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 October, 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






                           Converium Holding Ltd, Zug

Zug, Switzerland - October 5, 2005 - Converium informs about its progress in
commuting North American liabilities.

In the third quarter of 2005 Converium has commuted net reserves of close to US$
250 million relating to liabilities of Converium Reinsurance (North America)
Inc. (CRNA). The bottom-line impact on the third quarter result from these
commutations will be positive.

More than 90% of the commuted liabilities are associated with volatile and
long-tail lines of business, e.g. General and Special Liability, Professional
Liability and Workers' Compensation.

These figures demonstrate that Converium's strategy of systematically commuting
North American liabilities is on track. Converium reiterates its target to
commute or otherwise settle CRNA net liabilities of approximately US$ 500
million in 2005, further de-risking the Company's balance-sheet.


Enquiries:

Dr. Kai-Uwe Schanz                              Zuzana Drozd 
Chief Communication & Corporate                 Head of Investor Relations
Development Officer

kai-uwe.schanz@converium.com                    zuzana.drozd@converium.com
Phone:  +41 (44) 639 90 35                      Phone:  +41 (44) 639 91 20
Fax:    +41 (44) 639 70 35                      Fax:    +41 (44) 639 71 20


About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs about 600
people in 20 offices around the globe and is organized into four business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance, which are based principally on ongoing global lines of
business, as well as the Run-Off segment, which primarily comprises the business
from Converium Reinsurance (North America) Inc., excluding the US originated
Aviation business portfolio. Converium has a "BBB+" rating (outlook stable) from
Standard & Poor's and a "B++" rating (outlook stable) from A.M. Best Company.

Important Disclaimer

This document contains forward-looking statements as defined in the U.S. Private
Securities Litigation Reform Act of 1995. It contains forward-looking statements
and information relating to the Company's financial condition, results of
operations, business, strategy and plans, based on currently available
information. These statements are often, but not always, made through the use of
words or phrases such as ` seek to', `expects', `should continue', `believes',
`anticipates', `estimates' and `intends'. The specific forward-looking
statements cover, among other matters, the reinsurance market, the Company's
operating results, the rating environment and the prospect for improving results
and expense reductions. Such statements are inherently subject to certain risks
and uncertainties. Actual future results and trends could differ materially from
those set forth in such statements due to various factors. Such factors include
the impact of our ratings downgrade or a further lowering or loss of one of our
financial strength ratings; uncertainties of assumptions used in our reserving
process; risk associated with implementing our business strategies and our
capital improvement measures and the run-off of our North American business;
cyclicality of the reinsurance industry; the occurrence of natural and man-made
catastrophic events with a frequency or severity exceeding our estimates; acts
of terrorism and acts of war; changes in economic conditions, including interest
and currency rate conditions that could affect our investment portfolio; actions
of competitors, including industry consolidation and development of competing
financial products; a decrease in the level of demand for our reinsurance or
increased competition in our industries or markets; a loss of our key employees
or executive officers without suitable replacements being recruited within a
suitable period of time; our ability to address material weaknesses we have
identified in our internal control environment; political risks in the countries
in which we operate or in which we reinsure risks; the passage of additional
legislation or the promulgation of new regulation in a jurisdiction in which we
or our clients operate or where our subsidiaries are organized; the effect on
the insurance industry as a result of the investigations being carried out by
the US Securities and Exchange Commission and New York's Attorney General;
changes in our investment results due to the changed composition of our invested
assets or changes in our investment policy; failure of our retrocessional
reinsurers to honor their obligations or changes in the credit worthiness of our
reinsurers; our failure to prevail in any current or future arbitration or
litigation; and extraordinary events affecting our clients, such as bankruptcies
and liquidations , and other risks and uncertainties, including those detailed
in the Company's filings with the U.S. Securities and Exchange Commission and
the SWX Swiss Exchange. The Company does not assume any obligation to update any
forward-looking statements, whether as a result of new information, future
events or otherwise.

www.converium.com






                                   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: October 7, 2005