EXHIBIT 10.2

SECOND AMENDMENT

TO THE

STATE AUTO FINANCIAL CORPORATION

LEADERSHIP BONUS PLAN

Background Information

Amendment of the Plan

The Plan is hereby amended effective January 1, 2012 as follows:

2.5 “Change of Control” means the happening of any of the following:

(a) when any “person” as defined in Section 3(a)(9) of the Exchange Act and as used in Sections 13(d) and 14(d) thereof, including a “group” as defined in Section 13(d) of the Exchange Act, but excluding the Company and any employee benefit plan sponsored or maintained by the Company (including any trustee of such plan acting as trustee) and excluding State Automobile Mutual Insurance Company,

directly or indirectly, becomes the “beneficial owner” (as defined in Rule 13d-3 under the Exchange Act, as amended from time to time), of securities of the Company representing 30% or more of the combined voting power of the Company’s then outstanding securities; or

(b) when, during any period of 24 consecutive months during the existence of the Plan, the individuals who, at the beginning of such period, constitute the Board (the “Incumbent Directors”) cease for any reason other than death to constitute at least a majority of the Board; provided, however, that a director who was not a director at the beginning of such 24-month period shall be deemed to have satisfied such 24-month requirement (and be an Incumbent Director) if such director was elected by, or on the recommendation of, or with the approval of, at least two-thirds of the directors who then qualified as Incumbent Directors either actually (because they were directors at the beginning of such 24-month period) or by prior operation of this Section 2.5(b); or

(c) the occurrence of a transaction requiring shareholder approval for the acquisition of the Company by an entity other than the Company through purchase of assets, by merger or otherwise; or

(d) the occurrence of a “Rule 13e-3 transaction” (as defined in Rule 13e-3 under the Exchange Act) requiring approval by the shareholders of the Company.

A “Potential Change in Control” means the happening of any one of the following:

(a) the approval by shareholders of an agreement by the Company, the consummation of which would result in a Change in Control of the Company as defined in Section 2.5 above; or

(b) the acquisition of beneficial ownership, directly or indirectly, by any entity, person or group (other than the Company or any Company employee benefit plan (including any trustee of such plan acting as such trustee) and other than State Automobile Mutual Insurance Company) of securities of the Company representing 30% or more of the combined voting power of the Company’s outstanding securities and the adoption by the Board of a resolution to the effect that a Potential Change in Control of the Company has occurred for purposes of this Plan.

4.1 Performance Criteria. As to each Performance Period, the Administrator will establish in writing Performance Criteria based on one or more of the following performance measures of the State Auto Group over the Performance Period: (i) earnings; (ii) return on capital; (iii) return on equity; (iv) return on assets; (v) rate change; (vi) revenue; (vii) premiums; (viii) net income; (ix) earnings per share; (x) combined ratio; (xi) loss ratio; (xii) expense ratio; (xiii) assets; (xiv) equity; (xv) cash flow; (xvi) stock price; (xvii) total shareholders’ return; (xviii) premium growth; (xix) corporate surplus growth (defined as growth in State Auto Mutual’s surplus less the impact of the value of its

holdings of the Company); (xx) economic profit and (xxi) individual performance related to personal goals. The Administrator may, in its discretion, measure any of such Performance Criteria on an absolute or relative basis. Performance Criteria applicable to Covered Employees will not include item (xxi) above (individual performance related to personal goals), unless a separate Award is issued specific to such goals. Any Award issued to a Covered Employee that includes item (xxi) as a Performance Criteria will not be performance-based compensation governed by Code Section 162(m). Except as otherwise provided herein, the extent to which the Performance Criteria are satisfied will determine the amount, if any, of the Award that will be earned by each Participant. The Performance Criteria may vary for different Performance Periods and need not be the same for each Participant eligible for an Award for a Performance Period.

4.5 Change of Control or Potential Change of Control. If a Change of Control or Potential Change of Control, as defined in Section 2.5 of the Plan, occurs prior to the end of a specified Performance Period, the Administrator shall determine the Final Bonus in accordance with Section 4.4 of the Plan; provided, however, that such Final Bonus shall be determined based on the achievement of the Performance Criteria up to the date of the Change of Control or Potential Change of Control and then prorated based upon the length of time that the Participant was employed by the Company during the applicable Performance Period. The Final Bonus, thus determined, shall be paid per the terms of the Plan.

6.1 Termination of Employment Due to Death, Disability or Retirement. In the event a Participant’s employment is terminated during the applicable Performance Period by reason of death, Disability or retirement upon the attainment of early or normal retirement age as defined in the State Auto Insurance Companies Employee Retirement Plan (the “Retirement Plan”) (regardless of whether such Participant is eligible to retire from the Retirement Plan), the Final Bonus determined in accordance with Section 4.4 herein shall be reduced to reflect participation prior to termination only.

(a) Death or Disability. If the Participant’s employment is terminated due to death or Disability, the Final Bonus, if any, shall be equal to 100% of the Participant’s target bonus, prorated by multiplying the Final Bonus by a fraction, the numerator of which is the number of days of employment in the Performance Period through the date of employment termination, and the denominator of which is the number of days in the Performance Period. In the case of a Participant’s Disability, the employment termination shall be deemed to have occurred as of the date that the Administrator determines was the date on which the definition of Disability was satisfied. Notwithstanding the foregoing, if the Participant is a Covered Employee, the Final Bonus, if any, shall be based upon the achievement of the Performance Criteria during the applicable portion of the Performance Period and then prorated as described above.

(b) Retirement. If the Participant’s employment is terminated due to retirement (as defined above), the Final Bonus, if any, shall be based upon the achievement of the Performance Criteria during the applicable Performance Period and then prorated based upon the length of time that the Participant was employed by the Company during the Performance Period.

The Final Bonus thus determined shall be paid as soon as practicable and reasonable following the Participant’s death, Disability or retirement unless otherwise elected by the Participant as provided by the State Auto Property & Casualty Insurance Company Amended and Restated Incentive Deferred Compensation Plan (the “Deferred Compensation Plan”), as the same may be amended from time to time. The Administrator may establish such procedures as it deems appropriate for a Participant to designate a beneficiary to whom any amounts payable in the event of the Participant’s death are to be paid. If no beneficiary is designated, the right of the Participant to receive any payment under this Plan will pass to the Participant’s estate.

The Final Bonus thus determined shall be paid as soon as practicable and reasonable following the end of the Performance Period in which employment termination occurs, and shall be made at the same time payments are made to Participants who did not terminate employment during the applicable Performance Period unless otherwise elected by the Participant as provided in the Deferred Compensation Plan, as the same may be amended from time to time.