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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 December, 2003

                              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:

Newly created share capital
o        As at end of December 2003            No new shares
o        As at end of previous month           6'217 Shares

Conditional capital                            No. of shares      CHF
o        Reserved for Employee Participation   4'000'000 Shares   CHF 40'000'000
o        Of which total exercised by end of
         December 2003                         6'217 Shares       CHF     62'170
o        Remainder                         3'993'783 Shares       CHF 39'937'830

With best regards,

Converium Holding AG


--------------------                                    ---------------------
Barbara Barta                                           Livia Gassner
Senior Legal Counsel                                    Legal Counsel







                                   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:    Group General Counsel



Date:  January 6, 2004