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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 February, 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 - February 4, 2005 - Converium announces estimates of losses
from the South Asia tsunami and European winter storm Erwin as well as revised
estimates of losses from 2004 hurricanes and typhoons.

Following a diligent review of loss reports so far, Converium expects pre-tax
net losses from the devastating tsunami that hit South and South East Asia on
December 26, 2004 of approximately US$ 15 million. Expected losses are
concentrated in property and non-life personal accident lines of business.

Severe winter storm Erwin that swept across Northern Europe from January 7 to
January 9, 2005 is expected to result in pre-tax net losses for Converium of
between US$ 25 and 40 million which is reflective of the Company's market
position in the region. Total estimated industry losses from Erwin range from
US$ 1.3 to 1.8 billion.

In addition, Converium has increased its estimate of expected net losses arising
from third quarter Atlantic hurricane activity and Japan typhoons by US$ 23
million and US$ 13 million, respectively. Converium therefore expects total
pre-tax net losses of US$ 132 million related to these hurricanes and typhoons.
The majority of the development for the hurricanes stems from Ivan, where total
industry claims (including Caribbean losses) are now believed to reach US$ 9
billion, up from earlier estimates of between US$ 4 and 6 billion. This unusual
string of natural catastrophes is, however, not expected to materially weaken
Converium's strong capitalization.

                                  * * * * * * *

Enquiries:

Michael Schiendorfer                           Zuzana Drozd
Media Relations Manager                        Head of Investor Relations

michael.schiendorfer@converium.com             zuzana.drozd@converium.com

Phone:    +41 (0) 1 639 96 57                  Phone:    +41 (0) 1 639 91 20
Fax:      +41 (0) 1 639 76 57                  Fax:      +41 (0) 1 639 71 20


About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs more than 700
people in 20 offices around the globe and is organized into three business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance. 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 `expects', `should continue', `believes',
`anticipates', `estimates' and `intends'. The specific forward-looking
statements cover, among other matters, the reinsurance market, the outcome of
insurance regulatory reviews, the Company's operating results, the rating
environment and the prospect for improving results, the amount of capital
required and impact of its capital improvement measures, including the
restructuring of our U.S. business and its reserve position. 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 general economic conditions, including in
particular economic conditions; the frequency, severity and development of
insured loss events arising out of catastrophes, as well as man-made disasters;
the outcome of our regular quarterly reserve review, the ability to exclude and
to reinsure the risk of loss from terrorism; fluctuations in interest rates;
returns on and fluctuations in the value of fixed-income investments, equity
investments and properties; fluctuations in foreign currency exchange rates;
rating agency actions; changes in laws and regulations and general competitive
factors, 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/ Dirk Lohmann
                                               Name: Dirk Lohmann
                                               Title: CEO


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

Date: February 8, 2005