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 September, 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 - September 28, 2005 - Converium revises its loss estimate for
hurricane Katrina.

Based on an expected insured industry loss of US$ 50 billion, Converium now
estimates gross losses from hurricane Katrina to be in the range of US$ 20 - 40
million. This estimate compares with a range of US$ 10 - 20 million given early
September based on an expected industry loss of US$ 25 billion.

The revised loss amount represents about 1 - 2% of Converium's shareholders'
funds as of June 30, 2005 and is reflective of the Company's reduced exposure in
North America as a result of having placed Converium Reinsurance (North America)
Inc. into run-off as well as the decision to write North American business from
Zurich on a selective basis only.

Given the structure of Converium's exposure any ultimate industry loss in excess
of US$ 50 billion would have a disproportionately low impact on the Company's
loss estimate.


                                  * * * * * * *

Enquiries:

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 (0) 44 639 90 35                 Phone:    +41 (0) 44 639 91 20
Fax:       +41 (0) 44 639 70 35                 Fax:      +41 (0) 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: September 28, 2005