Exhibit 99.1

Aspen Announces Mandatory Conversion of Perpetual PIERS

Hamilton, Bermuda, April 25, 2013 – Aspen Insurance Holdings Limited (“Aspen”) (NYSE:AHL) announced that it is mandatorily converting its Perpetual PIERS (CUSIP Number: BMG053841133) with effect today. Aspen will be converting all of its 4,600,000 Perpetual PIERS. Each holder of a Perpetual PIERS will receive $50 in cash plus a number of ordinary shares as determined during the Stock Settlement Averaging Period as the Settlement Amount in accordance with the terms of the Perpetual PIERS. The conversion rate is 1.7121 shares of Aspen’s ordinary shares per $50 liquidation preference of the Perpetual PIERS. Aspen expects to deliver the Settlement Amount on May 30, 2013. In accordance with the terms of the Perpetual PIERS, no further dividends will be paid on the Perpetual PIERS as a result of such Mandatory Conversion.

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About Aspen Insurance Holdings Limited

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, 2012, Aspen reported $10.3 billion in total assets, $4.8 billion in gross reserves, $3.5 billion in total shareholders’ equity and $2.6 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, as well as factors such as the availability of financing to fund the cash portion of the settlement of the mandatory conversion of the Perpetual PIERS on favorable terms and the possibility, if Aspen cannot obtain adequate replacement capital on favorable terms, or at all, that its financial condition and operating results could be adversely affected. 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, 2012, filed with the U.S. Securities and Exchange Commission on February 26, 2013. 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:

Investors

Kerry Calaiaro, Senior Vice President, Investor Relations, Aspen

Kerry.Calaiaro@aspen.co

+1 646 502 1076

Media

Steve Colton, Head of Communications, Aspen

Steve.Colton@aspen.co

+44 20 7184 8337

International – Citigate Dewe Rogerson

Caroline Merrell or Jos Bieneman

caroline.merrell@citigatedr.co.uk

jos.bieneman@citigatedr.co.uk

+44 20 7638 9571

North America – Abernathy MacGregor

Allyson Vento

amv@abmac.com

+1 (212) 371 5999

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