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, 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 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 Mai 2004 No new shares As at end of previous month No shares Contingent capital No. of shares CHF Reserved for Option Rights and/or Conversion Rights 4'000'000 40'000'000 Of which total exercised by end of Mai 2004 0 0 Remainder 4'000'000 40'000'000 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: June 3, 2004