Exhibit 10.3

NON-INCENTIVE STOCK OPTION AGREEMENT

UNDER THE

FAIRMOUNT BANCORP, INC.

2010 STOCK OPTION PLAN

THIS AGREEMENT is entered into as of             , 2012, between FAIRMOUNT BANCORP, INC. (the “Company”) and                      (“Optionee”) (the “Agreement”), in accordance with the terms of the FAIRMOUNT BANCORP, INC. 2010 Stock Option Plan (the “Plan”). Capitalized terms shall have the same meaning as set forth in the Plan, unless the context clearly indicates otherwise.

1. Grant of Option

1.1 The Company hereby grants to Optionee effective                      (the “Date of Grant”), the option to purchase up to              shares of Common Stock (the “Option”) at an exercise price of $         per share (the “Exercise Price”). ⁽¹⁾ The Option shall vest, become exercisable and expire as provided in Section 2 below.

1.2 The Option is designated as a non-qualified stock option (a “Non-ISO”) and, therefore, is not intended to be treated as an incentive stock option (an “ISO”) under Section 422 of the Internal Revenue Code of 1986, as amended (the “Code”).

2. Time of Exercise

2.1 Subject to the provisions of the Plan and this Agreement, Optionee shall be entitled to exercise the Option as follows:

2.2 The Option shall expire and may not be exercised later than 10 years following the Date of Grant.

2.3 Notwithstanding the foregoing, the Option shall become accelerated and immediately exercisable in the event of Optionee’s termination of employment as a result of death or Disability and in the event of a Change in Control, as provided in the Plan.

2.4 The Option shall be exercised in the manner set forth in the Plan, using the exercise form attached hereto as Exhibit A. The exercise price may be paid in cash, check, Shares or through a cashless exercise program through a broker, all on the terms provided in the Plan.

3. Conditions for Exercise of Option

3.1 During Optionee’s lifetime, the Option may be exercised only by the Optionee or by Optionee’s guardian or legal representative. The Option must be exercised while Optionee is employed by the Company, or in the event of a termination of employment, for such period following termination and under certain circumstances, as may be provided in the Plan. Notwithstanding the foregoing, no Option may be exercised more than 10 years following the Date of Grant.

3.2 In the event Optionee is discharged from the employ of the Company or a subsidiary company for cause under Section 4.3 of the Plan, Optionee shall forfeit the right to exercise any portion of this Option, which shall be immediately null and void.

4. Additional Conditions

Anything in this Agreement to the contrary notwithstanding, if at any time the Company further determines, in its sole discretion, that the listing, registration or qualification (or any updating of any such document) of the shares of Common Stock issuable pursuant to the exercise of an Option is necessary on any securities exchange or under any federal or state securities or blue sky law, or that the consent or approval of any governmental regulatory body is necessary or desirable as a condition of, or in connection with the issuance of shares of Common Stock pursuant thereto, or the removal of any restrictions imposed on such shares, such shares of Common Stock shall not be issued, in whole or in part, unless such listing, registration, qualification, consent or approval shall have been effected or obtained free of any conditions not acceptable to the Company.

5. Taxes

The Company may make such provisions as it may deem appropriate for the withholding of any federal, state and local taxes that it determines are required to be withheld on the exercise of the Option. By signing this Option, the Optionee agrees that he or she is solely responsible for the satisfaction of any taxes that may arise (including taxes arising under Sections 409A or 4999 of the Code) and that the Company shall not have any obligation whatsoever to pay such taxes.

6. Binding Effect

This Agreement shall inure to the benefit of and be binding upon the parties hereto and their respective heirs, executors, administrators and successors.

7. Inconsistent Provisions

The Option granted hereby is subject to the provisions of the Plan. If any provision of this Agreement conflicts with a provision of the Plan, the Plan provision shall control.

8. Adjustments to Option

Appropriate adjustments shall be made to the number and class of shares of Common Stock subject to the Option and to the exercise price in accordance with the Plan.

9. Termination of Option

The Committee, in its sole discretion, may terminate the Option. However, no termination may adversely affect the rights of Optionee to the extent that the Option is currently vested on the date of such termination.

10. Designation of Beneficiary

Optionee may expressly designate beneficiary to his or her interest (the “Beneficiary”), if any, to this Option by completing and executing a designation of beneficiary agreement substantially in the form attached to this Agreement as Exhibit B (the “Designation of Beneficiary”) and delivering an executed copy of the Designation of Beneficiary to the Company.

11. Notices

Any notice or communication required or permitted by any provision of this Agreement to be given to Optionee shall be in writing and shall be delivered personally or sent by certified mail, return receipt requested, addressed to Optionee at the last address that the Company had for Optionee on its records. Each party may, from time to time, by notice to the other party hereto, specify a new address for delivery of notices relating to this Option. Any such notice shall be deemed to be given as of the date such notice is personally delivered or properly mailed.

12. Modifications

This Agreement may be modified or amended at any time, provided that Optionee must consent in writing to any modification that adversely alters or impairs any vested rights or obligations under this Option.

13. Headings

Section and other headings contained in this Option Agreement are for reference purposes only and are not intended to describe, interpret, define or limit the scope or intent of this Option or any provision hereof.

14. Severability

Every provision of this Option and of the Plan is intended to be severable. If any term hereof is illegal or invalid for any reason, such illegality or invalidity shall not affect the validity or legality of the remaining terms of this Award Agreement.

15. Governing Law

The laws of the State of Maryland shall govern the validity of this Award Agreement, the construction of its terms, and the interpretation of the rights and duties of the parties hereto.

16. Counterparts

This Option may be executed by the parties hereto in separate counterparts, each of which when so executed and delivered shall be an original, but all such counterparts shall together constitute one and the same instrument.

[Signature Page Follows]

IN WITNESS WHEREOF the parties hereto have caused this Option to be executed as of the day and year first above written.

Exhibit A

FAIRMOUNT BANCORP, INC.

Form for Exercise of Stock Option for 2010 Stock Option Plan

Fairmount Bancorp, Inc.

8216 Philadelphia Road

Baltimore, Maryland 21237

Dear Sir or Madam:

The undersigned elects to exercise his/her Stock Option to purchase             shares of Common Stock of Fairmount Bancorp, Inc. (the “Company”) under and pursuant to a Stock Option Agreement dated as of                      and the terms and conditions of the 2010 Stock Option Plan.

1. ¨ Delivered herewith is a check and/or shares of Common Stock, valued at the closing sale price of the stock on the business day prior to the date of exercise, as follows:

2. ¨ Delivered herewith are irrevocable instructions to a broker approved by the Company to deliver promptly to the Company the amount of sale or loan proceeds to pay the exercise price.

If method 1 is chosen, the name or names to be on the stock certificate or certificates and the address and Social Security Number of such person(s) is as follows:

Exhibit B

FAIRMOUNT BANCORP, INC.

Designation of Beneficiary

In the event of my death or “Disability” within the meaning of the FAIRMOUNT BANCORP, INC. 2010 Stock Incentive Plan (the “Plan”), I hereby designate the following person to be my beneficiary for the Award(s) (within the meaning of the Plan) identified below:

This beneficiary designation of mine relates to any and all of my rights under the following Award or Awards:

I understand that this beneficiary designation operates to entitle the above-named beneficiary to succeed, in the event of my death, to any and all of my rights under the Award(s) designated above, and shall be effective from the date this form is delivered to the Company until such date as I revoke this designation. A revocation shall occur only if I deliver to an executive officer of the Company either (i) a written revocation of this designation that is signed by me and notarized, or (ii) a designation of death beneficiary, in the form set forth herein, that is executed and notarized on a later date.