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                                    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



990231.3




Odey Asset Management LLP acquires 5.84% in Converium registered shares (held
and managed in various funds)

Converium Holding Ltd, Zug, has been notified pursuant to Art. 20 of the Swiss
Stock Exchange Act that Odey Asset Management LLP, 12 Upper Grosvenor Street,
London W1K 2ND, United Kingdom, has acquired 8,559,920 registered shares with
voting rights. This corresponds to 5.84% of Converium's registered share
capital. These shares are held and managed in various funds. None of these funds
is holding shares in an amount, which exceeds 5% of Converium registered share
capital.

Odey Asset Management LLP is a UK FSA registered fund management house, and acts
as the investment manager for several funds.


Zug, October 21, 2004


Contacts:

Zuzana Drozd
Head of Investor Relations
zuzana.drozd@converium.com
Phone +41 (0) 1 639 91 20
Fax   +41 (0) 1 639 71 20


Michael Schiendorfer
Media Relations Manager
michael.Schiendorfer@converium.com
Phone    +41 (0) 1 639 96 57
Fax      +41 (0) 1 639 76 57


www.converium.com





                                   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 22, 2004