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

Zug, Switzerland - August 31, 2004 - Converium today informs on the external
reserve review and resulting capital measures.

o    Converium's Board of Directors has approved a proposal to recommend to
     shareholders the raising of additional capital of the CHF equivalent of US$
     420 million by way of a share issue. The offering will be underwritten by a
     bank syndicate subject to customary conditions. An invitation to an
     Extraordinary General Meeting and details of the share issue will follow
     shortly.

o    An independent review conducted by Tillinghast confirms that Converium's
     net reserves as of June 30, 2004, for the segments reviewed, are within a
     reasonable range of actuarial estimates. As a result of information gained
     from the Tillinghast analysis Converium will consider an adjustment to its
     reserve position during the third quarter of 2004 to increase its carried
     reserves.

o    To provide additional comfort as regards the Company's reserve position,
     Converium has acquired a stop-loss, a retrospective retrocession cover from
     National Indemnity, a Standard & Poor's "AAA" rated member of the Berkshire
     Hathaway group of insurance companies. The stop-loss provides additional
     US$ 150 million cover against potential adverse reserve development of
     underwriting years 2003 and prior for all business written by Converium AG,
     Converium Reinsurance (North America) Inc., and Converium Insurance (North
     America) Inc.

o    The restructuring of Converium's asset portfolio and the commutation of
     prior years' business has reduced its capital requirement by more than US$
     100 million.

o    Converium's operations in North America will be restructured. Converium
     Reinsurance (North America) Inc. will be placed into orderly run-off. The
     underwriting of North American Specialty Lines long-tail risks will be
     transferred to Zurich. Converium Insurance (North America) will become the
     ongoing carrier in North America under a revised business plan. The capital
     base of this company will be enhanced.

External actuarial review confirms Converium's reserves to be within a
reasonable range of actuarial estimates for the segments reviewed

In order to obtain an external review of its overall reserve position, Converium
commissioned the actuarial consulting firm Tillinghast-Towers Perrin
("Tillinghast") to perform an independent actuarial review of its non-life
reserves as of June 30, 2004 in respect of the Zurich and New York originated
businesses. These reserves amount to US$ 6.8 billion and represent 94.9% of
Converium's total reserves. Tillinghast's analysis was based on data available
at the time Converium issued its second quarter 2004 financial statements
supplemented by recent commutations. Tillinghast have relied on the accuracy and
completeness of this data and information provided for their analysis.
Tillinghast note that there is inherent uncertainty with any estimation of loss
reserves. Actual results may vary from the estimates.

As a result of their independent review, Tillinghast have concluded that
Converium's overall net reserves as of June 30, 2004, in total, for the segments
reviewed, are below their point estimate, but fall within a range of reasonable
actuarial estimates. Tillinghast's point estimate for the relevant businesses
exceeds Converium's carried reserves as of June 30, 2004 by US$ 212.9 million or
by approximately 3.2%. Converium's equity as of June 30, 2004 was US$ 1.35
billion. The Tillinghast review was performed on Converium's overall net
reserves for the segments of business analyzed. Tillinghast have not expressed
an opinion on the reserves at the statutory entity level.



Converium is taking Tillinghast's study under consideration and, following a
detailed analysis of the specific recommendations, will consider making
adjustments to carried reserves in the third quarter 2004 to reflect the new
information received. Current estimates of anticipated adjustments indicate that
a further strengthening of overall net reserves by between US$ 50 million and
US$ 100 million may be appropriate in order to bring Converium's carried
reserves closer to Tillinghast's point estimate. The precise amount of reserve
increase and the resulting financial impact on Converium's consolidated
financial statements is dependent upon ongoing commutation discussions. Since
June 30, 2004, Converium has commuted US$ 176.8 million in loss reserves related
to prior years' business assumed by its North American operation, Converium
Reinsurance (North America) Inc. Currently, Converium Reinsurance (North
America) Inc. is in negotiations with several clients for offers of
commutations, and it is pursuing these diligently. A successful conclusion of
such commutations may result in a further reduction in the difference between
Tillinghast's point estimate and the Company's current level of reserves. The
inability to conclude any additional commutations between now and the end of the
third quarter would result in the reserve adjustment coming in at the higher end
of the range indicated above.

In order to provide additional comfort as regards the reserve position,
Converium entered into a retrospective retrocession agreement with National
Indemnity Company, a Standard & Poor's AAA-rated member of the Berkshire
Hathaway group of insurance companies. The retrospective retrocession agreement
includes two layers, a US$ 150 million out-of-the-money layer, and a US$ 235
million in-the-money layer. The out-of-the money layer provides an additional
US$ 150 million of cover against potential adverse reserve development on the
underwriting years 2003 and prior, for all business written by Converium AG,
Converium Reinsurance (North America) Inc. and Converium Insurance (North
America) Inc. The cover of US$ 150 million attaches US$ 100 million in excess of
the net reserves carried by these legal entities as of June 30, 2004. The
retrocession also includes an in-the-money layer, a cession on a discounted
basis of US$ 235 million of net reserves carried by these legal entities as of
June 30, 2004. The out-of-the money cover will be accounted for on a risk
transfer basis, respectively the in-the-money layer on a deposit accounting
basis. The reinsurance charge for this retrocession is US$ 20 million. Converium
has retained the right to commute the transaction on July 1, 2009, or thereafter
at mutually agreeable terms.

Converium is to raise US$ 420 million through a share issue to be underwritten

Against the backdrop of the reserve strengthening of US$ 384.7 million in the
second quarter of 2004, the Company announces a share issue of the CHF
equivalent of US$ 420 million that will be underwritten, subject to customary
conditions, by a syndicate of banks in order to restore the Company's strong
capitalization and protect its franchise.

Details of the share issue will be made available shortly along with specific
information on an Extraordinary General Meeting in which shareholders will be
asked to approve the proposed capital increase. It is expected that the
Extraordinary General Meeting will be held prior to the end of September and
that the share issue will close by mid October 2004.

Converium is to implement additional measures to de-risk its balance sheet

In order to secure the strong capitalization needed to successfully execute
Converium's strategy and protect the interests of its stakeholders, the Company
has taken steps to de-risk its balance sheet, which results in reduced capital
requirements from a solvency and rating agency perspective. Converium has
analyzed various options and has determined to take the following actions in
addition to the share offering:



o         Establish  run-off  unit  and  seek  commutations  wherever  adequate.
          Converium  is in the  process  of  establishing  a unit to  ensure  an
          orderly  run-off  of  business  written by its  Converium  Reinsurance
          (North  America) Inc.  business unit.  Included within the scope of an
          orderly  run-off will be the  entertainment  of offers of  commutation
          where adequate.  Commutations can accelerate the realization of profit
          inherent in long-tail  reserves by  crystallizing  outstanding  claims
          reserves into payments, which are discounted to reflect the time value
          of money. Since commutation  payments essentially reflect a discounted
          present value of future cash flows,  future  investment  income earned
          will decline as the assets  backing those  reserves are  liquidated to
          make payments. In addition, commutations reduce the amount of reserves
          carried on Converium's  balance sheet and therefore reduce the capital
          required to address reserve risk from a solvency perspective.

o        Reduce volatile lines of business. In the United States, Converium will
         substantially reduce its exposure to lines of business which are
         capital intensive due to their high volatility. This would include
         so-called national account writers of lead umbrella and excess &
         surplus lines, as well as heavy commercial auto lines written on an
         excess basis. In addition, Converium anticipates that it will
         significantly reduce its writings of directors' & officers' liability
         where it believes that a weakening in market and policy conditions
         would make it more challenging to achieve adequate risk-adjusted
         profitability targets.

o         Reduce investment  portfolio risks. Since June 30, 2004, Converium has
          adjusted its asset  allocation and lowered its exposure to investments
          in equity  securities by almost US$ 500 million.  This will reduce its
          equity   exposure   to  below  4%  of  total   invested   assets  from
          approximately  10% as of June 30,  2004.  These  sales  generated  net
          realized capital gains of approximately  US$ 17.6 million,  which will
          be  recorded  in the  third  quarter  of 2004.  The  proceeds  of this
          divestiture  will be  invested  in  highly  liquid  and  highly  rated
          fixed-income  instruments.  As  equity  securities  generally  have  a
          greater  volatility  associated  with them than other  assets  such as
          highly rated fixed-income  instruments,  they require a higher capital
          charge.  The sale of equities will therefore have a beneficial  impact
          by reducing Converium's capital requirements. In addition, in order to
          protect  shareholders'  equity from  potential  future  interest  rate
          rises, Converium has lowered the modified duration of its fixed-income
          portfolio from 3.8 as per June 30, 2004 to 3.6. Sales relating to this
          reduction in duration  generated net realized  capital  losses of less
          than US$ 2.0 million.  Fixed-income  securities  with a lower duration
          generally  exhibit lower interest rate  sensitivity  than  longer-term
          bonds.  Furthermore,  since June 30, 2004  Converium has increased the
          OECD government bonds portfolio  classified as held-to-maturity by US$
          300 million.  In total, the measures taken to reduce  investment risks
          provide Converium with a capital relief of up to US$ 100 million.

Strong capitalization necessary to protect the Converium franchise

A successful capital raising complemented by the various measures to reduce the
capital required by the business will be instrumental in maintaining Converium's
strong franchise. By restoring its capital adequacy the Company expects to
preserve a strong financial strength rating, which is a prerequisite for
retaining and gaining access to reinsurance business, as it is a key criteria
used by clients and intermediaries to assess counterparty risk. A strong
financial strength rating is particularly important in some of Converium's more
profitable lines, i.e. in specialty lines such as aviation & space and credit &
surety.

Converium is committed to the further development of its successful efforts in
building a lasting franchise in Standard Property & Casualty Reinsurance as well
as in various specialty lines, either as a leading reinsurer or through its
ongoing development and expansion of strategic alliances.

Against this backdrop Converium will continue to execute its strategy, which is
focused on:

o        applying state-of-the art cycle management practice, especially in the
         more price-sensitive Standard Property & Casualty Reinsurance segment,



o        profitably growing the Company's high-margin and expertise-intensive
         specialties book of business, especially in the areas of aviation,
         agribusiness, credit & surety and professional liability in Europe, and

o        expanding its Life & Health Reinsurance segment.

In implementing its strategy the Company remains committed to underwriting for
profit. As regards pricing, Converium's after-tax target return for each line of
business is 11% plus the higher of 4% or the local risk-free rate (i.e. at least
15% in total) on allocated risk-based capital in each market. Meeting these
targets requires a constant management of the underwriting cycle including the
avoidance of under-priced business.

North American business to be reorganized

While the overall strategy of the Company remains unchanged, Converium intends
to implement changes to the way it is executed. In conjunction with the
Company's goals to reduce exposure to highly capital-intensive lines of business
in the US, Converium will discontinue the local writing of long-tail specialty
lines reinsurance from North America. Going forward, these lines will be written
using Converium AG, Zurich, and its Bermuda branch as carrier. These steps are
expected to result in a reduction of North American gross premium volume by up
to US$ 500 million.

This new approach will be implemented by taking the following measures subject
to regulatory approval:

o        Converium Reinsurance (North America) Inc., ("CRNA"), will be placed
         into orderly run-off and Converium will seek to commute CRNA's
         liabilities wherever adequate. The statutory surplus for CRNA as of 30
         June, 2004 was US$ 394.1 million.

o        Converium intends to increase the shareholders' equity of Converium
         Insurance (North America) Inc., ("CINA"), by US$ 350 million. CINA will
         be made a direct operating subsidiary of Converium Holdings (North
         America) Inc., ("CHNA"). As a result of these actions, CINA's
         policyholders' surplus will be increased to over US$ 400 million. It is
         intended that CINA will become the issuing carrier for future local
         underwriting of Standard Property & Casualty Reinsurance, aviation
         insurance, agribusiness insurance/reinsurance, accident & health
         reinsurance and workers' compensation reinsurance.

o        In order to emphasize the core status of CINA within Converium, CINA
         will be granted a parental guarantee from Converium AG, Zurich.

Dirk Lohmann, CEO, said: "These organizational changes reflect a series of
painful lessons learned from prior year casualty underwriting in the United
States. A centralization of underwriting responsibilities for the long-tail
specialty lines is expected to facilitate the implementation of rigorous and
globally consistent underwriting standards." He continued: "In addition, we
believe that this course of action and the proposed changes to the legal entity
structure will help ensure that Converium can continue to offer its clients and
producers in North America a Converium entity with the highest financial
strength rating possible."

Peter Colombo, Chairman of the Board of Directors, stated: "The Board of
Directors has initiated and unanimously approved the course of action taken by
management. We believe that the proposed capital increase is in the interest of
our shareholders as it will help safeguard Converium's strong franchise. The
planned size of the share issue takes into account an independent assessment of
Converium's reserve position as well as the various measures which reduce the
Company's capital requirements. The Board will carefully monitor the
implementation of the comprehensive and balanced set of financial,
organizational and strategic measures announced today."



                                  * * * * * * *

Conference call details

Converium will hold a conference call for the investment community and is
pleased to invite you to participate. This call will be webcast live on the
Internet at www.converium.com. Please dial in 10 to 15 minutes before and ensure
that you have Real Media PlayerTM or Windows Media PlayerTM.

The conference call will be held on Tuesday, August 31, 2004
at       3:00 p.m. Central European Time (CET)
         2:00 p.m. Greenwich Mean Time (GMT)
         9:00 a.m. Eastern Standard Time (EST)
         6:00 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 450 #

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



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 (negative outlook) from both Standard & Poor's and 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.


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 3, 2004