AMENDMENT TO EMPLOYMENT AGREEMENT

Exhibit 10.8.1

AMENDMENT TO

EMPLOYMENT AGREEMENT

THIS AMENDMENT (the “Amendment”) is entered as of December 31, 2008, by and between The NASDAQ OMX Group, Inc. (the “Company”) and Robert Greifeld (the “Executive”).

WHEREAS, the Executive and the Company (f/k/a/ The Nasdaq Stock Market, Inc.) entered into an employment agreement, dated as of May 12, 2003 and subsequently amended and restated that employment agreement effective as of January 1, 2007 (the “2007 Agreement”); and

WHEREAS, the Executive and the Company now desire to amend and the 2007 Agreement so as to reflect the provisions of Section 409A of the Internal Revenue Code and the final regulations issued thereunder, which amendment is to be effective as of January 1, 2007.

NOW, THEREFORE, in consideration of the premises and mutual covenants herein and for other good and valuable consideration, the parties hereby amend the provisions of the 2007 Agreement, as set out below. Except to the extent so amended, all of the provisions of the 2007 Agreement shall remain in full force and effect in accordance with their terms.

The 2007 Agreement is hereby amended, as follows:

The Base Salary shall be payable in regular payroll installments in accordance with the Company’s payroll practices as in effect from time to time (but no less frequently than monthly).

(b) SERP Participation and Provisions. The Executive shall continue to participate in The NASDAQ OMX Group, Inc. Supplemental Executive Retirement Plan, as amended and restated effective as of December 31, 2008 (formerly, the Nasdaq Stock Market, Inc. Supplemental Executive Retirement Plan, the “SERP”). The Company reserves the right to modify or terminate the SERP at any time. Notwithstanding any term or condition contained in the SERP to the contrary, and subject to the Company’s right to modify or terminate the SERP at any time:

(i) Section 5.1 of the SERP shall be applied as if the age and service requirements stated therein were age 49 and four years of service rather than age 55 and ten years of service. Accordingly, the Executive shall be 100% vested in his accrued SERP benefit upon the later of his attainment of age 49 while employed and his completion of four years of service.

(ii) Section 5.1 of the SERP shall be applied as if the age and service requirements stated therein were satisfied upon the Executive’s termination of employment by the Company without Cause or by the Executive for Good Reason

pursuant to Section 8(b) below. Accordingly, under such circumstances, the Executive shall be 100% vested in his SERP benefit even if his employment terminates prior to his attaining age 49 and having completed four years of service with the Company.

(iii) The death benefit provided in Sections 8.1 and 8.2 of the SERP shall become payable if the Executive dies before his SERP benefit commences, but after having satisfied the requirements of Section 5.1 of the SERP prior to modification by Section 6(b) (i) above (and, if the foregoing conditions are satisfied, such death benefit will be payable even if the Executive’s death occurs after he has left employment with vested rights under the SERP, but before payment of the SERP benefit commences).

(iv) Sections 6.4 and 7.4 of the SERP (relating to early retirement) shall apply only if the Executive has at least five years of service; provided that this special rule shall not permit the Executive’s SERP benefit to start earlier than age 55.

(v) The provisions of this Section 6(b) shall not accelerate the rate at which the SERP benefit accrues so that the amount of the accrued SERP benefit shall be determined with reference to an accrual over a period of 3,650 days as provided in the SERP definition of “Accrued Benefit.”

All such reimbursements shall be made no later than the last day of the calendar year following the calendar year in which the Executive incurs the reimbursable expense. Additionally, the amount of expenses eligible for reimbursement during one calendar year may not affect the expenses eligible for reimbursement or any in-kind benefits to be provided in any other calendar year and the right to reimbursement is not subject to liquidation or exchange for another benefit.

The Company shall conduct a security audit of up to two of the Executive’s personal residences and reimburse the Executive during calendar year 2010 for up to $50,000 of the cost of upgrading or installing the Executive’s home security systems, regardless of whether such expenses were incurred in 2010 or in 2009; provided, however, that, to the extent elected by the Executive in writing no later than December 31, 2008, the Company shall instead reimburse the Executive during calendar year 2009 for up to $50,000 of the cost incurred in 2009 of upgrading or installing the Executive’s home security systems.

(i) any unpaid Base Salary through the Date of Termination, to be paid in accordance with the Company’s payroll practices as described in Section 3 above,

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Severance Payment. The Company shall pay the Executive an amount (the “Severance Payment”) equal to the sum of (I) the Base Salary paid to the Executive with respect to the calendar year immediately preceding the Executive’s Date of Termination and (II) the Annual Bonus for the calendar year immediately preceding the Executive’s Date of Termination, payable in substantially equal monthly installments for the twelve month period following the Executive’s Date of Termination, with the first installment to be paid in the month following the month in which the Date of Termination occurs (the “Severance Period”), or, if required to avoid the imposition of tax, interest or penalties under Section 409A of the Internal Revenue Code of 1986, as amended (“Section 409A”) beginning on the date that is six months and one day after the date of the Executive’s “separation from service” within the meaning of Section 409A, in which case the first payment shall include all amounts that would have been paid on earlier payroll dates but for such delay.

The Company shall provide the Executive with continued health care coverage with such cost of coverage to be provided, directly or indirectly, on at least a monthly basis for the lesser of (I) the period of twelve months beginning with the Termination Date or (II) the period beginning with the Termination Date and ending on the date that the Executive is eligible for coverage under the health care plans of a subsequent employer, such coverage to be conditioned upon the Executive (X) being covered by the Company’s health care plans immediately prior to the Date of Termination and (Y) paying his share of the applicable health care premiums, deductibles and co-payments for such period of coverage.

For purposes of this Agreement, “Permanent Disability” means either (i) the inability of the Executive to engage in any substantial gainful activity by reason of any medically determinable physical or mental impairment that can be expected to result in death or can be expected to last for a continuous period of not less than 12 months or (ii) the Executive is, by reason of any medically determinable physical or mental impairment that can be expected to result in death or can be expected to last for a continuous period of not less than 12 months, receiving income replacement benefits for a period of not less than three months under an accident and health plan covering employees of the Company. The Executive shall be deemed Permanently Disabled if he is determined to be (i) totally disabled by the Social Security Administration or (ii) disabled in accordance with a disability insurance program, provided such definition of

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disabled under the program complies with the definition of Permanent Disability hereunder. Otherwise, such Permanent Disability shall be certified by a physician chosen by the Company and reasonably acceptable to the Executive (if he is then able to exercise sound judgment).

Health and Welfare Benefits. The Company shall provide the Executive with continued health care coverage for the lesser of (I) twenty-four months beginning with the Termination Date or (II) the period beginning with the Termination Date and ending on the date that the Executive is eligible for coverage under the health care plans of a subsequent employer, such coverage to be conditioned upon the Executive (X) being covered by the Company’s health care plans immediately prior to the Date of Termination and (Y) paying his share of the applicable health care premiums, deductibles and co-payments for such period of coverage. The foregoing health care benefits are not intended to limit or otherwise reduce any entitlements that Executive may have under COBRA. In addition, the Company shall continue to provide the Executive with the same level of accident (AD&D) and life insurance benefits upon substantially the same terms and conditions (including contributions required by the Executive for such benefits) as existed immediately prior to the Executive’s Date of Termination (or, if more favorable to the Executive, as such benefits and terms and conditions existed immediately prior to the Change in Control) for the same period for which the Company shall provide the Executive with continued health care coverage.

(B) the date on which, within any twelve (12)-month period (beginning on or after the Effective Date), a majority of the directors then serving on the Board are replaced by directors is not endorsed by at least two-thirds ( ²/3) of the members of the Board before the date of appointment or election;

(D) the consummation of an agreement for the sale or disposition by the Company of all or substantially all of the Company’s assets (or any transaction having a similar effect), provided that such agreement or transaction of similar effect shall in all events require the disposition, within any twelve (12)-month period, of at least 40% of the gross fair market value of all of the Company’s then assets; other than a sale or disposition by the Company of all or substantially all of the Company’s assets to an entity, at least 50% of the combined voting power of the voting securities of which are owned directly or indirectly by stockholders of the Company in substantially the same proportions as their ownership of the Company immediately prior to such sale.

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Notwithstanding the foregoing, in no event shall a Change in Control be deemed to occur hereunder unless such event constitutes a change in ownership of the Company, a change in effective control of the Company or a change in ownership of a substantial portion of the Company’s assets within the meaning of Section 409A of the Code. Notwithstanding the foregoing, a Change in Control shall not be deemed to occur as a result of any transaction or event which causes the reduction in the Voting Securities held by the NASD below 50% which would not otherwise constitute a Change in Control pursuant to clauses (A) through (D) above.

Section 409A. Notwithstanding any other provision of this Agreement, any payment, settlement or benefit triggered by termination of the Executive’s employment with the Company shall not be made until six months and one day following Date of Termination if such delay is necessary to avoid the imposition of any tax, penalty or interest under Section 409A(a). For purposes of this Agreement, termination or severance of employment will be read to mean a “separation from service” within the meaning of Section 409A of the Code where it is reasonably anticipated that no further services would be performed after that date or that the level of services the Executive would perform after that date (whether as an employee or independent contractor) would permanently decrease to no more than 20 percent of the average level of bona fide services performed over the immediately preceding thirty-six (36)-month period. The Company, after consulting with the Executive, may amend this Agreement or the terms of any award provided for herein in any manner that the Company considers necessary or advisable to ensure that cash compensation, equity awards or other benefits provided for herein are not subject to United States federal income tax, state or local income tax or any equivalent taxes in territories outside the United States prior to payment, exercise, vesting or settlement, as applicable, or any tax, interest or penalties pursuant to Section 409A. Any such amendments shall be made in a manner that preserves to the maximum extent possible the intended benefits to the Executive. This paragraph 13(i) does not create an obligation on the part of the Company to modify this Agreement and does not guarantee that the amounts or benefits owed under the Agreement will not be subject to interest and penalties under Section 409A. For purposes of this Agreement, all rights to payments and benefits hereunder shall be treated as rights to receive a series of separate payments and benefits to the fullest extent allowed by Section 409A.

The reduction of the amounts payable hereunder, if applicable, shall be made by reducing first the payments under Section 8(g)(i)(A), then the payments in 8(g)(i)(B) and 8(g)(i)(C) in that order.

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The Reimbursement Payment under this Exhibit D with respect to any Payments shall be made no later than thirty (30) days following such Payment, but no later than the end of the calendar year following the calendar year in which the applicable Excise Tax is remitted to the Federal government.

In the event the amount of the Reimbursement Payment is less than the amount necessary to reimburse Executive for the Excise Tax, the Accounting Firm shall determine the amount of the Underpayment that has occurred and any such Underpayment (together with interest at the rate provided in Section 1274(b)(2)(B) of the Code) shall be promptly paid by the Company to or for the benefit of Executive, but no later than the end of the calendar year following the calendar year in which the applicable Excise Tax is remitted to the Federal government.

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IN WITNESS WHEREOF, the parties hereto have duly executed this Amendment as of the day and year first above written.

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