ARCH CAPITAL GROUP LTD. 20 Horseneck Lane Greenwich, Connecticut 06830 June 9, 2000 Ms. Debra M. O'Connor Debra O'Connor 14 Revere Road Riverside, CT 06880 Dear Debra: This letter confirms your and our agreement on the following terms: 1. Position & Responsibilities: Arch Capital Group Ltd. ("ACGL") shall employ you to serve as a Senior Vice President, Controller and Treasurer, and that in such capacity you shall report to the President and Chief Executive Officer of ACGL. The term of your employment shall terminate upon notice by either ACGL to you or by you to ACGL. 2. Compensation: Compensation for your services shall be at an annual base salary rate of $169,800 (subject to upward adjustments by the Board of Directors (the "Board") of ACGL), and an annual performance bonus opportunity to be determined by the Board. The target rate for the annual bonus for 2000 and thereafter shall be 40% of the base salary rate. 3. Additional Terms: You will be eligible to participate in employee benefit programs of ACGL as are in effect from time to time, including medical, dental, life insurance, short and long-term disability, 401(k), defined contribution retirement, stock incentive plans and stock purchase plans, subject to the respective terms and conditions of such plans. You also will be entitled to certain vacation pay and paid holidays, as outlined in and subject to ACGL's Employee Handbook. Notwithstanding anything to the contrary in paragraph 2 above, if your employment continues to (or ACGL terminates your employment other than for cause before) the later of (1) March 1, 2001 or (2) the filing of ACGL's Annual Report on Form 10-K for 2000, you shall receive your target annual bonus for 2000 and, if applicable, 2001 (in each case, pro -2- rated based on the number of days you are employed during the year) plus $50,000. Any amount payable under this paragraph shall be made within 10 business days after the determination thereof. "Cause" shall have the meaning set forth in Section 3(ii) of the Change in Control Agreement referred to in the next paragraph. Following the sale of ACGL's reinsurance operations to Folksamerica Reinsurance Company, you acknowledge receipt from ACGL of $505,897.30 under the Change in Control Agreement, dated as of February 25, 1999 (the "Change in Control Agreement"), between you and ACGL. Upon the execution of this letter, and in consideration of such payment and the above, you acknowledge and agree that all of ACGL's obligations under the Change in Control Agreement are terminated in their entirety, and hereby release ACGL from such obligations, except for those specified in Section 4(iv) and, solely in respect of such Section 4(iv), Section 6 of the Change in Control Agreement. It is understood that your obligations under Section 8 of the Change in Control Agreement shall remain in full force and effect. 4. This letter supersedes all prior discussions and agreements between ACGL and you with respect to the subject matter hereof and constitutes the entire agreement among the parties relating thereto, shall be governed by the laws of the State of Connecticut without regard to choice of law rules, and may be executed in one or more counterparts. Please confirm your agreement to the above by signing and returning the enclosed duplicate of this letter. Sincerely, ARCH CAPITAL GROUP LTD. By: /s/ Peter A. Appel --------------------------------------- Peter A. Appel President and Chief Executive Officer AGREED AND ACCEPTED as of the date hereof: /s/ Debra O'Connor - ---------------------------------- Debra O'Connor