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 June, 2007

                              CONVERIUM HOLDING AG
                 -----------------------------------------------
                 (Translation of registrant's name into English)

                             General Guisan-Quai 26
                                 CH-8022 Zurich
                                   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:

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

Title category: Registered shares

Security number: 1'299'771
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Issued equity capital                           Number of shares     CHF
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Status as of the end of June 2007:              146'689'462          733'447'310
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Status as at the end of the previous month:     146'689'462          733'447'310
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Conditional capital                             Number of shares     CHF
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Number of exercised securities*                 0                    0
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Amount of remaining conditional capital*        4'000'000            20'000'000
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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/ Inga Beale
                                                    Name:  Inga Beale
                                                    Title: CEO




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


Date: July 9, 2007