash, (ii) by surrender of Common Shares

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owned by the holder of the Option that are Mature Shares (as defined in the Plan), (iii) by means of a broker-assisted “cashless exercise,” (iv) by a “net exercise” method whereby the Company withholds from the delivery of Common Shares for which the Option was exercised that number of Common Shares having a Fair Market Value equal to the aggregate Option Price for the Common Shares for which the Option was exercised, or (v) by a combination of any such methods.

(b) Tax Withholding. At the time of exercise, the Optionee shall pay to the Company such amount as the Company deems necessary to satisfy its obligation, if any, to withhold federal, state or local income or other taxes incurred by reason of the exercise of Options granted hereunder. Such payment shall be made: (i) in cash, (ii) by having the Company withhold from the delivery of Common Shares for which the Option was exercised that number of Common Shares having a Fair Market Value equal to the minimum withholding obligation, (iii) by delivering Common Shares owned by the holder of the Option that are Mature Shares, or (iv) by a combination of any such methods. For purposes hereof, Common Shares shall be valued at Fair Market Value.

5. Issuance of Shares. Except as otherwise provided in the Plan, as promptly as practical after receipt of such written notification of exercise and full payment of the Option Price and any required income tax withholding, the Company shall issue or transfer to the Optionee the number of Option Shares with respect to which Options have been so exercised (less shares withheld for payment of the Option Price and/or in satisfaction of tax withholding obligations, if any), and shall deliver to the Optionee a certificate or certificates therefor, registered in the Optionee’s name.

6. Company; Optionee.

(a) The term “Company” as used in this Agreement with reference to employment shall include the Company and its Subsidiaries, as appropriate.

(b) Whenever the word “Optionee” is used in any provision of this Agreement under circumstances where the provision should logically be construed to apply to the beneficiaries, the executors, the administrators, or the person or persons to whom the Options may be transferred by will or by the laws of descent and distribution, the word “Optionee” shall be deemed to include such person or persons.

7. Non-Transferability. The Options are not transferable by the Optionee otherwise than to a designated beneficiary upon death or by will or the laws of descent and distribution, and are exercisable during the Optionee’s lifetime only by him (or his legal representative in the event of incapacity). No assignment or transfer of the Options, or of the rights represented thereby, whether voluntary or involuntary, by operation of law or otherwise (except to a designated beneficiary, upon death, by will or the laws of descent and distribution), shall vest in the assignee or transferee any interest or right herein whatsoever, but immediately upon such assignment or transfer the Options shall terminate and become of no further effect.

8. Change in Control. Upon the occurrence of a Change in Control, all outstanding Options shall automatically become vested and immediately exercisable in full.

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9. Rights as Shareholder. The Optionee or a transferee of the Options shall have no rights as shareholder with respect to any Option Shares until he shall have become the holder of record of such shares, and no adjustment shall be made for dividends or distributions or other rights in respect of such Option Shares for which the date on which shareholders of record are determined for purposes of paying cash dividends on Common Shares is prior to the date upon which he shall become the holder of record thereof.

10. Adjustments. The Options granted hereunder are subject to adjustment pursuant to Section 12 of the Plan.

11. Compliance with Law. Notwithstanding any of the provisions hereof, the Optionee hereby agrees that he will not exercise the Options, and that the Company will not be obligated to issue or transfer any shares to the Optionee hereunder, if the exercise hereof or the issuance or transfer of such shares shall constitute a violation by the Optionee or the Company of any provisions of any law or regulation of any governmental authority. Any determination in this connection by the Committee shall be final, binding and conclusive. The Company shall in no event be obliged to register any securities pursuant to the Securities Act of 1933 (as now in effect or as hereafter amended) or to take any other affirmative action in order to cause the exercise of the Options or the issuance or transfer of shares pursuant thereto to comply with any law or regulation of any governmental authority.

12. Notice. Every notice or other communication relating to this Agreement shall be in writing, and shall be mailed to or delivered to the party for whom it is intended at such address as may from time to time be designated by it in a notice mailed or delivered to the other party as herein provided; provided, that, unless and until some other address be so designated, all notices or communications by the Optionee to the Company shall be mailed or delivered to the Company at its principal executive office, and all notices or communications by the Company to the Optionee may be given to the Optionee personally or may be mailed to him at his address as recorded in the records of the Company.

13. Non-Qualified Stock Options. The Options granted hereunder are not intended to be incentive stock options within the meaning of Section 422 of the Code.

14. Binding Effect. Subject to Section 7 hereof, this Agreement shall be binding upon the heirs, executors, administrators and successors of the parties hereto.

15. Governing Law. This Agreement shall be construed and interpreted in accordance with the laws of the State of New York without regard to its conflict of law principles.

16. Plan. The terms and provisions of the Plan are incorporated herein by reference, and the Optionee hereby acknowledges receiving a copy of the Plan. In the event of a conflict or inconsistency between the terms and provisions of the Plan and the provisions of this Agreement, the Plan shall govern and control. All capitalized terms not defined herein shall have the meaning ascribed to them as set forth in the Plan.

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17. Interpretation. Any dispute regarding the interpretation of this Agreement shall be submitted by the Optionee or the Company to the Committee for review. The resolution of such a dispute by the Committee shall be binding on the Company and the Optionee.

18. No Right to Continued Employment. Nothing in this Agreement shall be deemed by implication or otherwise to impose any limitation on any right of the Company to terminate the Optionee’s employment.

19. Section 409A Limitation. The Company shall have no liability to the Optionee or any other person if an Option is determined to constitute “nonqualified deferred compensation” within the meaning of Section 409A of the Code and the terms of such Option do not satisfy the additional conditions applicable to nonqualified deferred compensation under Section 409A of the Code.

20. Severability. Every provision of this Agreement is intended to be severable and any illegal or invalid term shall not affect the validity or legality of the remaining terms.

21. Headings. The headings of the Sections hereof are provided for convenience only and are not to serve as a basis for interpretation of construction, and shall not constitute a part of this Agreement.

22. Signature in Counterparts. This Agreement may be signed in counterparts, each of which shall be deemed an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

[SIGNATURE PAGE FOLLOWS]

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date set forth below.

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