Exhibit 99.1

Max Capital Group completes acquisition of Max at Lloyd’s

HAMILTON, Bermuda, November 6, 2008 — Max Capital Group Ltd. (NASDAQ: MXGL; BSX: MXGL BH) (“Max Capital” or the “Company”) today announced that it has completed the previously announced acquisition of Imagine Group (UK) Limited (“Imagine Lloyd’s”), a Lloyd’s insurance operation, from Imagine Insurance Company Limited. Imagine Lloyd’s managing agent will be renamed Max at Lloyd’s Ltd. (“Max at Lloyd’s”). The acquisition includes Imagine Lloyd’s operations in Denmark and Japan.

Max at Lloyd’s, through Lloyd’s Syndicates 1400, 2525 and 2526, underwrites a diverse portfolio of specialty risks including property catastrophe, financial institutions, personal accident, employers’ and public liability, and professional indemnity business. Based in London, Max at Lloyd’s will complement Max Capital’s current underwriting operations in Bermuda, Ireland and the United States.

W. Marston (Marty) Becker, Chairman and Chief Executive Officer of Max Capital, said: “With our acquisition of Max at Lloyd’s, we have accomplished the key strategic objective of obtaining access to the Lloyd’s market and its important benefits with a team of high quality underwriters. Max at Lloyd’s will further diversify Max’s risk profile and enable us to provide our global clients with a wide range of products backed by both the financial strength of Max and the highly rated security common to all Lloyd’s syndicates. A Lloyd’s presence will also present new opportunities to add key specialty underwriting teams to our Company. We look forward to working with Max at Lloyd’s talented underwriting teams led by Matthew Petzold, and expect the company to quickly become an important contributor to the success and profitability of Max.”

Iain Bremner, Managing Director of Max at Lloyd’s, said: “The Max at Lloyd’s team is excited to be joining Max and has already made significant progress towards effectively integrating its operations with those of Max. We have been impressed by the level of expertise and diligence exhibited by our new colleagues at Max, and look forward to working with them to achieve our common goals. As Max at Lloyd’s, we believe we will build a stronger franchise that will benefit both our clients and capital providers.”

Lloyd’s is licensed to underwrite business in 79 territories and can accept risks proposed from more than 200 countries and territories in accordance with local laws and regulation. Lloyd’s licenses offer broad access to major direct and reinsurance markets worldwide.

Supplementary information concerning the transaction is available on Max Capital’s website at www.maxcapgroup.com.

Max Capital Group Ltd., through its operating subsidiaries, provides specialty insurance and reinsurance products to corporations, public entities, property and casualty insurers and life and health insurers.

This news release includes statements about future economic performance, finances, expectations, plans and prospects of the Company that constitute forward-looking statements for purposes of the safe harbor provisions of the Private Securities Litigation Reform Act of 1995. Such forward-looking statements are subject to certain risks and uncertainties that could cause actual results to differ materially from those suggested by such statements. For further information regarding cautionary statements and factors affecting future results, please refer to the Company’s most recent Annual Report on Form 10-K, Quarterly Reports on Form 10-Q filed subsequent to the Annual Report and other documents filed by the Company with the SEC. The Company undertakes no obligation to update or revise publicly any forward-looking statement whether as a result of new information, future developments or otherwise.

SOURCE: Max Capital Group Ltd.

Max Capital Group Ltd.

N. James Tees, 1-441-293-8800

Executive Vice President

jim.tees@maxcapservices.com

or

Kekst and Company

Roanne Kulakoff, 1-212-521-4837

roanne-kulakoff@kekst.com