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, 2004

                              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

Underwriting Agreement on Capital Increase

Zug, Switzerland, September 3, 2004 - Converium Holding AG (the "Company")
announces that its proposed capital increase has been underwritten by a
syndicate of banks for an amount of CHF 533 million (approximately US$ 420
million). The underwriting is subject to customary conditions, including
shareholder approval, the absence of material adverse changes or force majeure
events and confirmation of current ratings. The ordinary capital increase with
pre-emptive rights was initially announced on August 31, 2004.

Shareholders will be asked to approve the proposed capital increase at an
Extraordinary General Meeting to be held on September 28, 2004. The banks have
agreed to underwrite the new shares at a minimum issue price of CHF 10.00 per
share, representing a 55% discount to the closing share price of CHF 22.30 on
September 2, 2004.

The final issue price, together with the final number of shares to be issued
will be released by Converium on September 28, 2004, the date of the EGM, prior
to the opening of trading on the SWX Swiss Exchange.



                                  * * * * * * *

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 leading global multi-line reinsurer known for its
innovation, professionalism and service. Today Converium ranks among the top ten
professional reinsurers and employs approximately 850 people in 23 offices
around the globe.
 Converium is organized into three business segments: Standard Property &
Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance. Converium's
net losses for the September 11, 2001 terrorist attacks in the United States are
capped at US$ 289.2 million by its former parent, Zurich Financial Services.
Converium has minimal A&E exposures. Converium has an "A-" rating (watch
negative) from Standard & Poor's and a "B++" (outlook negative) rating 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, our ability to raise
capital and the success of our capital improvement measures, the ability to
obtain applicable regulatory approval for our capital improvement measures, 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.

Please note that the company has made it a policy not to provide any quarterly
or annual earnings guidance and it will not update any past outlook for full
year earnings. It will however provide investors with perspective on its value
drivers, its strategic initiatives and those factors critical to understanding
its business and operating environment.

This document does not constitute or form part of an offer or solicitation of an
offer, an invitation to subscribe for or purchase any securities. In addition,
the securities of the company to be issued in any share offering have not and
will not be registered under the United States securities laws and may not be
offered, sold or delivered within the United States or to US persons absent
registration under or an exemption from the registration requirements of the
United States securities laws.

In the United Kingdom this announcement is directed only at persons who have
professional experience in matters relating to investments or are high net worth
companies, unincorporated associations etc, for the purposes of Article 49 of
the Financial Services and Markets Act 2000 (Financial Promotion) Order 2001
(all such persons together being referred to as "relevant persons"). This
announcement must not be acted upon or relied on by persons who are not relevant
persons. Any investment or investment activity to which this announcement
relates is available only to relevant persons and will be engaged in only with
relevant persons. STABILIZATION/FSA.

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: September 8, 2004