------------------------ 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 October, 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 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: October 8, 2004 Wellington Management Company LLC adjusts its holding in Converium shares to below 5% Converium Holding Ltd has been notified pursuant to Art. 20 of the Swiss Stock Exchange Act that Wellington Management Company LLC, 75 State Street, Boston, MA, 02100, USA, has adjusted its holding in Converium Holding Ltd, Zug to below 5% of Converium's registered shares. Zug, October 5, 2004 Enquiries: Michael Schiendorfer Zuzana Drozd Media Relations Manager Head of Investor Relations michael.schiendorfer@converium.com zuzana.drozd@converium.com Phone: +41 (0) 1 639 96 57 Phone: +41 (0) 1 639 91 20 Fax: +41 (0) 1 639 76 57 Fax: +41 (0) 1 639 71 20 www.converium.com