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 April, 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 reporting of newly created equity securities from conditional capital to
the SWX Swiss Exchange

In accordance with the reporting requirements pursuant to the Listing Rules
(Art. 64 - 75) we have disclosed following information to the SWX Swiss
Exchange:

--------------------------------------------------------------------------------

The current capital structure of Converium Holding AG is as follows:




                                                                        
----------------------------------------------------------------------------------------------------------
Spent equity capital                                      Number of shares           CHF
----------------------------------------------------------------------------------------------------------
Status as of the end of March 2005:                       146'689'462                733'447'310
----------------------------------------------------------------------------------------------------------
Status as at the end of the previous month:               146'689'462                733'447'310
----------------------------------------------------------------------------------------------------------
Title category:
----------------------------------------------------------------------------------------------------------
Conditional capital                                       Number of shares           CHF
----------------------------------------------------------------------------------------------------------
Number of exercised securities*                           0                          0
----------------------------------------------------------------------------------------------------------
Amount of remaining conditional capital*                  4'000'000                  20'000'000
----------------------------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------------------------



This report is also made if no equity securities have been created from
conditional capital in the month in question.





                                   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: April 4, 2005