OMB APPROVAL OMB Number: 3235-0116 Expires: March 31, 2003 Estimated average burden hours per response: 8 Form 6-K SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 Report of Foreign Private Issuer Pursuant to Rule 13a-16 or 15d-16 of the Securities Exchange Act of 1934 For the month of June 2005 CONVERIUM HOLDING AG ------------------------------------------ (Translation of registrant's name into English) Baarerstrasse 8 CH-6300 Zug Switzerland ------------------------------------------------------- (Address of principal executive offices) Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F. Form 20-F X Form 40-F ------- ------- Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934. Yes No X ------- ------- If "Yes" is marked, indicate the file number assigned to the registrant in connection with Rule 12g3-2(b): 82- Not Applicable Monthly reporting of newly created equity securities from conditional capital to the SWX Swiss Exchange In accordance with the reporting requirements pursuant to the Listing Rules (Art. 64 - 75) we have disclosed following information to the SWX Swiss Exchange: -------------------------------------------------------------------------------- The current capital structure of Converium Holding AG is as follows: Title category: Registered shares Security number: 1'299'771 Issued equity capital Number of shares CHF Status as of the end of May 2005: 146'689'462 733'447'310 Status as at the end of the previous month: 146'689'462 733'447'310 Conditional capital Number of shares CHF Number of exercised securities* 0 0 Amount of remaining conditional capital* 4'000'000 20'000'000 -------------------------------------------------------------------------------- This report is also made if no equity securities have been created from conditional capital in the month in question. SIGNATURES Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized. CONVERIUM HOLDING AG By: /s/ Terry Clarke Name: Terry Clarke Title: CEO By: /s/ Christian Felderer Name: Christian Felderer Title: General Legal Counsel Date: June 6, 2005