<PAGE>
                                                                    EXHIBIT 10.3

                        TD AMERITRADE HOLDING CORPORATION

                          1996 LONG-TERM INCENTIVE PLAN

                            NOTICE OF GRANT OF OPTION

      Unless otherwise defined herein, the terms defined in the 1996 Long-Term
Incentive Plan (the "Plan") will have the same defined meanings in this Notice
of Grant of Option (the "Notice of Grant") and Terms and Conditions of Option
Grant, attached hereto as Exhibit A (together, the "Agreement").

      PARTICIPANT:                               Fredric J. Tomczyk

      Participant has been granted an Option to purchase Stock of the Company,
subject to the terms and conditions of the Plan and this Agreement, as follows:

      Date of Grant                               May 15, 2008

      Vesting Commencement Date                   October 1, 2008

      Number of Shares Granted                    1,150,000

      Exercise Price per Share                    $18.21

      Total Exercise Price                        $20,941,500.00

      Type of Option                              Non-Statutory Stock Option

      Term/Expiration Date                        May 15, 2018

      Vesting Schedule:

      Subject to accelerated vesting as set forth below or in the Plan, this
Option will be exercisable, in whole or in part, in accordance with the
following schedule:

      Twenty-five percent (25%) of the Shares subject to the Option will vest
twelve (12) months after the Vesting Commencement Date, and thereafter an
additional twenty-five percent (25%) shall vest on each yearly anniversary of
the Vesting Commencement Date, subject to Participant continuing to be an
Employee and/or Director through each such date. As provided in Section 4(c) of
the Participant's written employment agreement (the "Employment Agreement"), if
the Participant does not become the Chief Executive Officer of the Company as of
October 1, 2008, then this Option shall be immediately forfeited and none of the
Shares subject to the Option shall ever have become vested and/or exercisable.

                                      -1-

<PAGE>

      Termination Period:

      This Option will be exercisable for three (3) months after Participant
ceases to be an Employee and/or Director, unless such termination is due to
Participant's death or Disability, in which case this Option will be exercisable
for twelve (12) months after Participant ceases to be an Employee and/or
Director. Notwithstanding the foregoing, in no event may this Option be
exercised after the Term/Expiration Date as provided above and may be subject to
earlier termination as provided in Section 13.1 of the Plan.

      By Participant's signature and the signature of the Company's
representative below, Participant and the Company agree that this Option is
granted under and governed by the terms and conditions of the Plan and this
Agreement. Participant has reviewed the Plan and this Agreement in their
entirety, has had an opportunity to obtain the advice of counsel prior to
executing this Agreement and fully understands all provisions of the Plan and
Agreement. Participant hereby agrees to accept as binding, conclusive and final
all decisions or interpretations of the Board or the Committee upon any
questions relating to the Plan and Agreement. Participant further agrees to
notify the Company upon any change in the residence address indicated below.

PARTICIPANT                              TD AMERITRADE HOLDING CORPORATION

/s/ FRED TOMCZYK                         /s/ JOSEPH H. MOGLIA
---------------------------------        --------------------------------
Signature                                By

Fred Tomczyk                             Chief Executive Officer
---------------------------------        --------------------------------
Print Name                               Title

Address:

---------------------------------

---------------------------------

                                      -2-

<PAGE>

                                    EXHIBIT A

                      TERMS AND CONDITIONS OF OPTION GRANT

      1. Grant. The Company hereby grants to the Participant named in the Notice
of Grant (the "Participant") an option (the "Option") to purchase the number of
Shares, as set forth in the Notice of Grant, at the exercise price per Share set
forth in the Notice of Grant (the "Exercise Price"), subject to all of the terms
and conditions in this Agreement and the Plan, which is incorporated herein by
reference. Subject to Section 15.3 of the Plan, in the event of a conflict
between the terms and conditions of the Plan and the terms and conditions of
this Agreement, the terms and conditions of the Plan will prevail.

      2. Vesting Schedule. Except as otherwise provided in the Notice of Grant
and Section 3, 4 and 5 of this Agreement, the Option awarded by this Agreement
will vest in accordance with the vesting provisions set forth in the Notice of
Grant. Shares scheduled to vest on a certain date or upon the occurrence of a
certain condition will not vest in Participant in accordance with any of the
provisions of this Agreement, unless Participant will have been continuously an
Employee and/or Director from the Date of Grant until the date such vesting
occurs.

      3. Death or Disability. In the event that the Participant ceases to be an
Employee and/or Director due to his death or Disability, then notwithstanding
anything in the LTIP or this Agreement to the contrary, (1) the Shares subject
to the Option will become fully vested, and the Option will become fully
exercisable, as of the date of termination, and (2) the Participant shall have
at least twelve months after termination of employment to exercise such vested
Option (subject to the ten year term of the Option).

      4. Retirement. In the event that the Participant ceases to be an Employee
and/or Director due to his Retirement (as defined below), then notwithstanding
anything in the LTIP or this Agreement to the contrary, (1) the Shares subject
to the Option will not be forfeited upon such termination and instead become
exercisable pursuant to the Vesting Schedule set forth in the Notice of Grant,
regardless of whether or not the Participant is then employed by the Company,
and (2) the Participant shall have at least twelve months after the date the
Option has become fully exercisable pursuant to this Section to exercise such
Option (subject to the ten year term of the Option). For the purposes of this
Option, "Retirement" shall mean a termination of employment for any reason,
other than "Cause" (as defined in Section 12(b) of the Employment Agreement),
after attaining age fifty-five (55) and after having at least ten (10) years of
continuous service with the Company.

      5. Termination without Cause or Resignation for Good Reason. In the event
that the Participant ceases to be an Employee and/or Director due to his
termination by the Company without Cause or if the Participant resigns for Good
Reason (both pursuant to the terms and conditions of Section 8(a) of the
Employment Agreement), then notwithstanding anything in the LTIP or this
Agreement to the contrary, (1) the Shares subject to the Option will not be
forfeited upon such termination and instead become exercisable pursuant to the
Vesting Schedule set forth in the Notice of Grant, regardless of whether or not
the Participant is then employed by the Company, and (2) the Participant shall
have at least twelve months after the date the Option has become fully
exercisable pursuant to this Section to exercise such Option (subject to the ten
year term of the Option).

                                      -3-

<PAGE>

      6. Board and Committee Discretion. The Board or the Committee, in its
discretion, may accelerate the vesting of the balance, or some lesser portion of
the balance, of the unvested Option at any time, subject to the terms of the
Plan. If so accelerated, such Option will be considered as having vested as of
the date specified by the Board or the Committee.

      7. Exercise of Option. This Option may be exercised only within the term
set out in the Notice of Grant, and may be exercised during such term only in
accordance with the Plan and the terms of this Agreement.

            This Option is exercisable by delivery of an exercise notice, in the
form attached as Exhibit B (the "Exercise Notice") or in a manner and pursuant
to such procedures as the Board or the Committee may determine, which will state
the election to exercise the Option, the number of Shares in respect of which
the Option is being exercised (the "Exercised Shares"), and such other
representations and agreements as may be required by the Company pursuant to the
provisions of the Plan. The Exercise Notice will be completed by Participant and
delivered to the Company. The Exercise Notice will be accompanied by payment of
the aggregate Exercise Price as to all Exercised Shares together with any
applicable tax withholding. This Option will be deemed to be exercised upon
receipt by the Company of such fully executed Exercise Notice accompanied by
such aggregate Exercise Price.

      8. Method of Payment. Payment of the aggregate Exercise Price will be by
any of the following, or a combination thereof, at the election of Participant:

            (a) cash;

            (b) check;

            (c) through a net exercise program implemented by the Company in
connection with the Plan;

            (d) consideration received by the Company under a cashless exercise
program implemented by the Company in connection with the Plan; or

            (e) surrender of other Shares which meet the conditions established
by the Committee to avoid any adverse financial accounting consequences.

      9. Tax Obligations.

            (a) Withholding of Taxes. Notwithstanding any contrary provision of
this Agreement, no certificate representing the Shares will be issued to
Participant, unless and until satisfactory arrangements (as determined by the
Board or the Committee) will have been made by Participant with respect to the
payment of income, employment and other taxes which the Company determines must
be withheld with respect to such Shares. To the extent determined appropriate by
the Board or the Committee in its discretion, it will have the right (but not
the obligation) to satisfy any tax withholding obligations through the surrender
of Shares which Participant already owns, or by reducing the number of Shares
otherwise deliverable to Participant. If Participant fails to make satisfactory
arrangements for the payment of any required tax withholding obligations
hereunder at

                                      -4-

<PAGE>

the time of the Option exercise, Participant acknowledges and agrees that the
Company may refuse to honor the exercise and refuse to deliver Shares if such
withholding amounts are not delivered at the time of exercise.

            (b) Code Section 409A. Under Code Section 409A, an option that vests
after December 31, 2004 that was granted with a per share exercise price that is
determined by the Internal Revenue Service (the "IRS") to be less than the fair
market value of a share of common stock on the date of grant (a "Discount
Option") may be considered "deferred compensation." A Discount Option may result
in (i) income recognition by Participant prior to the exercise of the option,
(ii) an additional twenty percent (20%) federal income tax, and (iii) potential
penalty and interest charges. The Discount Option may also result in additional
state income, penalty and interest charges to the Participant. Participant
acknowledges that the Company cannot and has not guaranteed that the IRS will
agree that the per Share exercise price of this Option equals or exceeds the
Fair Market Value of a Share on the Date of Grant in a later examination.
Participant agrees that if the IRS determines that the Option was granted with a
per Share exercise price that was less than the Fair Market Value of a Share on
the date of grant, Participant will be solely responsible for Participant's
costs related to such a determination.

      10. Rights as Stockholder. Neither Participant nor any person claiming
under or through Participant will have any of the rights or privileges of a
stockholder of the Company in respect of any Shares deliverable hereunder unless
and until certificates representing such Shares will have been issued, recorded
on the records of the Company or its transfer agents or registrars, and
delivered to Participant. After such issuance, recordation and delivery,
Participant will have all the rights of a stockholder of the Company with
respect to voting such Shares and receipt of dividends and distributions on such
Shares.

      11. No Guarantee of Continued Employment or Service as a Director.
PARTICIPANT ACKNOWLEDGES AND AGREES THAT THE VESTING OF SHARES PURSUANT TO THE
VESTING SCHEDULE HEREOF IS EARNED ONLY BY CONTINUING AS AN EMPLOYEE AND/OR
DIRECTOR AT THE WILL OF THE COMPANY (OR THE RELATED ENTITY EMPLOYING
PARTICIPANT) AND NOT THROUGH THE ACT OF BEING HIRED, BEING GRANTED THE OPTION OR
ACQUIRING SHARES HEREUNDER. PARTICIPANT FURTHER ACKNOWLEDGES AND AGREES THAT
THIS AGREEMENT, THE TRANSACTIONS CONTEMPLATED HEREUNDER AND THE VESTING SCHEDULE
SET FORTH HEREIN DO NOT CONSTITUTE AN EXPRESS OR IMPLIED PROMISE OF CONTINUED
EMPLOYMENT FOR THE VESTING PERIOD, FOR ANY PERIOD, OR AT ALL, AND WILL NOT
INTERFERE IN ANY WAY WITH PARTICIPANT'S RIGHT OR THE RIGHT OF THE COMPANY (OR
THE RELATED ENTITY EMPLOYING PARTICIPANT) TO TERMINATE PARTICIPANT'S EMPLOYMENT
AT ANY TIME, WITH OR WITHOUT CAUSE.

      12. Address for Notices. Any notice to be given to the Company under the
terms of this Agreement will be addressed to the Company in care of its Chief
Human Resources Officer, at 4211 South 102nd Street, Omaha, Nebraska 68127, or
at such other address as the Company may hereafter designate in writing.

                                      -5-

<PAGE>

      13. Grant is Not Transferable. This Option 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 lifetime of Participant only by Participant.

      14. Binding Agreement. Subject to the limitation on the transferability of
this grant contained herein, this Agreement will be binding upon and inure to
the benefit of the heirs, legatees, legal representatives, successors and
assigns of the parties hereto.

      15. Additional Conditions to Issuance of Stock. If at any time the Company
will determine, in its discretion, that the listing, registration or
qualification of the Shares upon any securities exchange or under any state or
federal law, or the consent or approval of any governmental regulatory authority
is necessary or desirable as a condition to the issuance of Shares to
Participant (or his or her estate), such issuance will not occur unless and
until such listing, registration, qualification, consent or approval will have
been effected or obtained free of any conditions not acceptable to the Company.
The Company will make all reasonable efforts to meet the requirements of any
such state or federal law or securities exchange and to obtain any such consent
or approval of any such governmental authority. Assuming such compliance, for
income tax purposes the Exercised Shares will be considered transferred to
Participant on the date the Option is exercised with respect to such Exercised
Shares.

      16. Plan Governs. This Agreement is subject to all terms and provisions of
the Plan. In the event of a conflict between one or more provisions of this
Agreement and one or more provisions of the Plan, the provisions of the Plan
will govern. Capitalized terms used and not defined in this Agreement will have
the meaning set forth in the Plan.

      17. Board or Committee Authority. The Board or the Committee will have the
power to interpret the Plan and this Agreement and to adopt such rules for the
administration, interpretation and application of the Plan as are consistent
therewith and to interpret or revoke any such rules (including, but not limited
to, the determination of whether or not any Shares subject to the Option have
vested). All actions taken and all interpretations and determinations made by
the Board or the Committee in good faith will be final and binding upon
Participant, the Company and all other interested persons. No member of the
Board or the Committee will be personally liable for any action, determination
or interpretation made in good faith with respect to the Plan or this Agreement.

      18. Electronic Delivery. The Company may, in its sole discretion, decide
to deliver any documents related to Options awarded under the Plan or future
Options that may be awarded under the Plan by electronic means or request
Participant's consent to participate in the Plan by electronic means.
Participant hereby consents to receive such documents by electronic delivery and
agrees to participate in the Plan through any on-line or electronic system
established and maintained by the Company or another third party designated by
the Company.

      19. Captions. Captions provided herein are for convenience only and are
not to serve as a basis for interpretation or construction of this Agreement.

      20. Agreement Severable. In the event that any provision in this Agreement
will be held invalid or unenforceable, such provision will be severable from,
and such invalidity or

                                      -6-

<PAGE>

unenforceability will not be construed to have any effect on, the remaining
provisions of this Agreement.

      21. Modifications to the Agreement. This Agreement constitutes the entire
understanding of the parties on the subjects covered. Participant expressly
warrants that he or she is not accepting this Agreement in reliance on any
promises, representations, or inducements other than those contained herein.
Modifications to this Agreement or the Plan can be made only in an express
written contract executed by a duly authorized officer of the Company.

      22. Amendment, Suspension or Termination of the Plan. By accepting this
Award, Participant expressly warrants that he or she has received an Option
under the Plan, and has received, read and understood a description of the Plan.
Participant understands that the Plan is discretionary in nature and may be
amended, suspended or terminated by the Company at any time.

      23. Governing Law. This Agreement will be governed by the laws of the
State of New York, without giving effect to the conflict of law principles
thereof. The Participant agree that any and all disputes arising out of the
terms of this Agreement, their interpretation and any of the matters herein
released, will be subject to binding arbitration in Jersey City, New Jersey
before the American Arbitration Association under its National Rules for the
Resolution of Employment Disputes, supplemented by the New Jersey Rules of Civil
Procedure. The Company and the Participant agree that the prevailing party in
any arbitration will be entitled to injunctive relief in any court of competent
jurisdiction to enforce the arbitration award. THE COMPANY AND THE PARTICIPANT
HEREBY AGREE TO WAIVE THEIR RIGHT TO HAVE ANY DISPUTE BETWEEN THEM RESOLVED IN A
COURT OF LAW BY A JUDGE OR JURY. This paragraph will not prevent either party
from seeking injunctive relief (or any other provisional remedy) from any court
having jurisdiction over the Company and the Participant and the subject matter
of their dispute relating to Participant's obligations under this Agreement.

                                      -7-

<PAGE>

                                    EXHIBIT B

                        TD AMERITRADE HOLDING CORPORATION

                          1996 LONG-TERM INCENTIVE PLAN

                                 EXERCISE NOTICE

TD AMERITRADE Holding Corporation
4211 South 102nd Street
Omaha, Nebraska 68127

Attention:  Chief Human Resources Officer

      1. Exercise of Option. Effective as of today, ________________, _____, the
undersigned ("Purchaser") hereby elects to purchase ______________ shares (the
"Shares") of the Stock of TD AMERITRADE Holding Corporation (the "Company")
under and pursuant to the 1996 Long-Term Incentive Plan (the "Plan") and the
Stock Option Agreement dated ________ (the "Agreement"). The purchase price for
the Shares will be $_____________, as required by the Agreement.

      2. Delivery of Payment. Purchaser herewith delivers to the Company the
full purchase price of the Shares and any required tax withholding to be paid in
connection with the exercise of the Option.

      3. Representations of Purchaser. Purchaser acknowledges that Purchaser has
received, read and understood the Plan and the Agreement and agrees to abide by
and be bound by their terms and conditions.

      4. Rights as Stockholder. Until the issuance (as evidenced by the
appropriate entry on the books of the Company or of a duly authorized transfer
agent of the Company) of the Shares, no right to vote or receive dividends or
any other rights as a stockholder will exist with respect to the Shares subject
to the Option, notwithstanding the exercise of the Option. The Shares so
acquired will be issued to Participant as soon as practicable after exercise of
the Option. No adjustment will be made for a dividend or other right for which
the record date is prior to the date of issuance, except as provided in Section
5.3 of the Plan.

      5. Tax Consultation. Purchaser understands that Purchaser may suffer
adverse tax consequences as a result of Purchaser's purchase or disposition of
the Shares. Purchaser represents that Purchaser has consulted with any tax
consultants Purchaser deems advisable in connection with the purchase or
disposition of the Shares and that Purchaser is not relying on the Company for
any tax advice.

      6. Entire Agreement; Governing Law. The Plan and Agreement are
incorporated herein by reference. This Exercise Notice, the Plan and the
Agreement constitute the entire agreement of

                                      -8-

<PAGE>

the parties with respect to the subject matter hereof and supersede in their
entirety all prior undertakings and agreements of the Company and Purchaser with
respect to the subject matter hereof, and may not be modified adversely to the
Purchaser's interest except by means of a writing signed by the Company and
Purchaser. This agreement is governed by the internal substantive laws, but not
the choice of law rules, of the State of New York.

Submitted by:                              Accepted by:

PURCHASER                                  TD AMERITRADE HOLDING CORPORATION

-----------------------------              -----------------------------------
Signature                                  By

-----------------------------              -----------------------------------
Print Name                                 Its

Address:

-----------------------------

-----------------------------

                                           Date Received
                                           -----------------------------------

                                      -9-