FILED BY ENDURANCE SPECIALTY HOLDINGS LTD.

PURSUANT TO RULE 425 UNDER THE SECURITIES ACT OF 1933

AND DEEMED FILED PURSUANT TO RULE 14a-12

UNDER THE SECURITIES EXCHANGE ACT OF 1934

SUBJECT COMPANY: ASPEN INSURANCE HOLDINGS LIMITED

COMMISSION FILE NO. 001-31909

PEMBROKE, Bermuda, June 2, 2014 – In response to the Aspen news release issued today, an Endurance spokesperson stated:

“The shrill rhetoric of Aspen’s deeply entrenched board merely underscores the need to give Aspen shareholders the voice they deserve, which is exactly what our actions this morning are designed to do.

“It is clear that Aspen’s board and management, with less than 1.4% ownership, are not aligned with the best interests of their shareholders and have presented no credible plan to deliver value that can compete with what we are offering, which represents a 19.5% premium over Aspen’s all-time high stock price prior to our offer.

“What Aspen’s board and management have failed to achieve for 10 years, we are prepared to deliver today.”

Additional Information about the Proposed Transaction and Where to Find It

This material relates to the offer to be commenced by Endurance to exchange each issued and outstanding common share of Aspen (together with associated preferred share purchase rights) for $49.50 in cash, 0.9197 Endurance common shares, or a combination of cash and Endurance common shares, subject to a customary proration mechanism. This material is for informational purposes only and does not constitute an offer to exchange, or a solicitation of an offer to exchange, Aspen common shares, nor is it a substitute for the Tender Offer Statement on Schedule TO or the preliminary Prospectus/Offer to Exchange to be included in the Registration Statement on Form S-4 (including the Letter of Transmittal and Election and related documents and as amended from time to time, the “Exchange Offer Documents”) that Endurance intends to file with the SEC. The Endurance exchange offer will be made only through the Exchange Offer Documents.

This material is not a substitute for any other relevant documents that Endurance may file with the SEC or any other documents that Endurance may send to its or Aspen’s shareholders in connection with the proposed transaction. On June 2, 2014, Endurance

filed with the SEC a preliminary solicitation statement with respect to the solicitation of (i) written requisitions that the board of directors of Aspen convene a special general meeting of Aspen’s shareholders to vote on an increase in the size of Aspen’s board of directors from 12 to 19 directors and (ii) Aspen shareholder support for the proposal of a scheme of arrangement by Endurance which will entail the holding of a court-ordered meeting of Aspen shareholders at which Aspen’s shareholders would vote to approve a scheme of arrangement under Bermuda law pursuant to which Endurance would acquire all of Aspen’s outstanding common shares on financial terms no less favorable than those contained in its acquisition proposal announced on June 2, 2014 (the “Solicitation Statement”).

INVESTORS AND SECURITY HOLDERS ARE URGED TO READ THE EXCHANGE OFFER DOCUMENTS AND THE SOLICITATION STATEMENT AND ANY OTHER RELEVANT DOCUMENTS THAT ENDURANCE HAS FILED OR MAY FILE WITH THE SEC IF AND WHEN THEY BECOME AVAILABLE BECAUSE THEY CONTAIN OR WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED TRANSACTION. All such documents, when filed, are available free of charge at the SEC’s website (www.sec.gov) or by directing a request to Endurance at the Investor Relations contact below.

Participants in the Solicitation

Endurance and its directors and certain of its executive officers and employees may be deemed to be participants in any solicitation of shareholders in connection with the proposed transaction. Information about Endurance’s directors, executive officers and employees who may be deemed to be participants in the solicitation, including a description of their direct and indirect interests, by security holdings or otherwise, is set forth in the Solicitation Statement and Endurance’s proxy statement, dated April 9, 2014, for its 2014 annual general meeting of shareholders.