SHARE EXCHANGE AGREEMENT by and between THE BEAR STEARNS COMPANIES INC.

Exhibit 2.2

     SHARE EXCHANGE AGREEMENT

by and between

THE BEAR STEARNS COMPANIES INC.

     SHARE EXCHANGE AGREEMENT dated as of March 24, 2008 (this “Agreement”) between The Bear Stearns Companies Inc., a Delaware corporation (“Company”) and JPMorgan Chase & Co., a Delaware corporation (“Parent”).

     Concurrently, and in connection herewith, Parent and the Company are entering into a Amendment No. 1 to the Agreement and Plan of Merger, dated March 16, 2008, (the “Amendment”) by and between the Company and Parent (such agreement as amended by such Amendment the “Merger Agreement”). Capitalized terms used but not defined herein shall have the meaning given to such terms in the Merger Agreement.

     The Company desires to issue and sell 95 million shares (the “Shares”) of common stock, par value $1.00 per share, of the Company (the “Common Stock”), in exchange for (i) 20,665,350 shares of common stock, par value $1.00 per share, of Parent ( the “Exchange Shares”), on the terms and subject to the conditions s et forth herein (the “Exchange”), and (ii) the entry by Parent into each of the Amendment, the Amended and Restated Guaranty and the Fed Guaranty, on the terms set forth in Schedules 6.12(a) and 6.12(b) to the Merger Agreement.

     The Audit Committee of the Board of Directors of the Company has unanimously determined, that the delay in securing stockholder approval of the exchange contemplated hereby would seriously jeopardize the financial viability of the Company and has expressly approved the reliance by the Company on the exception under Para. 312.05 of the New York Stock Exchange (the “NYSE”) Listed Company Manual.

     In consideration of the mutual covenants and agreements contained in this Agreement, the receipt and sufficiency of which are herby acknowledged, and intending to be legally bound, the parties herby agree as follows:

THE SHARES AND THE EXCHANGE SHARES

     Section 1.1 The Common Stock. The Shares shall be issued to Parent, and the Exchange Shares shall be issued to the Company, pursuant to Article II hereof.

     Section 2.1 Share Exchange. Upon the terms and subject to the conditions of this Agreement, the Company agrees to issue and sell to Parent, 95 million Shares, and in exchange therefor (i) at the Share Exchange Closing, Parent shall issue to the Company 20,665,350 shares of Parent Common Stock, and (ii) as of the date hereof, Parent is entering into each of the Amended and Restated Guaranty and the Fed Guaranty.

     (a) The Company will deliver a certificate representing the Shares and registered in the name of Parent, and Parent will deliver a certificate representing the Exchange Shares and registered in the name of the Company. Subject to the satisfaction of the conditions set forth in Article VI, the time and date of such deliveries shall be 10:00 a.m., New York City time, on a date and at a place to be specified by the parties (the “Share Exchange Closing”), which date shall be no later than the day after satisfaction or waiver of the latest to occur of the conditions set forth in Article VI.

     (b) The documents to be delivered at the Share Exchange Closing by or on behalf of the parties hereto pursuant to this Article II and any additional documents requested by Parent pursuant to Article VI, will be delivered at the Share Exchange Closing at the offices of Parent at 270 Park Avenue New York, NY 10017.

REPRESENTATIONS AND WARRANTIES OF THE COMPANY

The Company represents and warrants to Parent as of the date hereof that:

     Section 3.1 Existence and Power. The Company is a corporation duly incorporated, validly existing and in good standing under the laws of the State of Delaware. The Company has the requisite corporate power and authority to own or lease all of its properties and assets and to carry on its business as it is now being conducted, and is duly licensed or qualified to do business in each jurisdiction in which the nature of the business conducted by it or the character or location of the properties and assets owned or leased by it makes such licensing or qualification necessary.

     Section 3.2 Capitalization. The authorized capital stock of Company consists of 500,000,000 shares of Common Stock, par value $1.00 per share, of which, as of February 20, 2008 (the “Capitalization Date”), 145,633,335 shares were issued and outstanding, and 10,000,000 shares of preferred stock, par value $1.00 per share (the “Preferred Stock”), of which, as of the Capitalization Date, (i) 818,113 shares were designated, issued and outstanding as Cumulative Pr eferred Stock, Series E, and (ii) 428,825 shares were designated, issued and outstanding as Cumulative Preferred Stock Series F, and (iii) 511,169 shares were designated, issued and outstanding as Cumulative Preferred Stock, Series G. As of the Company Capitalization Date, 27,316,339 of such issued and outstanding shares of Common Stock were held in The Bear Stearns Companies Inc. 2008 Trust (the “Trust”). The Trust was established to hold shares of Common Stock underlying awards granted under the Capital Accumulation Plan for Senior Managing Directors Amended and Restated November 29, 2000, as subsequently amended, and the Capital Accumulation Plan for Senior Managing Directors Amended and Restated as of October 28, 1999, as subsequently amended (the “Company Cap Plans” and each share unit with respect to such shares underlying such awards, the “Company Cap Units”) and The Bear Stearns Companies Inc. Restricted Stock Unit Plan. As of the Capitalization Date, no shares of Common Stock or Preferred Stock were either reserved for issuance or issued and

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outstanding and held in the Trust except for (i) 19,102,427 shares of Common Stock that are reserved for issuance in connection with options to purchase shares of Common Stock granted under the Stock Award Plan, as amended and restated as of March 31, 2004, as subsequently amended, the Non-Employee Directors’ Stock Option and Stock Unit Plan, amended and restated as of January 8, 2002, as subsequently amended, the Restricted Stock Unit Plan, as amended and restated as of March 31, 2004, as subsequently amended or the Company Cap Plan (collectively, the “Company Stock Plans”) that were outstanding as of the Capitalization Date, (ii) 7,603,576 shares of Common Stock that are either reserved for issuance upon, or issued and outstanding and held in the Trust pending, settlement of restrict ed share units with respect to shares of Common Stock granted under a Company Stock Plan (the “Company RSUs”) that were outstanding as of the Capitalization Date, (iii) 20,141,864 shares of Common Stock that are either reserved for issuance upon, or issued and outstanding and held in the Trust pending, settlement of Company Cap Units that were outstanding as of the Capitalization Date and (iv) 255,408 shares of Common Stock that are reserved for issuance upon settlement of all amounts denominated in Common Stock and held in participant accounts (other than Company RSUs and Company Cap Units) that were outstanding as of the Capitalization Date. All of the issued and outstanding shares of Common Stock have been duly authorized and validly issued and are fully paid, nonassessable and free of preemptive rights, with no personal liability attaching to the ownership t hereof. As of the date hereof, the Shares are all of the authorized shares of Company common stock other than those shares that are either issued and outstanding or reserved for issuance.

     Section 3.3 Authorization. The execution, delivery and performance of this Agreement has been duly authorized by all necessary action on the part of the Company, and this Agreement is a valid and binding obligation of the Company, enforceable against it in accordance with their terms.

     Section 3.4. Board Approvals. The transactions contemplated by this Agreement, including without limitation the issuance of the Shares and the compliance with the terms of this Agreement, have been unanimously adopted, approved and declared advisable unanimously by the Board of Directors of the Company. The Audit Committee of the Board of Directors of the Company has unanimously and expressly approved, and the Board of Directors of the Company has unanimously concurred with, the Company’s reliance on the exception under Para. 312.05 of the NYSE Listed Company Manual to issue the Shares without seeking a stockholder vote.

     Section 3.5 Valid Issuance of Common Stock. The Shares have been duly authorized by all necessary corporate action. When issued and sold against receipt of the consideration therefor, the Shares will be validly issued, fully paid and nonassessable, will not subject the holders thereof to personal liability and will not be issued in violation of preemptive rights.

     Section 3.6 Non-Contravention. The execution, delivery and performance of this Agreement, and the consummation by the Company of the transactions contemplated hereby, will not conflict with, violate or result in a breach of any provision of, or constitute a default (or an event which, with notice or lapse of time or both would constitute a default) under, or result in the termination of or accelerate the performance required by, or result in a right of termination or acceleration under, any provision of the Restated Certificate of Incorporation or By-laws of the

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Company or the certificate of incorporation, charter, by-laws or other governing instrument of any Subsidiary of the Company.

     Section 3.7 Purchase for Own Account. The Company is acquiring the Exchange Shares for its own account and not with a view to the distribution thereof in violation of the Securities Act of 1933, as amended, and the rules and regulations of the Securities and Exchange Commission (the “SEC”) promulgated thereunder (the “Securities Act”).

     Section 3.8 Private Placement. The Company understands that (i) the Exchange Shares have not been registered under the Securities Act or any state securities laws, by reason of their issuance by Parent in a transaction exempt from the registration requirements thereof and (ii) the Exchange Shares may not be sold unless such disposition is registered under the Securities Act and applicable state securities laws or is exempt from registration thereunder. The Company represents that it is an institutional “accredited investor” (as defined in Rule 501(a) of Regulation D under the Securities Act).

     Section 3.9 Legend. Each certificate representing an Exchange Share will bear a legend to the following effect unless Parent determines otherwise in compliance with applicable law:

     “THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION. THE SHARES HAVE BEEN ACQUIRED FOR INVESTMENT AND NEITHER THIS SHARE NOR ANY INTEREST OR PARTICIPATION HEREIN MAY BE REOFFERED, SOLD, ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED OR OTHERWISE DISPOSED OF IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS SUCH TRANSACTION IS EXEMPT FROM, OR NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT.”

REPRESENTATIONS AND WARRANTIES OF PARENT

Parent represents and warrants to the Company as of the date hereof that:

     Section 4.1 Existence and Power. Parent is duly organized and validly existing under the laws of the state of its organization and has all requisite power and authority to enter into and perform its obligations under this Agreement.

     Section 4.2 Authorization. The execution, delivery and performance of this Agreement has been duly authorized by all necessary action on the part of Parent, and this Agreement is a valid and binding obligation of Parent, enforceable against it in accordance with its terms.

     Section 4.3 Valid Issuance. The Exchange Shares have been duly authorized by all necessary corporate action. When issued and sold against receipt of the consideration

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therefor, the Exchange Shares will be validly issued, fully paid and nonassessable, will not subject the holders thereof to personal liability and will not be issued in violation of preemptive rights.

     Section 4.4 Non-Contravention. The execution, delivery and performance of this Agreement will not conflict with, violate or result in a breach of any provision of, or constitute a default (or an event which, with notice or lapse of time or both would constitute a default) under, or result in the termination of or accelerate the performance required by, or result in a right of termination or acceleration under, any provision of the organizational or governing documents of Parent.

     Section 4.5. Purchase for Own Account. Parent is acquiring the Shares for its own account and not with a view to the distribution thereof in violation of the Securities Act.

     Section 4.6 Private Placement. Parent understands that (i) the Shares have not been registered under the Securities Act or any state securities laws, by reason of their issuance by the Company in a transaction exempt from the registration requirements thereof and (ii) the Shares may not be sold unless such disposition is registered under the Securities Act and applicable state securities laws or is exempt from registration thereunder. Parent represents that it is an institutional “accredited investor” (as defined in Rule 501(a) of Regulation D under the Securities Act).

     Section 4.7 Legend. Each certificate representing a Share will bear a legend to the following effect unless the Company determines otherwise in compliance with applicable law:

     “THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION. THE SHARES HAVE BEEN ACQUIRED FOR INVESTMENT AND NEITHER THIS SHARE NOR ANY INTEREST OR PARTICIPATION HEREIN MAY BE REOFFERED, SOLD, ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED OR OTHERWISE DISPOSED OF IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS SUCH TRANSACTION IS EXEMPT FROM, OR NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT.”

     Section 5.1 NYSE Notice to Stockholders. As soon as practicable after the date hereof, and in any event not later than one week after the date hereof, the Company shall mail the notice to the stockholders of the Company that the Company will issue Shares without obtaining stockholder approval as required by, and in compliance with, Para. 312.05 of the NYSE Listed Company Manual. On or about the date hereof, pursuant to Para. 312.05 of the NYSE Listed Company Manual, the Company will deliver to the New York Stock Exchange

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notice of and the requisite documents relating to its intent to issue Shares without obtaining approval of the stockholders of the Company.

CONDITIONS TO SHARE EXCHANGE CLOSING

     Section 6.1 Conditions to Each Party’s Obligation To Effect the Exchange. The respective obligations of the parties hereunder to effect the Exchange shall be subject to the following condition:

     (a) No Injunctions or Restraints; Illegality. No order, injunction or decree issued by any court or agency of competent jurisdiction or other law preventing or making illegal the consummation of the Exchange shall be in effect.

     Section 6.2 Conditions to the Obligations of Parent. The obligations of Parent hereunder to effect the Exchange shall be subject to the satisfaction, or waiver by Parent, of the following conditions:

     (a) NYSE Notice Period. The Company shall have provided notice to the stockholders of the Company that the Company will issue Shares without obtaining stockholder approval as required by, and in compliance with, Para. 312.05 of the NYSE Listed Company Manual, and the ten (10) day notice period set forth in Para. 312.05 of the NYSE Listed Company Manual shall have passed after such notice has been provided.

     (b) No Injunctions or Restraints; Illegality. No order, injunction or decree issued by any court or agency of competent jurisdiction or other law preventing or making illegal Parent’s unrestricted and unlimited right to vote the Shares shall be in effect.

     (c) Regulatory Approvals. All regulatory approvals set forth in Section 4.4 of the Merger Agreement the failure of which to obtain would reasonably be expected to materially impede or impair Parent’s ability to acquire or vote the Shares, in each case required to consummate the transactions contemplated by this Agreement, including the Exchange, shall have been obtained and shall remain in full force and effect and all statutory waiting periods in respect thereof shall have expired.

     Section 7.1 Injunction; Illegality. This Agreement may be terminated at any time prior to the Share Exchange Closing by Parent (a) if an order, injunction or decree shall have been issued by any court or agency of competent jurisdiction and shall be nonappealable, or other law shall have been issued preventing or making illegal either (i) the completion of the Exchange or the other transactions contemplated by this Agreement, or (ii) Parent’s unrestricted and unlimited right to vote the Shares or (b) the Merger Agreement terminates pursuant to its

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terms. Termination of this Agreement in and of itself shall in no way affect the Amended and Restated Guaranty or the Fed Guaranty.

     Section 8.1 Notices. All notices and other communications required or permitted to be given under this Agreement shall be in writing and shall be deemed to have been given if delivered personally or by facsimile or seven days after having been sent by certified mail, return receipt requested, postage prepaid, to the parties to this Agreement at the following address or to such other address either party to this Agreement shall specify by notice to the other party:

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     Section 8.2 Further Assurances. Each party hereto shall do and perform or cause to be done and performed all further acts and shall execute and deliver all other agreements, certificates, instruments and documents as any other party hereto reasonably may request in order to carry out the intent and accomplish the purposes of this Agreement and the consummation of the transactions contemplated hereby.

     Section 8.3 Amendments and Waivers. Any provision of this Agreement may be amended or waived if, but only if, such amendment or waiver is in writing and is duly executed and delivered by the Company and Parent. No failure or delay by any party in exercising any right, power or privilege hereunder shall operate as a waiver thereof nor shall any single or partial exercise thereof preclude any other or further exercise thereof or the exercise of any other right, power or privilege. The rights and remedies herein provided shall be cumulative and not exclusive of any rights or remedies provided by law.

     Section 8.4 Fees and Expenses. Each party hereto shall pay all of its own fees and expenses (including attorneys’ fees) incurred in connection with this Agreement and the transactions contemplated hereby.

     Section 8.5 Successors and Assigns. The provisions of this Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns, provided that neither party may assign, delegate or otherwise transfer any of its rights or obligations under this Agreement without the consent of the other party hereto.

     Section 8.6 Governing Law. This Agreement shall be governed and construed in accordance with the internal laws of the State of Delaware applicable to contracts made and wholly-performed within such state, without regard to any applicable conflicts of law principles. The parties hereto agree that any suit, action or proceeding brought by either party to enforce any provision of, or based on any matter arising out of or in connection with, this Agreement or the transactions contemplated hereby shall be brought in any federal or state court located in the State of Delaware. Each of the parties hereto submits to the jurisdiction of any such court in any

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suit, action or proceeding seeking to enforce any provision of, or based on any matter arising out of, or in connection with, this Agreement or the transactions contemplated hereby and hereby irrevocably waives the benefit of jurisdiction derived from present or future domicile or otherwise in such action or proceeding. Each party hereto irrevocably waives, to the fullest extent permitted by law, any objection that it may now or hereafter have to the laying of venue of any such suit, action or proceeding in any such court or that any such suit, action or proceeding brought in any such court has been brought in an inconvenient forum.

     Section 8.7 Waiver Of Jury Trial. EACH OF THE PARTIES HERETO HEREBY IRREVOCABLY WAIVES ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATED TO THIS AGREEMENT AND THE TRANSACTIONS CONTEMPLATED HEREBY.

     Section 8.8 Entire Agreement. This Agreement constitutes the entire agreement between the parties with respect to the subject matter of this Agreement and supersedes all prior agreements and understandings, both oral and written, between the parties and/or their affiliates with respect to the subject matter of this Agreement.

     Section 8.9 Effect of Headings. The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

     Section 8.10 Severability. If one or more provisions of this Agreement are held to be unenforceable under applicable law, such provision shall be deemed to be excluded from this Agreement and the balance of this Agreement shall be interpreted as if such provision were so excluded and shall be enforced in accordance with its terms to the maximum extent permitted by law.

     Section 8.11 Counterparts; Third Party Beneficiaries. This Agreement may be signed in any number of counterparts, each of which shall be an original, with the same effect as if the signatures were upon the same instrument. No provision of this Agreement shall confer upon any person other than the parties hereto any rights or remedies hereunder.

     Section 8.12 Specific Performance. The parties agree that irreparable damage would occur in the event that any of the provisions of this Agreement were not performed in accordance with their specific terms. It is accordingly agreed that the parties shall be entitled to seek specific performance of the terms hereof, this being in addition to any other remedies to which they are entitled at law or equity.

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     IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed by their respective authorized officers as of the day and year first above written.

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