Exhibit 99.1

Aspen Prices Public Offering of $150 Million of Perpetual Non-Cumulative Preference Shares

4/3/2012 6:32:09 PM

HAMILTON, Bermuda—(BUSINESS WIRE)—Apr. 3, 2012— Aspen Insurance Holdings Limited (“Aspen”) (NYSE:AHL) has priced an underwritten public offering of 6,000,000 shares of 7.25% of Perpetual Non-Cumulative Preference Shares (the “Preference Shares”).

The Preference Shares have a liquidation preference of $25 per share (or $150,000,000 in aggregate liquidation preference). The underwriters have the option to purchase from Aspen up to an additional 900,000 Preference Shares (or $22,500,000 in aggregate liquidation preference).

The offering was made pursuant to an effective shelf registration statement and is expected to close on April 11, 2012, subject to customary closing conditions. Aspen intends to use the net proceeds from the offering for general corporate purposes, including supporting its insurance and reinsurance activities through its operating subsidiaries as well as repurchasing its outstanding ordinary shares as determined from time to time.

The Preference Shares rank equally with preference shares previously issued by Aspen, and have no fixed maturity date. Aspen may redeem all or a portion of the shares at a redemption price of $25 per share on or after July 1, 2017. Aspen intends to list the Preference Shares on the New York Stock Exchange under the symbol “AHLPRB”.

The offering was led by Citigroup Global Markets Inc., Barclays Capital Inc., UBS Securities LLC and Wells Fargo Securities, LLC as joint book-running managers.

This offering may be made only by means of a preliminary prospectus supplement and accompanying prospectus. Copies of the preliminary prospectus supplement and the final prospectus may be obtained, when available, from the U.S. Securities and Exchange Commission’s website at www.sec.gov. Alternatively, these documents are available from the underwriters by contacting any of the following:

This press release shall not constitute an offer to sell or a solicitation of an offer to buy the Preference Shares, nor shall there be any sale of the Preference Shares in any state or jurisdiction in which such offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such state or jurisdiction.

About Aspen Insurance Holdings Limited (“Aspen”)

Aspen provides reinsurance and insurance coverage to clients in various domestic and global markets through wholly-owned subsidiaries and offices in Bermuda, France, Germany, Ireland, Singapore, Switzerland, the United Kingdom and the United States. For the year ended December 31, 2011, Aspen reported $9.5 billion in total assets, $4.5 billion in gross reserves, $3.2 billion in shareholders’ equity and $2.2 billion in gross written premiums. Its operating subsidiaries have been assigned a rating of “A” (“Strong”) by Standard & Poor’s, an “A” (“Excellent”) by A.M. Best and an “A2” (“Good”) by Moody’s Investors Service.

Application of the Safe Harbor of the Private Securities Litigation Reform Act of 1995

This press release may contain written “forward-looking statements” within the meaning of the U.S. federal securities laws. These statements are made pursuant to the safe harbor provisions of the Private Securities Litigation Reform Act of 1995. Forward-looking statements include all statements that do not relate solely to historical or current facts, and can be identified by the use of words such as “expect,” “intend,” “plan,” “believe,” “project,” “anticipate,” “seek,” “will,” “estimate,” “may,” “continue,” and similar expressions of a future or forward-looking nature.

All forward-looking statements rely on a number of assumptions, estimates and data concerning future results and events and are subject to a number of uncertainties and other factors, many of which are outside Aspen’s control that could cause actual results to differ materially from such statements, including changes in market conditions and their impact on our business. For a detailed description of uncertainties and other factors that could impact the forward-looking statements in this press release, please see the “Risk Factors” section in Aspen’s Annual Report on Form 10-K for the year ended December 31, 2011, filed with the U.S. Securities and Exchange Commission on February 28, 2012. Aspen undertakes no obligation to update or revise publicly any forward-looking statements, whether as a result of new information, future events or otherwise.

For further information

Please visit www.aspen.co or contact:

Source: Aspen Insurance Holdings Limited

Investors

Aspen

Kerry Calaiaro, +1 646-502-1076

Senior Vice President, Investor Relations

Kerry.Calaiaro@aspen.co

or

Media

Aspen

Tim Dickenson, +44 20 7184 8034

Global Head of Communications

Tim.Dickenson@aspen.co

or

Europe and Asia – Citigate Dewe Rogerson

Justin Griffiths, +44 20 7638 9571

Justin.Griffiths@citigatedr.co.uk

or

North America – Abernathy MacGregor

Allyson Vento, +1 212-371-5999

amv@abmac.com

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