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 January, 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





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:


Issued equity capital                 Number of shares       CHF
Status at end of 31.12.2004           146'689'462            733'447'310
                                      146'689'462            733'447'310

Conditional capital                   Number of shares       CHF
Number of securities issued           4'000'000              20'000'000

Amount of remaining conditional       4'000'000              20'000'000
capital





                                   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:  January 5, 2005