Exhibit 10.3

Mr. John R. Charman

c/o Endurance Specialty Holdings Ltd.

Waterloo House

100 Pitts Bay Road

Pembroke HM08

Bermuda

June 2, 2014

Endurance Specialty Holdings Ltd.

Waterloo House

100 Pitts Bay Road

Pembroke HM08

Bermuda

Re:    Equity Commitment

Ladies and Gentlemen:

In connection with the proposed acquisition of 100% of the issued and outstanding ordinary shares of Aspen Insurance Holdings Limited (“Aspen”) (including, without limitation, by merger, consolidation, reorganization, exchange offer, scheme of arrangement, amalgamation or otherwise, or a series of related transactions) by Endurance Specialty Holdings Ltd. (the “Company”) (such transaction, an “Acquisition Transaction”), this letter agreement memorializes the parties’ understanding with respect to the undersigned’s equity commitment to the Company, on the terms and subject to the conditions set forth below, in the event the Company enters into a definitive written agreement with respect to, or completes, an Acquisition Transaction, and certain other matters related thereto.

1. Commitment. Subject to and conditioned upon (a) the receipt of any required regulatory approvals and the expiration of any applicable waiting periods, including under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 and applicable foreign antitrust laws, and (b) the completion of an Acquisition Transaction, the undersigned hereto or the undersigned’s trusts or estate planning vehicles, in each case for the benefit of the undersigned, the undersigned’s spouse, and/or the undersigned’s descendants (collectively, the “Management Investor”), hereby irrevocably commits to purchase and shall purchase, immediately following the fulfillment of the conditions set forth in clauses (a) and (b) above, newly issued ordinary shares, par value $1.00 per share, of the Company (the “Ordinary Shares”), for an aggregate purchase price of $25,000,000 (the “Aggregate Commitment Amount”), at a price per Ordinary Share equal to $53.51, as adjusted for any stock splits, stock dividends or combinations prior to the closing of such investment (the “Investment”). The Ordinary Shares issued to the Management Investor pursuant to the Investment will be duly authorized, validly issued, fully paid and non-assessable.

2. Termination. This letter agreement and the obligations of the Management Investor herein will terminate automatically and immediately upon (a) December 31, 2014 if the Company does not enter into a definitive written agreement with respect to an Acquisition Transaction on or prior to December 31, 2014, (b) if the Company enters into a definitive written agreement with respect to an Acquisition Transaction on or prior to December 31, 2014, the termination of such definitive written agreement and (c) the date of termination of Mr. Charman’s employment with the Company for any reason. This Section 2 and Sections 4, 5, 6, 7 and 9 of this letter agreement shall survive any termination.

3. Assignment; Reliance. The Management Investor may not assign all or a portion of its obligations to fund its Aggregate Commitment Amount without the prior written consent of the Company, which shall not be unreasonably withheld in the case of an assignment to any other trust or estate planning vehicle meeting the requirements of Section 1 hereof. The Company shall not assign any of its rights or obligations hereunder.

4. Third Party Beneficiaries; Amendment; Waiver. This letter agreement may be relied upon only by the parties hereto. No amendment of any provision of this letter agreement will be valid and binding unless it is in writing and signed by the parties hereto. No waiver of any provision of this letter agreement will be valid and binding unless it is in writing and signed by the party against whom such waiver is sought to be enforced. No waiver by any party of any breach or violation of, or default under, this letter agreement, whether intentional or not, will be deemed to extend to any prior or subsequent breach, violation or default hereunder or affect in any way rights arising by virtue of any prior or subsequent such occurrence. No delay or omission on the part of any party in exercising any right, power or remedy under this letter agreement will operate as a waiver thereof.

5. Entire Agreement. This letter agreement constitutes the entire agreement among the parties with respect to the subject matter hereof and supersede any prior agreement or understanding between them (whether written or oral) with respect to such subject matter.

6. Counterparts. This letter agreement may be executed in any number of counterparts, each such counterpart being deemed to be an original instrument, and all such counterparts shall together constitute the same agreement. This letter agreement and any signed agreement entered into in connection herewith or contemplated hereby, and any amendments hereto or thereto, to the extent signed and delivered by facsimile, by electronic mail in “portable document format” (“.pdf”) form, or any other electronic transmission, shall be treated in all manner and respects as an original contract and shall be considered to have the same binding legal effects as if it were the original signed version thereof delivered in person.

7. Governing Law; Jurisdiction; Venue; Waiver of Jury Trial.

(a) This letter agreement shall be governed by, and construed in accordance with, the laws of the State of Delaware applicable to contracts executed in and to be performed in that State, without giving effect to any conflict of law principles thereof that would require the application of the laws of another jurisdiction. Each party irrevocably and unconditionally consents to submit to the exclusive personal jurisdiction of the courts of the State of New York and the United States of America, in each case located in the county of New York, New York,

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for such actions, suits or proceedings concerning the subject matter of this letter agreement (and agrees not to commence any action, suit or proceeding concerning the subject matter of this letter agreement except in such courts). Notwithstanding the foregoing, any party may commence an action, suit or proceeding with any governmental entity anywhere in the world for the sole purpose of seeking recognition and enforcement of a judgment of any court referred to in the preceding sentence. Each party irrevocably and unconditionally waives any objection to the laying of venue of any action, suit or proceeding concerning the subject matter of this letter agreement in the courts of the State of New York and the United States of America, in each case in the county of New York, New York, and further waives the right to, and agrees not to, plead or claim that any such action, suit or proceeding brought in any such court has been brought in an inconvenient forum. Service of any process, summons, notice or document by U.S. registered mail to c/o Endurance Services Limited, 750 Third Avenue, New York, NY 10017, in the case of each of the Management Investor and the Company (or in any other manner permitted by applicable law) shall be effective service of process for any action, suit or proceeding brought against the Management Investor or the Company, as applicable, in any court of competent jurisdiction concerning the subject matter of this letter agreement.

(b) EACH PARTY ACKNOWLEDGES AND AGREES THAT ANY CONTROVERSY (WHETHER AT LAW, IN CONTRACT, IN TORT OR OTHERWISE) THAT CONCERNS THE SUBJECT MATTER OF THIS LETTER AGREEMENT IS LIKELY TO INVOLVE COMPLICATED AND DIFFICULT ISSUES, AND THEREFORE EACH SUCH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT SUCH PARTY MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION CONCERNING THE SUBJECT MATTER OF THIS LETTER AGREEMENT. EACH PARTY CERTIFIES AND ACKNOWLEDGES THAT (i) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER, (ii) EACH PARTY UNDERSTANDS AND HAS CONSIDERED THE IMPLICATION OF THIS WAIVER, (iii) EACH PARTY MAKES THIS WAIVER VOLUNTARILY AND (iv) EACH PARTY HAS BEEN INDUCED TO ENTER INTO THIS LETTER AGREEMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 8.

8. Specific Performance. The parties hereto agree that if any of the provisions of this letter agreement were not to be performed as required by their specific terms or were to be otherwise breached, irreparable damage will occur, no adequate remedy at law would exist and damages would be difficult to determine, and that such parties shall be entitled to an injunction or injunctions to prevent breaches, and to specific performance of the terms, of this letter agreement, in addition to any other remedy at law or equity which might otherwise be available.

9. Expenses. Each party hereto shall be responsible for its own expenses in the negotiation and performance of its obligations under this letter agreement.

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[SIGNATURE PAGE TO CHARMAN LETTER AGREEMENT]

Accepted and Agreed:

[SIGNATURE PAGE TO CHARMAN LETTER AGREEMENT]