<Page> EXHIBIT 10.1 AMENDMENT NO. 4 Reference is made to the Shareholders Agreement dated as of November 20, 2001, as amended (the "SHAREHOLDERS AGREEMENT"), by and among Arch Capital Group Ltd., a company organized under the laws of Bermuda (the "COMPANY"), the parties listed on the signature pages hereto and certain other persons. This amendment ("AMENDMENT") to the Shareholders Agreement is made as of September 16, 2002. 1. Section 1.1 of the Shareholders Agreement is amended to add the following definitions: "H&F REPRESENTATIVE" shall mean the individual designated by the H&F Purchasers to act on behalf of H&F, as shareholders of the Company, under Section 3.3, which individual is identified to the Company in writing from time to time; PROVIDED that the H&F Representative shall not be an H&F Director. "WARBURG REPRESENTATIVE" shall mean the individual designated by the Warburg Purchasers to act on behalf of Warburg, as shareholders of the Company, under Section 3.3, which individual is identified to the Company in writing from time to time; PROVIDED that the Warburg Representative shall not be a Warburg Director. 2. The first paragraph of Section 3.3 (preceding clauses (1) - (17)) of the Shareholders Agreement is amended and restated in its entirety as follows: Section 3.3. INVESTOR PROTECTION MATTERS. Except as specifically set forth herein, in accordance with the Company's Bye-laws, the Board shall act by the vote of a majority of the Directors present at a meeting, and the required quorum for a meeting of the Board shall be a majority of the whole Board. Notwithstanding the foregoing, and except as specifically set forth in the Subscription Agreement, (a) prior to the Approval Date, unless also approved by the Warburg Representative and the H&F Representative, and (b) following the Approval Date, unless also approved by (i) the Warburg Representative, if at such time Warburg's Retained Percentage equals or exceeds 25%, and (ii) the H&F Representative, if at such time H&F's Retained Percentage equals or exceeds 50%, the Company shall not (and shall not permit any of its Subsidiaries to): 3. The validity and effects of this Amendment shall be governed by and construed and enforced in accordance with the laws of the State of New York. 4. This Amendment may be executed in any number of counterparts, each of which shall be considered an original and all of which together shall be deemed to be one and the same instrument. [Signature Pages Follow] <Page> IN WITNESS WHEREOF, each party has executed this Amendment as of the date first above-written. ARCH CAPITAL GROUP LTD. By: /s/ John D. Vollaro --------------------------------------- Name: John D. Vollaro Title: Executive Vice President & Chief Financial Officer WARBURG PINCUS NETHERLANDS INTERNATIONAL PARTNERS I, C.V., WARBURG PINCUS NETHERLANDS INTERNATIONAL PARTNERS II, C.V., By: Warburg, Pincus & Co., its General Partner By: /s/ Kewsong Lee --------------------------------- Name: Kewsong Lee Title: Partner WARBURG PINCUS (BERMUDA) PRIVATE EQUITY VIII, L.P. By: Warburg Pincus (Bermuda) Private Equity Ltd., its General Partner By: /s/ Kewsong Lee --------------------------------- Name: Kewsong Lee Title: Partner <Page> WARBURG PINCUS (BERMUDA) INTERNATIONAL PARTNERS, L.P. By: Warburg Pincus (Bermuda) International Ltd., its General Partner By: /s/ Kewsong Lee --------------------------------- Name: Kewsong Lee Title: Partner <Page> HFCP IV (BERMUDA), L.P., By: H&F Investors IV (Bermuda), L.P. By: H&F Corporate Investors IV (Bermuda) Ltd., its General Partner By: /s/ Georgia Lee ------------------------------- Name: Georgia Lee Title: Vice President H&F INTERNATIONAL PARTNERS IV-A (BERMUDA), L.P. By: H&F Investors IV (Bermuda), L.P., its General Partner By: H&F Corporate Investors IV (Bermuda), Ltd., its General Partner, By: /s/ Georgia Lee ------------------------------- Name: Georgia Lee Title: Vice President <Page> HFCP IV (BERMUDA), L.P., By: H&F Investors IV (Bermuda), L.P. By: H&F Corporate Investors IV (Bermuda) Ltd., its General Partner By: /s/ Georgia Lee ------------------------------- Name: Georgia Lee Title: Vice President H&F INTERNATIONAL PARTNERS IV-A (BERMUDA), L.P. By: H&F Investors IV (Bermuda), L.P., its General Partner By: H&F Corporate Investors IV (Bermuda), Ltd., its General Partner, By: /s/ Georgia Lee ------------------------------- Name: Georgia Lee Title: Vice President