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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 January 2006

                              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:

Title category: Registered shares

Security number: 1'299'771


Issued equity capital                        Number of shares   CHF

Status as of the end of December 2005:       146'689'462        733'447'310

Status as at the end of the previous month:  146'689'462        733'447'310

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: January 5, 2006