Exhibit 99.1

Aspen announces adjustment to the Conversion Rate on its 5.625% Perpetual Preferred Income Equity Replacement Securities (Perpetual PIERS)

HAMILTON, Bermuda – April 4, 2013 – Aspen Insurance Holdings Limited (“Aspen”) (NYSE: AHL) announced today an adjustment to the conversion rate on its 5.625% Perpetual Preferred Income Equity Replacement Securities (Perpetual PIERS) in connection with its previously announced dividends payable on May 25, 2012, August 28, 2012, November 26, 2012 and March 7, 2013. As a result of these dividends, the conversion rate was adjusted to 1.7121 shares of Aspen’s ordinary shares per $50 liquidation preference of the Perpetual PIERS. The adjusted conversion rate is equivalent to an adjusted conversion price of $29.20 per share. The original conversion rate was 1.7077 of Aspen’s ordinary shares, equivalent to an original conversion price of $29.28.

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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 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 contains “forward-looking” statements regarding future results and events, including, without limitation, statements regarding the Company’s securities and their conversion into ordinary shares. 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 our ability to consummate the transactions contemplated by the terms of the accelerated share repurchase agreement, the share price and share volumes which may impact timing of repurchases, changes in market conditions and the impact on our business of such factors. 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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