Exhibit 10.2

FORM OF STOCK APPRECIATION RIGHT AWARD AGREEMENT

This Stock Appreciation Right Award Agreement (this “Agreement”), dated as of             , 20    , is made between Intervest Bancshares Corporation (the “Company”) and the individual named below (the “Participant”) to record the granting of Stock Appreciation Rights (“SARs”) to the Participant pursuant to the Company’s 2013 Equity Incentive Plan (the “Plan”) by the Compensation Committee of the Company’s Board of Directors.

The Company and the Participant hereby agree as follows:

1. Terms of Award. The following terms used in this Agreement shall have the meanings set forth in this Section 1:

Capitalized terms used in this Agreement but not defined herein shall have the meanings given to such terms in the Plan.

2. Grant of SAR Award. The Company hereby grants to the Participant, as of the Grant Date, SARs on the number of shares of the Company’s common stock (the “Shares”) specified above. This SAR Award is a “Free Standing Award” within the meaning of Section 7.1(a) of the Plan. This SAR Award represents the right, upon exercise, to receive a cash payment only of an amount determined by multiplying (a) the difference between the fair market value of a Share on the date of exercise (the “Fair Market Value”) over the Exercise Price, by (b) the number of Shares with respect to which the SAR Award is exercised (the product of (a) and (b) is referred to herein as the “SAR Payment Amount”). In no event shall this SAR Award entitle the Participant to receive any Shares. For purposes of computing the SAR Payment Amount, the Fair Market Value shall mean the closing price for one share as reported by the principal stock exchange on which the Shares are traded on the date the SAR Exercise Election, as that term is defined below, is received by the Company; provided, however, that if a SAR Exercise Election is received after the close of trading for a particular day but prior to the opening of trading for the following trading day, then the closing price for one Share as of the most recent close of trading on such exchange will be deemed to be the Fair Market Value, even if such close occurred on a previous day.

3. Vesting. Subject to the Participant’s continued service with the Corporation or its Subsidiaries unless otherwise provided in Section 4(b) and Section 6 below, the SARs shall become vested and may be exercised as follows: (a) with respect to one-third (1/3) of the Shares, on the first anniversary of the Grant Date, or             , 20    ; (b) with respect to an additional one-third (1/3) of the Covered Shares, on the second anniversary of the Grant Date, or             , 20    ; and (c) with respect to the remaining one-third (1/3) of the Covered Shares, on the third anniversary of the Grant Date, or             , 20    . [Notwithstanding the foregoing, the Committee may, in its sole discretion, provide for accelerated vesting of the SARs at any time and for any reason.] [Notwithstanding the foregoing vesting date, if, prior to the third anniversary of the Grant Date, there is a Change of Control of the Company (as that term is defined in the Plan) or the Participant’s employment terminates because of death or disability, all Shares not yet vested shall become immediately vested.]

4. Exercise.

(a) The SAR Award shall be exercisable by written notice (in the form attached hereto) which shall state the election to exercise the SARs and the number of Shares as to which the SARs are to be exercised (a “SAR Exercise Election”). Such written notice shall be signed by the Participant and shall be delivered in person, by certified mail or by such other means as approved in writing by the Company and which results in written confirmation of actual receipt by the Secretary of the Company. Such SARs shall be deemed to be exercised upon receipt by the Company of such written notice. In no event may this SAR Award be exercised for less than the lesser of (i) 500 shares and (ii) the number of unexercised Shares remaining under the SAR Award. This SAR Award shall be exercisable only when the Fair Market Value per share of common stock subject to the SAR Award exceeds the Exercise Price.

(b) The Committee may suspend the right to exercise the SARs during any period for which the Committee determines, in its sole discretion, that such suspension would be advisable or necessary in order to comply with the requirements of (i) any applicable federal securities law or rule or regulation thereunder, (ii) any rule of a national securities exchange, national securities association, or other self-regulatory organization, (iii) any other federal or state law or regulation, or (iv) any written policy of the Company in effect on the date of the proposed exercise (each a “SAR Exercise Suspension”). Notwithstanding the foregoing, no SAR Exercise Suspension shall extend the term of this SAR Award beyond the Expiration Date (as defined below) or in a manner that would otherwise result in the SARs becoming nonqualified deferred compensation subject to Section 409A of the Code.

5. Settlement of SAR. Settlement of the SAR Payment Amount shall be made by delivering a cash payment to the Participant equal to the SAR Payment Amount. Such payment shall be made within thirty (30) days following a SAR Exercise Election, and shall be subject to any applicable tax withholding obligations. The Company may direct that any of its Subsidiaries (a “Designated Subsidiary”) deliver the SAR Payment Amount, subject to any applicable tax withholding obligations, to the Participant and, in such case, such payment shall be treated as having been made directly by such Designated Subsidiary to the Participant. If this SAR Award remains outstanding on the Expiration Date, the entire remaining vested but unexercised portion of this SAR Award shall be deemed to have been exercised as of the Expiration Date and such automatic exercise shall be treated as a SAR Exercise Election.

6. Termination of Services; Forfeiture. Notwithstanding any other provision of this Agreement, upon a termination of Participant’s services with the Company and its Subsidiaries, (i) regardless of the reason for such termination, each unvested SAR shall be immediately canceled and terminated, (ii) unless such termination of Participant’s service was for “cause” (as determined by the Committee in its sole discretion), each vested SAR shall be exercisable for a period of ninety (90) days following such termination and, if not exercised prior to the end of such ninety (90) day period shall be deemed to have been exercised as of the last day of such ninety (90) day period and such automatic exercise shall be treated as a SAR Exercise Election, and (iii) if the termination of the Participant’s services with the Company and its Subsidiaries was for “cause” (as determined by the Committee in its sole discretion), each vested SAR shall be immediately canceled and terminated. For clarity, this SAR Award shall expire and shall no longer be exercisable when all of the SARs hereunder have been either exercised or canceled and terminated.

7. Rights as a Stockholder. Participant shall have no rights as a stockholder with respect to any Shares subject to this SAR Award.

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8. Adjustments. In the event of any stock dividend, reclassification, subdivision or combination or similar transaction affecting this SAR Award, the rights of the Participant will be adjusted as provided in Section 11 of the Plan.

9. Non-Transferability. Without the express written consent of the Committee, which may be withheld for any reason in its sole discretion, the SARs may not be transferred in any manner otherwise than by will or by the laws of descent or distribution and may be exercised during the Participant’s lifetime only by the Participant. The terms of the Plan and this Agreement shall be binding upon the Participant’s executors, administrators, heirs, successors and assigns. Any attempt to transfer the SARs in any manner, contrary to the terms and provisions of this Agreement and/or the Plan shall be null and void and without legal force or effect.

10. Tax Withholding The Participant hereby agrees that the Company or any applicable Designated Subsidiary may take any reasonable actions necessary to comply with income and employment tax withholding obligations as may be required of the Company or any applicable Designated Subsidiary under applicable law on account of this SAR Award. Pursuant to Section 5 above, any such withholding required as a result of delivery of a SAR Payment Amount shall be taken from such SAR Payment Amount to the extent possible. Any withholding required of the Company as a result of delivery of this SAR Award or for any other reason that cannot be taken immediately from a SAR Payment Amount may be withheld from payroll or other amounts payable to Participant.

11. No Employment Rights. Neither the Plan nor this SAR Award shall confer upon the Participant any right with respect to continuing employment by the Company or any subsidiary of the Company nor shall they interfere in any way with the right of the Company or any subsidiary of the Company to terminate the Participant’s employment at any time, with or without Cause.

12. The Plan; Amendment This SAR Award is subject in all respects to the terms, conditions, limitations and definitions contained in the Plan. In the event of any discrepancy or inconsistency between this Agreement and the Plan, the terms and conditions of the Plan shall govern and control. The Committee shall have the right, in its sole discretion, to modify or amend this Agreement from time to time in accordance with and as provided in the Plan. The Company shall give written notice to the Participant of any such modification or amendment of this Agreement as soon as practicable after the adoption thereof. This Agreement may also be modified or amended by a writing signed by both the Company and the Participant, without the consent of any other person.

13. Binding Agreement; Assignment. This Agreement shall inure to the benefit of, be binding upon, and be enforceable by the Company and its successors and assigns. The Participant shall not assign (except in accordance with Section 10 hereof) any part of this Agreement without the prior express written consent of the Company.

14. Headings. The titles and headings of the various sections of this Agreement have been inserted for convenience of reference only and shall not be deemed to be a part of this Agreement.

15. Counterparts. This Agreement may be executed in one or more counterparts, each of which shall be deemed to be an original, but all of which shall constitute one and the same instrument.

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16. Severability. The invalidity or unenforceability of any provision of this Agreement in any jurisdiction shall not affect the validity, legality or enforceability of the remainder of this Agreement in such jurisdiction or the validity, legality or enforceability of any provision of this Agreement in any other jurisdiction, it being intended that all rights and obligations of the parties hereunder shall be enforceable to the fullest extent permitted by law.

17. Acquired Rights. The Participant acknowledges and agrees that: (a) the Company may terminate or amend the Plan at any time; (b) the award of SARs made under this Agreement is completely independent of any other award or grant and is made at the sole discretion of the Company; (c) no past grants or awards (including, without limitation, the SARs awarded hereunder) give the Participant any right to any grants or awards in the future whatsoever; and (d) any benefits granted under this Agreement are not part of the Participant’s ordinary salary, and shall not be considered as part of such salary in the event of severance, redundancy or resignation.

18. Applicable Law. This Agreement shall be governed by and construed in accordance with the domestic laws of the State of New York without giving effect to any choice or conflict of law provision or rule (whether of the State of New York or any other jurisdiction) that would cause the application of the laws of any jurisdiction other than the State of New York.

19. Notices. All notices to the Company shall be in writing and sent to the Company’s Secretary at the Company’s offices. Notices to the Participant shall be addressed to the Participant at the Participant’s address as it appears in the Company’s records.

[Signature page follows]

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IN WITNESS WHEREOF, the Company and the Participant have caused this Stock Appreciation Right Award Agreement to be executed on the date set forth opposite their respective signatures, it being understood that the Grant Date is set forth on the first page of this Agreement and may differ from the date of signature.

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EXHIBIT A

STOCK APPRECIATION RIGHT (“SAR”) EXERCISE NOTICE

Intervest Bancshares Corporation

One Rockefeller Plaza, Suite 400

New York, New York 10020-2002

Attention: Secretary

By this exercise, Participant agrees to provide such additional documents as the Company may require pursuant to the Plan and to provide for the payment by the Participant to the Company, in the manner designated by the Company, of Participant’s withholding obligations, if any, relating to this exercise which is not satisfied from the SAR Payment Amount.

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