------------------------
                                                              OMB APPROVAL
                                                        ------------------------
                                                        OMB Number: 3235-0116
                                                        ------------------------
                                                        Expires: March 31, 2003
                                                        ------------------------
                                                        Estimated average burden
                                                        hours per response: 8
                                                        ------------------------



                                    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



                                   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 27, 2004



                           Converium Holding Ltd, Zug

Zug, Switzerland - September 27, 2004 - Converium committed to raising capital

After considering various options and following today's announcement from
Standard & Poor's indicating its intention to upgrade Converium to a BBB+
financial strength rating, subject to the successful completion of a US$ 420
million capital increase, Converium's Board of Directors reaffirms its proposal
to the Extraordinary General Meeting (EGM) to approve an increase in ordinary
capital on a with-rights basis in the CHF equivalent of US$ 420 million. The
Board believes that such a share issue will maximize shareholder value. The
commitment to raising additional capital is based on Converium's strong non-US
franchise, the continuing support from cedents and brokers and the Company's
well-established direct distribution platform. In order to draw a line under its
US legacy issues Converium is also examining the possibility of a sale of its
US-based subsidiary.


Converium will proceed with the proposed with-rights capital increase
At the EGM on September 28, 2004 shareholders will be asked to approve a share
issue in the CHF equivalent of US$ 420 million with pre-emption rights for all
existing shareholders. This capital increase is expected to be fully
underwritten by a banking syndicate at the terms and conditions, which will be
announced prior to the EGM.

Converium is pleased with today's announcement by Standard & Poor's. The Board
of Directors therefore believes that the proposed capital increase is the best
way of protecting the value of Converium's non-US franchise and the embedded
value of the Company's business for shareholders. Following an analysis of other
options such as a trade sale, a sale to a financial investor, participation by a
strategic investor or a run-off, the Board of Directors believes that Converium
as a going concern, possibly in conjunction with a sale of its US operations,
will maximize shareholder value.

Strong franchise and high level of broker and client support outside the US
Converium has a track record of building profitable businesses in key regional
markets such as Europe, Asia-Pacific and Latin America. Since Converium's
Initial Public Offering (IPO) the Company has generated net income in excess of
US$ 500 million excluding business underwritten by the North American entity.

Converium believes that despite the setbacks suffered in the United States, it
continues to enjoy a strong and stable franchise among its customers in the
remaining markets. This franchise is founded upon Converium's financial
strength, its direct distribution platform which provides access to profitable
business, the quality of its client relationships and intellectual capital. A
recent independent survey from Flaspohler Research Group conducted in the first
half of 2004 among European cedents indicates that Converium's clients rank the
Company third in terms of overall excellence among all reinsurers surveyed. The
foundations of some of these client relationships have been in place and
enriched over the past 20 years. The Flaspohler survey also demonstrates primary
insurers' desire for choice and diversification when entering into a reinsurance
transaction. Given the limited number of professional reinsurers with direct
distribution capabilities, clients and brokers in many markets have recently
reiterated strong support for Converium in its intention of continuing to write
business.



North America: Tough decisions taken to protect shareholder value
As announced on September 10, 2004 Converium will place its US operations into
run-off. The Company will discontinue the writing of reinsurance from offices
located in North America. However, Converium will offer reinsurance for
attractive US-originated business to select US-based clients. This business will
be underwritten and managed through Converium AG, Zurich, and its Bermuda
branch. Converium believes that this resolute course of action represents the
best option for the Company's shareholders. In order to draw a line under its US
legacy issues Converium is also examining the possibility of a sale of its
US-based subsidiary.

Converium's future shape and priorities as a stand-alone entity

Reduction of top-line due to geographic realignment and focus on target clients
Going forward, Converium will focus on markets where its franchise remains
strong, i.e. Europe, Asia and Latin America. The Company will seek to capitalize
on its successful record of building a profitable market position in these
regions. In general, Converium will focus on small and medium-sized clients who
have limited access to capital markets and rely on additional services from
their reinsurers, such as reinsurance structuring advice and risk modelling
capabilities. Among this target group of clients are mutuals, cooperatives,
public body insurers, regional insurers and specialist insurers. Based on market
research the Company believes that these carriers place a greater weight on
relationship orientation than other reinsurer selection criteria. Accordingly,
in order to enhance its position with these clients Converium will continue its
successful Client Relationship Management (CRM) strategy launched in 2001 prior
to the IPO.

Given the discontinuation of local underwriting in the US, Converium's North
American business will be reduced by US$ 1.0 billion or more for underwriting
year 2005, predominantly in Standard Property & Casualty Reinsurance and
Specialty Lines. In Europe, Asia-Pacific and Latin America Converium's writings
will reduce to a sustainable level. Currently the Company expects its non-US
premium volume for underwriting year 2005 to be reduced by up to 40% compared to
2004 mainly because of the lower ratings but also due to Converium's continued
stringent target returns for underwriting. Accordingly, Converium's preliminary
estimates are that in underwriting year 2005, total gross written premiums will
be in the order of half the total for 2004. The Company expects profitable
growth to resume in 2006.

Further development and reinforcement of strategic alliances
Converium will continue to reinforce and develop its joint venture relationships
such as Global Aerospace Underwriting Managers Ltd (GAUM) in global aviation
insurance, Satec in global space insurance, the Medical Defence Union (MDU) in
UK medical malpractice insurance and Converium's corporate name at Lloyd's
(Converium Underwriting Ltd.). In 2003, these operations accounted for premium
income of more than US$ 600 million. These source-controlled businesses are
either not rating-sensitive or Converium will seek to secure them through
suitable fronting arrangements currently under negotiation.



Underwriting results no longer affected by US legacy issues
Converium has resolutely addressed its North American reserving deficiencies.
Going forward, the Company's profitable non-US record is no longer expected to
be impaired by reserve shortfalls in the US. Converium also emphasizes that,
irrespective of the recent rating decisions, its commitment to a strict
underwriting discipline will be maintained. In addition, the Company will adjust
its cost base to the reduced top-line in order to remain cost-competitive.

Investment results expected to remain strong
Converium's total invested assets plus cash amount to almost US$ 8 billion. The
Company's conservative asset allocation is driven by Asset and Liability
Management considerations. It is expected to continue to generate strong
investment results.

Aim for a stronger financial strength rating within a reasonable time frame
In order to preserve its economic value Converium will seek to restore a strong
financial strength rating within a reasonable time frame. The Company believes
that its portfolio, following the recent reserve strengthening, has a strong
embedded earnings potential. Converium regards this, in conjunction with a
strong capital adequacy following a successful share issue, as the foundation
upon which a restoration of a higher rating will be based.

Active management of capital base
Converium aims at generating attractive returns on capital. If capital cannot be
fully deployed in future periods Converium will consider returning such capital
to shareholders. At the same time, the Company is committed to maintaining its
capital at a level that is consistent with an "A"-level rating.

Peter C. Colombo, Chairman of the Board of Directors, said: "Having reviewed
various strategic options the Board of Directors has concluded that the proposed
capital increase is the best option for Converium's shareholders. There is
evidence, further validated today by Standard & Poor's announcement, that our
non-US franchise continues to be profitable in our chosen markets and our
clients want Converium to stay in business as an independent company."

Dirk Lohmann, CEO, added: "We firmly believe that our revised strategy lays the
foundation for a profitable and sustainable future as a going concern. There
have been shortcomings in North America but we have taken resolute actions in
order to allow Converium's profitable non-US track record and strong franchise
to maximize future shareholder value."

Telephone conference

Converium will hold a conference call for the investment community and is
pleased to invite you to participate. This call will be held on Tuesday,
September 28, 2004

at                9:00 a.m.  Central European Time (CET)
                  8:00 a.m.  Greenwich Mean Time (GMT)
                  3:00 a.m.  Eastern Standard Time (EST)
                  12:00 a.m. Pacific Standard Time (PST)



call              +41 (0) 91 610 5600       Europe
                  +44 (0) 207 107 0611      UK
                  +1 (1) 866 291 4166       Toll Free USA only
                  +1 866 519 5086           Toll Free Canada
                  +1 866 519 5087           Toll Free Mexico

and quote "Converium"

For those of you unable to participate actively in this conference call, an
audio recording will be available one hour after the event for 24 hours. The
number to dial and the access code are as follows:

       +44 (0) 207 866 4300  from UK
       +41 (0) 91 612 4330   from Europe
       +1 412 317 0088       from North America

followed by the access code 284 #

A few hours after the event the full webcast with Q&A will be available for a
period of one month on www.converium.com.


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


Dr Kai-Uwe Schanz
Chief Communication Officer

kai-uwe.schanz@converium.com

Phone:     +41 (0) 1 639 90 35
Fax        +41 (0) 1 639 70 35



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 has minimal A&E exposures. Converium has a "BBB"
rating (watch positive) 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 Company's strategy, anticipated
premium volumes, 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; client acceptance of
our rating and capital position and business generally, 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. STABILISATION/FSA.

www.converium.com
-----------------