STOCK APPRECIATION RIGHTS AGREEMENT UNDER THE ARBINET-THEXCHANGE, INC.

Exhibit 10.2

STOCK APPRECIATION RIGHTS AGREEMENT

UNDER THE ARBINET-THEXCHANGE, INC.

2004 STOCK INCENTIVE PLAN, AS AMENDED

Pursuant to the Arbinet-thexchange, Inc. 2004 Stock Incentive Plan as amended through the date hereof (the “Plan”), Arbinet-thexchange, Inc. (the “Company”) hereby grants to the Participant named above an award (the “Award”) equal to the number of Stock Appreciation Rights (“SARs”) specified above. This Award shall give the Participant the right to exercise on or prior to the Expiration Date specified above all or part of the number of SARs specified above at the Exercise Price per Share specified above, and to receive a payment in accordance with Section 2 of this Agreement, subject to the terms and conditions set forth herein and in the Plan. Each of the SARs granted herein relates to one share of the Common Stock, par value $0.001 per share (the “Stock”), of the Company.

1. Acceptance of Award. The Participant shall have no rights with respect to this Award unless he shall have accepted this Award prior to the close of business on the Expiration Date specified above by signing and delivering to the Company a copy of this Agreement.

2. Vesting Schedule. No SARs may be exercised until they have vested. Except as set forth below, these SARs shall be vested and exercisable on the dates indicated so long as the Participant remains an employee or director of, or consultant or advisor to, the Company or a subsidiary (an “Eligible Participant”) on such dates:

Once vested, these SARs shall continue to be exercisable at any time or times prior to the close of business on the Expiration Date, subject to the provisions hereof and of the Plan. SARs may be subject to accelerated vesting in accordance with Section 5 below.

3. Exercise of Stock Appreciation Rights.

(a) The Participant may elect to exercise vested SARs in the following manner: Prior to the close of business on the Expiration Date, the Participant may give written notice to the Company of his election to exercise a specified number of vested SARs. The Participant shall, subject to tax withholding in accordance with Section 9 below, thereupon receive a payment equal to the product of (i) the Fair Market Value of a share of Stock at the close of business on the date of exercise less the Exercise Price per Share specified in this Agreement, multiplied by (ii) the number of SARs exercised. Such payment shall be in the form of shares of Stock.

(b) The minimum number of SARs which may be exercised at any one time shall be 100, unless the number of SARs being exercised is the total number of SARs subject to exercise at the time.

(c) Notwithstanding any other provision hereof or of the Plan, no SAR shall be exercisable after the Expiration Date hereof.

4. Termination of Relationship. If the Participant’s ceases to be an Eligible Participant, any SARs not yet exercised may be exercised, to the extent vested and exercisable on the date of such termination, for a period of time determined according to the following schedule:

provided, however, that no SARs may be exercised after the Expiration Date hereof. Any SARs that are not vested and exercisable on the date of the termination of the Participant’s relationship with the Company shall immediately and automatically be forfeited and become null and void. The Company’s determination of the reason for termination of the Participant’s relationship shall be conclusive and binding on the Participant and his representatives or legatees. “Cause” shall mean willful misconduct by the Participant or willful failure by the Participant to perform his responsibilities to the Company (including, without limitation, breach by the Participant of any provision of any employment, consulting, advisory, nondisclosure, non-competition or other similar agreement between the Participant and the Company), as determined by the Company, which determination shall be conclusive. The Participant shall be considered to have been discharged for “Cause” if the Company determines, within 30 days after the Participant’s resignation, that discharge for Cause was warranted.

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5. Change in Control.

(a) Should a Change in Control (as defined below) occur while the Participant remains in service as an Eligible Participant, then this Award, to the extent outstanding at the time of that Change in Control but not otherwise fully vested and exercisable, shall automatically vest on an accelerated basis so that this Award shall, immediately prior to the effective date of such Change in Control, vest and become exercisable as to fifty percent (50%) of the SARs for which this Award would not otherwise at that time be vested and exercisable in accordance with the normal vesting schedule set forth in Section 2 of this Agreement. This Award shall vest and become exercisable for the remaining fifty percent (50%) of the unvested SARs equally over the remaining vesting term as set forth in Section 2 of this Agreement. However, this Award shall, immediately prior to the effective date of a Change in Control, vest and become exercisable as to all the SARs if and to the extent: (i) this Award is not to be assumed by the successor corporation (or parent thereof) or is not otherwise to be continued in full force and effect after the Change in Control or (ii) this Award is not to be replaced with a program of the successor corporation which preserves the spread existing at the time of the Change in Control on any unvested SARs (the excess of the fair market value of those unvested SARs over the aggregate Exercise Price payable for such SARs) and provides for subsequent payout of that spread in accordance with the same vesting schedule for such SARs as set forth in Section 2 of this Agreement. At the effective time of the Change in Control, this Award shall terminate and cease to be outstanding, except to the extent assumed by the successor corporation (or parent thereof) or otherwise continued in effect after the Change in Control. Notwithstanding anything to the contrary herein, the Company shall have the right, but not the obligation, in connection with a Change in Control, to make or provide for a cash payment to the Participant, in exchange for the cancellation of this Award, in an amount equal to the difference between (x) the value as determined by the Board of the consideration payable or otherwise to be received by the Company’s stockholders, per share of Stock, in connection with the Change in Control, multiplied by the number of SARs and (y) the aggregate Exercise Prices of the SARs.

(b) To the extent this Award does not, at the time of the Change in Control, vest and become exercisable as to all the SARs, then this Award shall be subject to accelerated vesting in accordance with the following provision:

Should the Participant’s service as an Eligible Participant be terminated by the Company other than for Cause on or within twelve (12) months after the effective date of that Change in Control, then this Award shall immediately vest and become exercisable as to all the SARs until the earlier of (i) the Expiration Date or (ii) the sooner termination of this Award pursuant to Section 4 of this Agreement.

If the Award is replaced with a program of the successor corporation as set forth above, the accelerated vesting provided by this Section 5 shall apply equally to the replacement cash incentive program.

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(c) If this Award is assumed in connection with a Change in Control or otherwise continued in effect, then this Award shall be appropriately adjusted, immediately after such Change in Control, to apply to the number and class of securities which would have been issuable to Participant in consummation of such Change in Control had the Award been exercised immediately prior to such Change in Control, and appropriate adjustments shall also be made to the Exercise Price, provided the aggregate Exercise Price shall remain the same. To the extent the actual holders of the Company’s outstanding Stock receive cash consideration for their Stock in consummation of the Change in Control, the successor corporation may, in connection with the assumption or continuation of this Award, substitute one or more shares of its own common stock with a fair market value equivalent to the cash consideration paid per share of Stock in such Change in Control, provided such common stock is readily tradable on an established U.S. securities exchange or market.

(d) For purposes of this Agreement, a “Change in Control” of the Company shall mean a change in ownership or control of the Company effected through any of the following transactions:

(i) a merger, consolidation or other reorganization approved by the Company’s stockholders, unless securities representing more than 50% of the total combined voting power of the voting securities of the successor corporation are immediately thereafter beneficially owned, directly or indirectly and in substantially the same proportion, by the persons who beneficially owned the Company’s outstanding voting securities immediately prior to such transaction, or

(ii) a stockholder-approved sale, transfer or other disposition of all or substantially all of the Company’s assets, or

(iii) the closing of any transaction or series of related transactions pursuant to which any person or any group of persons comprising a “group” within the meaning of Rule 13d-5(b)(1) of the Exchange Act (other than the Company or a person that, prior to such transaction or series of related transactions, directly or indirectly controls, is controlled by or is under common control with, the Company) becomes directly or indirectly the beneficial owner (within the meaning of Rule 13d-3 of the Exchange Act) of securities possessing (or convertible into or exercisable for securities possessing) more than 50% of the total combined voting power of the Company’s securities (as measured in terms of the power to vote with respect to the election of members of the board of directors) outstanding immediately after the consummation of such transaction or series of related transactions, whether such transaction involves a direct issuance from the Company or the acquisition of outstanding securities held by one or more of the Company’s existing stockholders.

6. Reorganization Event.

(a) Upon the occurrence of a Reorganization Event (as defined in the Plan) other than a liquidation or dissolution of the Company, if the Award is assumed or otherwise continued by the Company’s successor, the rights of the Company under this Award shall inure to the benefit of the Company’s successor and shall apply to the cash, securities or other property which the Stock was converted into or exchanged for pursuant to such Reorganization Event in

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the same manner and to the same extent as they applied to the Stock subject to the Award. Upon the occurrence of a Reorganization Event involving the liquidation or dissolution of the Company, except to the extent specifically provided to the contrary in the instrument evidencing this Award or any other agreement between a Participant and the Company, the SARs subject to this Award then outstanding shall automatically be deemed fully vested and exercisable.

(b) This Agreement shall not in any way affect the right of the Company to adjust, reclassify, reorganize or otherwise change its capital or business structure or to merge, consolidate, dissolve, liquidate or sell or transfer all or any part of its business or assets.

7. Incorporation of Plan. Notwithstanding anything herein to the contrary, these SARs shall be subject to and governed by all the terms and conditions of the Plan. Capitalized terms in this Agreement shall have the meaning specified in the Plan, unless a different meaning is specified herein.

8. Transferability. This Agreement is personal to the Participant, is non-assignable and is not transferable in any manner, by operation of law or otherwise, other than by will or the laws of descent and distribution. These SARs are exercisable, during the Participant’s lifetime, only by the Participant, and thereafter, only by the Participant’s legal representative or legatee.

9. Tax Withholding. The Participant shall, not later than the date as of which the exercise of these SARs becomes a taxable event for Federal income tax purposes, pay to the Company or make arrangements satisfactory to the Committee for payment of any Federal, state, and local taxes required by law to be withheld on account of such taxable event. The Participant may elect to have such tax withholding obligation satisfied, in whole or in part, by authorizing the Company to withhold from shares of Stock to be issued.

10. No Obligation to Continue Employment. Neither the Company nor any subsidiary is obligated by or as a result of the Plan or this Agreement to continue the Participant in employment and neither the Plan nor this Agreement shall interfere in any way with the right of the Company or any subsidiary to terminate the employment of the Participant at any time.

11. Notices. Notices hereunder shall be mailed or delivered to the Company at its principal place of business and shall be mailed or delivered to the Participant at the address on file with the Company or, in either case, at such other address as one party may subsequently furnish to the other party in writing.

12. Amendment. This Agreement may be amended or modified only by a written instrument executed by both the Company and the Participant.

13. Governing Law. This Agreement shall be construed, interpreted and enforced in accordance with the internal laws of the State of New Jersey without regard to any applicable conflicts of laws.

14. Participant’s Acknowledgments. The Participant acknowledges that he: (i) has read this Agreement; (ii) has been represented in the preparation, negotiation and execution of this Agreement by legal counsel of the Participant’s own choice or has voluntarily declined to seek such counsel; (iii) understands the terms and consequences of this Agreement; and (iv) is fully aware of the legal and binding effect of this Agreement.

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The foregoing Agreement is hereby accepted and the terms and conditions thereof hereby agreed to by the undersigned.

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