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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 October, 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 AG, Zug


Close to 100% of rights exercised in Converium's capital increase

Zug, Switzerland, October 13, 2004 - Converium informs that close to 100
percent of purchase rights were exercised in its CHF 533 million capital
increase (approx. US$ 420 million).

The capital increase consisted of an offering of 106,683,245 new registered
shares at an issue price of CHF 5.00 per share. The purchase rights exercise
period ended on October 12, 2004, 12.00 (noon) CET. The new shares start trading
today, October 13 and the capital increase will close on Friday, October 15,
2004.

Due to the successful take-up of the capital increase, only a limited
number of shares will be placed by the joint global coordinators in the market.


                                  * * * * * * *
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
approximately 850 people in 23 offices around the globe and is organized into
three business segments: Standard Property & Casualty Reinsurance, Specialty
Lines and Life & Health Reinsurance. Converium Ltd has a "BBB" rating (watch
positive) from Standard & Poor's. Converium Holding Ltd has a "B++" (outlook
stable) 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:  October 15, 2004