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 May, 2004 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 990231.3 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/ Dirk Lohmann Name: Dirk Lohmann Title: CEO By: /s/ Christian Felderer Name: Christian Felderer Title: General Legal Counsel Date: May 5, 2004 Monthly disclosure of equity securities newly created from conditional capital Issuer: Converium Holding AG Sec. ID no.: 1'299'771 ISIN: CH0012997711 In accordance with art. 3a of the Articles of Incorporation of Converium Holding Ltd and with para. 5.02 (conditional capital) of the checklist published as enclosure 1 of the "Reports required in order to maintain a listing" (Art. 64 - 75 KR), we inform about the creation of following share capital: Newly created share capital -- As at end of April 2004 No new shares -- As at end of previous month 6'217 Shares Conditional capital No. of shares CHF -- Reserved for Employee Participation 4'000'000 Shares CHF 40'000'000 -- Of which total exercised by end of April 2004 6'217 Shares CHF 62'170 -- Remainder 3'993'783 Shares CHF 39'937'830 Converium Holding Ltd's Annual General Meeting, held on April 27, 2004, approved to delete art. 3a of the Articles of Incorporation. Therefore as of the registration of the deletion of art. 3a in the register of commerce, this disclosure will be dropped.