WARRANT AGREEMENT BETWEEN

Exhibit 10.3

WARRANT AGREEMENT BETWEEN

PEGASYSTEMS INC.

AND

INTERNATIONAL BUSINESS MACHINES CORPORATION

TABLE OF CONTENTS

SECTION

STOCK PURCHASE WARRANT

Neither this Warrant nor the Warrant Shares as defined herein have been registered under the Securities Act of 1933, as amended, or any applicable state securities laws. Neither this Warrant nor the Warrant Shares may be sold or transferred in the absence of such registration or any exemption from such registration.

Right to Purchase 26,738 Shares of Common Stock

Dated as of July 12, 2004

Pegasystems Inc., a Massachusetts corporation (the “Company”), grants International Business Machines Corporation, a New York corporation (“IBM” and each of its successors and assigns, a “Holder”), a warrant (this “Warrant”) to purchase the Warrant Shares at the Purchase Price. Capitalized terms not otherwise defined have the definitions set forth in Appendix A.

1. Exercise and Expiration of Warrant.

(a) This Warrant is immediately exercisable and will expire upon the four year anniversary of the date hereof. “Exercise Period” shall mean the period of time between the date hereof and the expiration of this Warrant in accordance with the terms hereof.

(b) This Warrant may be exercised during the Exercise Period by the Holder, in whole or in part, by delivering this Warrant to the Company with payment of the Purchase Price in U.S. dollars. In lieu of such cash payment, the Holder may also exercise the Warrant by delivery to the Company of a written notice of an election to effect a cashless exercise for Warrant Shares pursuant to this Section 1(b) (“Cashless Exercise”). To effect a Cashless Exercise, the Holder will surrender this Warrant for that number of shares of Common Stock determined by multiplying the number of Warrant Shares to which it would otherwise be entitled by a fraction, the numerator of which shall be the difference between (i) the then current Market Price of a share of the Common Stock on the date of exercise and (ii) the Purchase Price, and the denominator of which shall be the then current Market Price per share of Common Stock. In the event that this Warrant is not exercised in full immediately prior to the end of the Exercise Period and at such time the then current Market Price of a share of the Common Stock is greater than the Purchase Price, this Warrant shall be deemed automatically exercised as to the remaining Warrant Shares at such time by Cashless Exercise without the delivery of any written notice from the Holder.

(c) Upon exercise of this Warrant, the Company will issue to the Holder (i) a certificate or certificates for the number of full Warrant Shares to which the Holder shall be entitled upon such exercise plus the value of any fractional share to which the Holder would otherwise be entitled, and (ii) in case such exercise is in part only, a new warrant or warrants representing the remaining Warrant Shares.

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(d) Each exercise of this Warrant shall be deemed to have been effected immediately prior to the close of business on the day on which this Warrant shall have been surrendered pursuant to Section 1(b).

2. Representations.

(a) By the Holder. The Holder represents and warrants to the Company as follows:

(i) It is an “accredited investor” within the meaning of Rule 501 of the Securities Act. This Warrant is acquired for the Holder’s own account for investment purposes and not with a view to any offering or distribution within the meaning of the Securities Act and any applicable state securities laws. The Holder has no present intention of selling or otherwise disposing of the Warrant or the Warrant Shares in violation of such laws; and

(ii) The Holder has sufficient knowledge and expertise in financial and business matters so as to be capable of evaluating the merits and risks of its investment in the Company. The Holder understands that this investment involves a high degree of risk and could result in a substantial or complete loss of its investment. The Holder is capable of bearing the economic risks of such investment.

The Holder acknowledges that the Company has indicated that the Warrant and the Warrant Shares have not been registered under the Securities Act by reason of their issuance in a transaction exempt from the registration requirements thereof, and that the Warrant Shares will bear a legend stating that such securities have not been registered under the Securities Act and may not be sold or transferred in the absence of such registration or an exemption from such registration.

(b) By the Company. The Company represents and warrants that:

(i) It (A) is a corporation duly organized, validly existing and in good standing under the laws of the state of its organization, and (B) has all requisite power and authority to conduct its business as now conducted and as presently contemplated and to consummate the transactions contemplated hereby.

(ii) The execution, delivery and performance by the Company of this Warrant (A) has been duly authorized by all necessary corporate action, (B) does not and will not contravene the Company’s charter or bylaws or any other organizational document and (C) does not and will not contravene any applicable law or any contractual restriction binding on or otherwise affecting the Company or any of its properties or result in a default under any agreement or instrument to which the Company is a party or by which the Company or its properties may be subject.

(iii) This Warrant has been duly executed and delivered by the Company, and is a legal, valid and binding obligation of the Company, enforceable against the Company in

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accordance with its terms, except as may be limited by applicable bankruptcy, insolvency, moratorium and other laws affecting the rights of creditors generally and general principles of equity.

(iv) Assuming the accuracy of the representations made by the Holder in Section 2(a) hereof, no authorization, consent, approval, license, exemption or other action by, and no registration, qualification, designation, declaration or filing with, any governmental authority is or will be necessary in connection with the execution and delivery by the Company of this Warrant, the issuance by the Company of the Warrant Shares, the consummation of the transactions contemplated hereby, the performance of or compliance with the terms and conditions hereof, or to ensure the legality, validity, and enforceability hereof.

(v) The Company has reserved solely for issuance and delivery upon the exercise of this Warrant, such number of shares of Common Stock to provide for the exercise in full of this Warrant.

(vi) Neither the Company, nor any of its Affiliates, nor any person acting on its or their behalf, has directly or indirectly made any offers or sales of any security or solicited any offers to buy any security under circumstances that would require registration, or the filing of a prospectus qualifying the distribution, of this Warrant being issued hereby under the Securities Act or cause the issuance of this Warrant to be integrated with any prior offering of securities of the Company for purposes of the Securities Act.

3. Certain Agreements of the Company. The Company agrees as follows:

(a) Shares to be Fully Paid. All Warrant Shares will, upon issuance in accordance with the terms of this Warrant, be validly issued, fully paid, and nonassessable and free from all taxes, liens, claims and encumbrances.

(b) Authorization and Reservation of Shares. During the Exercise Period, the Company shall have duly authorized a sufficient number of shares of Common Stock, free from preemptive rights and from any other restrictions imposed by the Company without the consent of the Holder, to provide for the exercise in full of this Warrant. The Company shall at all times during the Exercise Period reserve and keep available out of such authorized but unissued shares of Common Stock such number of shares to provide for the exercise in full of this Warrant.

(c) Listing. In connection with the Holder’s exercise hereof, the Company shall use commercially reasonable efforts to promptly secure the listing of the shares of Common Stock issuable upon exercise of this Warrant upon each national securities exchange or automated quotation system, if any, upon which shares of Common Stock are then listed or become listed (subject to official notice of issuance upon exercise of this Warrant) and shall maintain such listing for so long as any other shares of Common Stock shall be so listed.

(d) Certain Actions Prohibited. The Company will not, by amendment of its charter or through any reorganization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities, or any other voluntary action, avoid or seek to avoid the observance or performance

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of any of the terms to be observed or performed by it hereunder, but will at all times in good faith assist in the carrying out of all the provisions of this Warrant and in the taking of all such action as may reasonably be requested by the Holder of this Warrant in order to protect the exercise privilege of the Holder of this Warrant against dilution or other impairment, consistent with the tenor and purpose of this Warrant.

(e) Successors and Assigns. Except as expressly provided otherwise herein, this Warrant will be binding upon any entity succeeding to the Company by merger, consolidation, or acquisition of all or substantially all of the Company’s assets.

(f) Blue Sky Laws. The Company shall, on or before the date of issuance of any Warrant Shares, take such actions as the Company shall reasonably determine are necessary to qualify the Warrant Shares for, or obtain exemption for the Warrant Shares for, sale to the Holder of this Warrant upon the exercise hereof under applicable securities or “blue sky” laws of the states of the United States, and shall provide written evidence of any such action so taken to the Holder of this Warrant prior to such date; provided, however, that the Company shall not be required to qualify as a foreign corporation or file a general consent to service of process in any such jurisdiction.

(g) Rule 144 Reports. If the Company becomes subject to the reporting requirements of Section 13 or 15(d) of the Exchange Act, but only for so long as the Company is so subject, the Company shall take all actions reasonably necessary to enable the Holder to sell the Warrant Shares without registration under the Securities Act within the limitations of the exemptions provided by Rule 144 under the Securities Act, as such rule may be amended from time to time, or any similar rule or regulation hereafter adopted by the SEC, including filing on a timely basis all reports required to be filed by the Exchange Act. Upon the request of the Holder, the Company shall deliver to the Holder a written statement as to whether it has complied with such requirements.

4. Antidilution Adjustments. The Purchase Price and the number of Warrant Shares may be adjusted from time to time as set forth in Appendix B.

5. Mergers; Transfer of Assets. If there shall occur any capital reorganization or reclassification of the Company’s Common Stock (other than a subdivision or combination as provided for in paragraph (a) of Appendix B), or any consolidation or merger of the Company with or into another corporation, or a transfer of all or substantially all of the assets of the Company, then, as part of any such reorganization, reclassification, consolidation, merger or sale, as the case may be, lawful provision shall be made so that the Holder of this Warrant shall have the right thereafter to receive upon the exercise hereof the kind and amount of shares of stock or other securities or property which such Holder would have been entitled to receive if, immediately prior to any such reorganization, reclassification, consolidation, merger or sale, as the case may be, such Holder had held the number of shares of Common Stock which were then purchasable upon the exercise of this Warrant. In any such case, appropriate adjustment (as reasonably determined in good faith by the Board) shall be made in the application of the provisions set forth herein with respect to the rights and interests thereafter of the Holder of this Warrant, such that the provisions set forth herein shall thereafter be applicable, as nearly as is reasonably practicable, in relation to any shares of stock or other securities or property thereafter deliverable upon the exercise of this Warrant.

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6. Transfer, Exchange, and Replacement

(a) Transferability. (i) The Holder covenants not to transfer this Warrant or the Warrant Shares except in compliance with this Section 6(a). Subject to compliance with the transfer restrictions set forth in clause (ii) of this Section 6(a), this Warrant, the Warrant Shares and the rights granted to the Holder hereof are freely transferable, in whole or in part, upon surrender of this Warrant, together with an assignment form, at the office or agency of the Company referred to in Section 7 below.

(ii) The Holder shall not effect any transfer except pursuant to a transaction either registered, or exempt from registration, under the Securities Act. Prior to any transfer in reliance upon an exemption from such registration other than Rule 144 of the Securities Act, the Holder shall provide to the Company an opinion letter from counsel to the Holder (which counsel may include in-house counsel), reasonably satisfactory to the Company, opining that such transfer does not require registration under the Securities Act. The transferee, by acceptance of this Warrant, acknowledges that it takes such warrant subject to the terms and conditions hereof. Until due presentment for registration of transfer on the books of the Company, the Company may treat the registered Holder hereof as the owner hereof for all purposes, and the Company shall not be affected by any notice to the contrary.

(b) Warrant Exchangeable for Different Denominations. This Warrant is exchangeable, upon the surrender hereof by the Holder hereof at the office or agency of the Company referred to in Section 7 below, for new warrants of like tenor of different denominations representing in the aggregate the right to purchase the number of shares of Common Stock which may be purchased hereunder, each of such new warrants to represent the right to purchase such number of shares as shall be designated by the Holder hereof at the time of such surrender.

(c) Replacement of Warrant. Upon receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction, or mutilation of this Warrant and, in the case of any such loss, theft, or destruction, upon delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company, or, in the case of any such mutilation, upon surrender and cancellation of this Warrant, the Company, at its expense, will execute and deliver, in lieu thereof, a new Warrant of like tenor.

(d) Cancellation; Payment of Expenses. Upon the surrender of this Warrant in connection with any transfer, exchange, or replacement as provided in this Section 6, this Warrant shall be promptly canceled by the Company. The Company shall pay all taxes (other than securities transfer taxes) and all other expenses (other than legal expenses, if any, incurred by the Holder or transferees) and charges payable in connection with the preparation, execution, and delivery of warrants pursuant to this Section 6. The Company shall indemnify and reimburse the Holder of this Warrant for all costs and expenses (including legal fees) incurred by such Holder in connection with the enforcement of its rights hereunder.

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(e) Warrant Register. The Company shall maintain, at its principal executive offices (or such other office or agency of the Company as it may designate by notice to the Holder hereof), a register for this Warrant, in which the Company shall record the name and address of the person in whose name this Warrant has been issued, as well as the name and address of each transferee and each prior owner of this Warrant.

7. Notices. Any notices required or permitted to be given under the terms of this Warrant shall be sent by certified or registered mail (return receipt requested) or delivered personally or by courier or by confirmed telecopy, and shall be effective five days after being placed in the mail, if mailed, or upon receipt or refusal of receipt, if delivered personally or by courier, or by confirmed telecopy, in each case addressed to a party. The addresses for such communications shall be:

If to any other Holder, at such address as such Holder shall have provided in writing to the Company, or at such other address as any Holder furnishes by notice given in accordance with this Section 7.

8. Governing Law; Jurisdiction and Venue. This Warrant shall be governed by the laws of The Commonwealth of Massachusetts, without regard to conflicts or choice of law rules or principles. Each of the Company and the Holder submits to the exclusive jurisdiction and venue of the federal and state courts of New York, County of Westchester, to resolve all issues that may arise out of or relate to this Warrant. The parties waive any right to a jury trial.

9. Miscellaneous.

(a) Amendments. This Warrant and any provision hereof may only be amended by an instrument in writing signed by the Company and all Holders hereof.

(b) U.S. Dollars. All references in this Warrant to “dollars” or “$” shall mean the U.S. dollar.

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(c) Fractional Shares. The Company shall not be required upon the exercise of this Warrant to issue any fractional shares, but shall make an adjustment therefor in cash on the basis of the fair market value per share of Common Stock, as determined in good faith by the Board.

(d) Descriptive Headings. The descriptive headings of the several sections of this Warrant are inserted for purposes of reference only, and shall not affect the meaning or construction of any of the provisions hereof.

(e) Business Day. For purposes of this Warrant, the term “business day” means any day, other than a Saturday or Sunday or a day on which banking institutions in New York, New York or the city and state provided in Section 7 hereof for notices to the Company, are authorized or obligated by law, regulation or executive order to close.

(f) Counterparts. This agreement may be executed in counterparts, and any such executed counterpart shall be, and shall be deemed to be, an original instrument.

(g) Severability. If any term, provision, covenant or restriction of this Agreement is held by a court of competent jurisdiction to be invalid, void or unenforceable, it shall be deemed replaced with a valid and enforceable provision, which comes as close as possible to the economic purpose of the invalid, void or unenforceable provision, and the remainder of the terms, provisions, covenants and restrictions of this Agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

(h) Successors and Assigns. This Agreement shall be binding on, and shall inure to the benefit of, the parties hereto and their respective successors and assigns, including all Holders.

(i) Survival. The representations, warranties and covenants made by the parties hereto shall survive the execution and delivery of this Agreement.

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IN WITNESS WHEREOF, the undersigned have executed this Warrant as of the date first written above.

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APPENDIX A — DEFINITIONS

“Affiliate” shall mean any entity directly or indirectly controlled by, controlling or under common control with another entity.

“Board” shall mean the Board of Directors of the Company.

“Cashless Exercise” shall have the meaning specified in Section 1(b) of the Warrant.

“Company” shall have the meaning specified in the initial paragraph of the Warrant.

“Common Stock” shall mean the common shares of the Company.

“Exchange Act” shall mean the Securities Exchange Act of 1934, as amended.

“Exercise Period” shall have the meaning specified in Section 1(a) of the Warrant.

“Holder” shall have the meaning specified in the initial paragraph of the Warrant.

“IBM” shall have the meaning specified in the initial paragraph of the Warrant.

“Market Price” shall mean the following: (i) the average of the closing sale prices for the shares of Common Stock as reported on the principal trading exchange or the Nasdaq National Market for the Common Stock for the five (5) consecutive trading days immediately preceding such date, or if no sale price is so reported for such period, the last bid price for such period, or (ii) if the foregoing does not apply, the last sale price of such security in the over-the-counter market on the pink sheets or bulletin board for such security on the last trading day immediately preceding such date, or if no sale price is so reported for such security, the average of the last bid and ask price for such security on the last trading day immediately preceding such date, or (iii) if market value cannot be calculated as of such date on any of the foregoing bases, the Market Price shall be the fair market value as reasonably determined by an investment banking firm selected by the Company and reasonably acceptable to the Holder, with the costs of the appraisal to be borne by the Company.

“Person” or “person” shall mean all natural persons, corporations, business trusts, associations, companies, partnerships, joint ventures, governments, agencies, political subdivisions and other entities.

“Purchase Price” shall mean $9.75 per share of Common Stock, as may be adjusted from time to time pursuant to Appendix B.

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“Securities Act” shall mean the Securities Act of 1933, as amended.

“Warrant” shall have the meaning specified in the initial paragraph of the Warrant.

“Warrant Shares” shall mean 26,738 shares of Common Stock, as may be adjusted from time to time pursuant to Appendix B.

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APPENDIX B — ANTIDILUTION PROVISIONS

(a) Recapitalizations. If outstanding shares of the Company’s Common Stock shall be subdivided into a greater number of shares or a dividend in Common Stock shall be paid in respect of Common Stock, the Purchase Price in effect immediately prior to such subdivision or at the record date of such dividend shall simultaneously with the effectiveness of such subdivision or immediately after the record date of such dividend be proportionately reduced. If outstanding shares of Common Stock shall be combined into a smaller number of shares, the Purchase Price in effect immediately prior to such combination shall, simultaneously with the effectiveness of such combination, be proportionately increased.

(b) Adjustment in Number of Warrant Shares. When any adjustment is required to be made in the Purchase Price, the number of Warrant Shares purchasable upon the exercise of this Warrant shall be changed to the number determined by dividing (i) an amount equal to the number of shares issuable upon the exercise of this Warrant immediately prior to such adjustment, multiplied by the Purchase Price in effect immediately prior to such adjustment, by (ii) the Purchase Price in effect immediately after such adjustment.

(c) Certificate of Adjustment. When any adjustment is required to be made pursuant to this Appendix B, the Company shall promptly mail to the Holder a certificate setting forth the Purchase Price after such adjustment and setting forth a brief statement of the facts requiring such adjustment. Such certificate shall also set forth the kind and amount of stock or other securities or property into which this Warrant shall be exercisable following such adjustment.

(d) Other Notices. In case at any time:

(i) the Company shall declare any dividend upon the Common Stock payable in shares of stock of any class or make any other distribution (other than dividends or distributions payable in cash out of retained earnings consistent with the Company’s past practices with respect to declaring dividends and making distributions) to the holders of the Common Stock;

(ii) the Company shall offer for subscription pro rata to the holders of the Common Stock any additional shares of stock of any class or other rights;

(iii) there shall be any capital reorganization of the Company, or reclassification of the Common Stock, or consolidation or merger of the Company with or into, or sale of all or substantially all of its assets to, another corporation or entity; or

(iv) there shall be a voluntary or involuntary dissolution, liquidation or winding-up of the Company;

then, in each such case, the Company shall give to the Holder (a) notice of the date on which the books of the Company shall close or a record shall be taken for determining the holders of Common Stock entitled to receive any such dividend, distribution, or subscription rights or for determining the holders of Common Stock entitled to vote in respect of any such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation or winding-up and (b) in the case of any such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation or winding-up, notice of the date (or, if not then known, a reasonable estimate thereof by the Company) when the same shall take place. Such notice shall also specify the date on which the holders of Common Stock shall be entitled to receive such dividend, distribution, or subscription rights or to exchange their Common Stock for stock or other securities or property deliverable upon such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation, or winding-up, as the case may be. Such notice shall be given at least thirty (30) days prior to the record date or the date on which the Company’s books are closed in respect thereto. Failure to give any such notice or any defect therein shall not affect the validity of the proceedings referred to in clauses (i), (ii), (iii) and (iv) above.

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