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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 March, 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


Odey Asset Management LLP adjusts its holding in Converium registered
shares from 5.84% to 11.2% (held and managed in various funds)

Zug, Switzerland - March 10, 2005 - Converium Holding Ltd 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 increased
its holding of registered shares with voting rights to 16,395,960. This
corresponds to 11.2% 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 British Financial Services Authority
registered fund management house, and acts as the investment manager for several
funds.





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


Esther Gerster
Head of Public Relations
esther.gerster@converium.com
Phone    +41 (0) 1 639 90 22
Fax      +41 (0) 1 639 70 22



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/ Terry Clarke
                                    Name:      Terry Clarke
                                    Title:     CEO




                               By:  /s/ Christian Felderer
                                    Name:      Christian Felderer
                                    Title:     General Legal Counsel



Date: March 11, 2005