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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



                                       1



                           Converium Holding Ltd, Zug

Zug, Switzerland - October 26, 2004 - Converium today reports on its
financial results for the third quarter of 2004.


Converium reports a third quarter 2004 loss of US$ 116.3 million. This
result reflects the continuing satisfactory underlying performance of its
in-force book and a number of previously announced extraordinary charges. The
main items are an additional reserve strengthening of US$ 96.4 million net based
on an in-depth analysis of Tillinghast's actuarial review, losses of US$ 95.8
million from an unusual cumulation of hurricanes and typhoons and a US$ 20.0
million expense for a retrospective stop-loss retrocession cover purchased from
National Indemnity Company. Adjusted for the reserve action and natural
catastrophes, Converium recorded a third quarter non-life combined ratio of
96.0%, which testifies to the favorable performance of the Company's more recent
underwriting years. In addition, investment activities continued to exhibit very
satisfactory results, with total investment income yield improving further to
4.9%.


Third quarter 2004 highlights



                                                                                        
o        Operating loss:                                                                 US$ -125.0 million
o        Impact from reserve strengthening and hurricanes/typhoons:                      US$ -192.2 million
o        Net loss:                                                                       US$ -116.3 million
o        Gross premiums written:                                                         US$ 1,033.3 million
o        Non-life combined ratio:                                                        117.3%
o        Impact from reserve strengthening and hurricanes/typhoons:                      21.3%
o        Adjusted non-life combined ratio:                                               96.0%
o        Total investment income yield:                                                  4.9%
o        Shareholders' equity:                                                           US$ 1,275.1 million
o        Cash flows:                                                                     US$ 21.1 million



Overview of third quarter performance and short-term outlook

The following developments had measurable effects on Converium's third
quarter 2004 financial results:

o    The business written by Converium in the underwriting years 2002, 2003, and
     2004 continued to show a satisfactory performance, both for the non-life
     segments as well as for the Life & Health Reinsurance segment. Excluding
     prior years' reserves, the non-life combined ratio was 106.6% (including a
     10.6% impact by hurricanes and typhoons) for the third quarter 2004,
     respectively 98.3% for the first nine months of 2004.

o    Following a detailed analysis of the specific conclusions in Tillinghast's
     actuarial study, Converium has - as anticipated on August 31, 2004 - made
     additional adjustments to carried reserves aggregating to a net increase of
     US$ 96.4 million net in the third quarter of 2004. This amount equals 1.3%
     of Converium's non-life net reserves as of September 30, 2004. The reserve
     strengthening primarily arose from prior years' North American professional
     liability, umbrella, excess & surplus, workers' compensation, and non-US
     motor liability business. It added 10.7 percentage points to the quarter's
     non-life combined ratio.

o    Since June 30, 2004, Converium has commuted approximately US$ 265.0 million
     in loss reserves related to prior years' business assumed by the Company's
     North American operation, Converium Reinsurance (North America) Inc.
     ("CRNA"), with a corresponding reduction in cash and invested assets.
     Currently, CRNA is in negotiations with several clients for additional
     offers of commutation, and is pursuing these diligently. The third quarter
     reserve adjustment of US$ 96.4 million net takes into account recent
     commutations. In general, 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.


                                       2


o    As announced on August 31, 2004, Converium has acquired a retrospective
     stop-loss retrocession cover from National Indemnity Company, a Standard &
     Poor's AAA-rated member of the Berkshire Hathaway group of insurance
     companies. The cost of this cover represents a one-off charge to the third
     quarter of 2004 of US$ 20.0 million.

o    Net losses from Hurricanes Charley, Frances, Ivan and Jeanne and typhoons
     in Japan amounted to US$ 95.8 million and added 10.6 percentage points to
     the quarter's non-life combined ratio.

o    In the third quarter of 2004 Converium has incurred restructuring charges
     of US$ 3.4 million related to severance payments and the discontinuation of
     the Company's North American operations.

Against this backdrop there is a marked difference between Converium's
reported results and its performance adjusted for the various extraordinary
items. For the third quarter 2004 Converium reported an operating loss of US$
125.0 million and a net loss of US$ 116.3 million that reflect total charges of
US$ 215.6 million due to an additional strengthening of reserves, losses from
hurricanes and typhoons, the cost of a retrospective stop-loss cover and
restructuring charges.

The increase in gross premiums written, net premiums written, and net
premiums earned in the third quarter of 2004 (by 2.3%, 5.2% and 10.4%,
respectively) reflects market conditions, new client relationships in certain
key markets and the weakening of the US$ compared to other major currencies;
special terminations did not materially impact the quarter's top line.

Converium reports a non-life combined ratio of 117.3% for the third quarter
of 2004. Adjusted for the additional strengthening of reserves by US$ 96.4
million net and the losses from hurricanes and typhoons of US$ 95.8 million, the
non-life combined ratio was 96.0%, which is indicative of a continuing favorable
performance of recent underwriting years.

Converium's Life & Health Reinsurance segment reported a segment income of
US$ 5.7 million, an improvement of US$ 20.5 million compared to the same period
of the previous year, when Converium recorded an adverse development of its
Guaranteed Minimum Death Benefits (GMDB) book. No further reserving actions were
required for GMDB in 2004.

Converium's investment results continued to improve markedly. The Company's
net investment income increased for the three and nine months ended September
30, 2004 as compared to the same periods of 2003. This increase largely resulted
from growth in invested assets over 2003, particularly in Converium's
fixed-maturities portfolio, as well as income received from the transition of a
fixed-income bond to a direct fixed-income investment portfolio.

The Company's average annualized net investment income yield (pre-tax) was
3.9% and 3.8% for the three and nine months ended September 30, 2004,
respectively, as compared to 3.0% and 3.4% for the same periods of 2003,
reflecting increasing interest rates in 2004.

Converium's average annualized total investment income yield (pre-tax) was
4.9% and 4.5% for the three and nine months ended September 30, 2004,
respectively, as compared to 2.9% and 3.5% for the same periods of 2003. During
the third quarter 2004, the total investment income yields were positively
impacted by the increase in realized gains as well as the decline in impairment
charges compared to 2003 resulting from the sale of equity securities to adjust
our asset allocation to reduce investment portfolio risks.

Converium has reached an agreement in principle on the main terms of a new
US$ 1.6 billion credit facility, comprising a US$ 1.5 billion tranche for
letter-of-credit issuance and a US$ 0.1 billion stand-by revolving credit
tranche with its principal international relationship banks. The parties intend
to finalize the transaction by mid-November 2004. This facility will replace the
existing syndicated credit line of US$ 0.9 billion that was signed in July 2003.

The Company believes that its "BBB+" rating from Standard & Poor's and the
availability of adequate letter-of-credit facilities will support Converium's
efforts to maintain its franchise in its European, Asian and Latin American
target markets and to retain relationships with key clients and intermediaries
in the upcoming January 2005 renewals.

                                       3





  ------------------------------------------------------ ------------------------ ------------------------ ------------
  Financial highlights: Income statement, return on        Three months ended           Nine months        Year ended
  equity                                                      September 30                 ended             Dec. 31
                                                                                       September 30
  In US$ million, unless noted
                                                             2004         2003        2004         2003        2003
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
                                                                                                 
  Gross premiums written                                      1,033.3     1,009.6      3,444.5     3,222.1      4,223.9
  - growth (%)                                                  +2.3%                    +6.9%
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Net premiums written                                          933.8       887.4      3,181.2     2,971.3      3,827.0
  - growth (%)                                                  +5.2%                    +7.1%
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Net premiums earned                                         1,013.9       918.6      3,016.8     2,715.4      3,676.5
  - growth (%)                                                 +10.4%                   +11.1%
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Non-life loss ratio1                                          91.9%       69.2%        92.7%       72.1%        71.5%
  - change in percentage points                              +22.7pts                 +20.6pts
  - impact of hurricanes/typhoons                               10.6%                     3.6%
  - impact of reserve strengthening2                            10.7%                    19.6%
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Non-life underwriting expense ratio3                          20.9%       22.5%        21.2%       21.6%        22.0%
  - change in percentage points                               -1.6pts                  -0.4pts
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Non-life administration expense ratio4                         4.5%        4.0%         4.0%        4.0%         4.4%
  - change in percentage points                               +0.5pts                        -
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Non-life combined ratio5                                     117.3%       95.7%       117.9%       97.7%        97.9%
  - change in percentage points                              +21.6pts                 +20.2pts
  - impact of hurricanes/typhoons                               10.6%                     3.6%
  - impact of reserve strengthening                             10.7%                    19.6%
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Non-life combined ratio5 excluding                            96.0%                    94.7%
  hurricanes/typhoons and reserve strengthening2
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Life & Health technical result6                                 5.2       -12.6         13.8       -11.1         -8.0
  - growth (%)                                                   n.m.                     n.m.
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Total investment results7                                      97.3        52.9        266.8       183.4        251.4
  - growth (%)                                                 +83.9%                   +45.5%
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Total investment income yield8                                 4.9%        2.9%         4.5%        3.5%         3.5%
  - change in percentage points                              +2.0 pts                   +1.0pt
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Total investment return9                                       6.4%        3.5%         3.7%        5.7%         5.7%
  - growth (%)                                                +2.9pts                  -2.0pts
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Operating income10                                           -125.0        56.4       -348.2       144.7        206.0
  - change (%)                                                   n.m.                     n.m.
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------
  Net (loss) income                                            -116.3        44.3       -710.6       128.9        185.1
  - change (%)                                                   n.m.                     n.m.
  ------------------------------------------------------ ------------ ----------- ------------ ----------- ------------


--------

1    Non-life loss ratio is defined as losses and loss adjustment expenses
     divided by net premiums earned.

2    US$ 96.4 million net of prior years' reserve strengthening in the third
     quarter of 2004.

3    Non-life underwriting expense ratio is defined as underwriting acquisition
     costs divided by net premiums earned.

4    Non-life administration expense ratio is defined as other operating and
     administration expenses divided by net premiums written.

5    Non-life combined ratio is defined as non-life loss ratio (to premiums
     earned) plus non-life underwriting expense ratio (to premiums earned) plus
     non-life administration expense ratio (to premiums written).

6    Life & Health technical result is defined as net premiums earned minus
     losses, loss adjustment expenses and life benefits minus underwriting
     acquisition costs plus technical interests.

7    Total investment results are defined as net investment income plus net
     realized capital gains (losses).

8    Total investment income yield is defined as net investment income plus net
     realized capital gains (losses) divided by average total invested assets
     (including cash and cash equivalents), pre-tax and annualized.

9    Total investment return is defined as net investment income plus net
     realized capital gains (losses) plus change in net unrealized capital gains
     (losses) divided by average total invested assets (including cash and cash
     equivalents), pre-tax and annualized.

10   Operating income is defined as pre-tax income excluding pre-tax net
     realized capital gains (losses), impairment of goodwill and restructuring
     costs.


                                       4





  --------------------------------------------------- ------------------------ --------------------------- ------------
  Financial highlights: Income statement, return on     Three months ended            Nine months          Year ended
  equity                                                   September 30                  ended               Dec 31
                                                                                      September 30
  in US$ million, unless noted
  ---------------------------------------------------
                                                          2004         2003         2004          2003         2003
  --------------------------------------------------- ------------ ----------- ------------- ------------- ------------
                                                                                                 
  (Loss) earnings per share (US$)                            -2.91        1.12        -17.83          3.24         4.65
  - growth (%)                                                n.m.                      n.m.
  --------------------------------------------------- ------------ ----------- ------------- ------------- ------------
  --------------------------------------------------- ------------ ----------- ------------- ------------- ------------
  Adjusted (loss) earnings per share11 (US$)                 -0.79                     -4.84
  --------------------------------------------------- ------------ ----------- ------------- ------------- ------------
  --------------------------------------------------- ------------ ----------- ------------- ------------- ------------
  Return on equity12                                        -22.3%       10.2%        -45.5%          9.9%        10.7%
  - change in percentage points                           -32.5pts                  -55.4pts
  --------------------------------------------------- ------------ ----------- ------------- ------------- ------------





  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Financial highlights: Balance sheet                                          September 30,   June 30,    December 31,
                                                                                    2004         2004          2003
  In US$ million, unless noted
  ---------------------------------------------------------------------------- ------------- ------------ -------------
                                                                                                      
  Total invested assets plus cash                                                   7,965.1      7,926.4       7,809.5
  - growth (%)                                                                        -0.5%        +1.5%
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Claims supporting capital13                                                       1,665.9      1,739.9       2,473.9
  - growth (%)                                                                        -4.3%       -29.7%
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Shareholders' equity                                                              1,275.1      1,349.2       2,083.3
  - growth (%)                                                                        -5.5%       -35.2%
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Total tangible equity14                                                           1,250.7      1,322.8       1,732.2
  - growth (%)                                                                        -5.5%       -23.6%
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Book value per share (US$)                                                          31.99        33.90         52.38
  - growth (%)                                                                        -5.6%       -35.3%
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Book value per share (CHF)                                                          39.95        42.45         65.21
  - growth (%)                                                                        -5.9%       -34.9%
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Adjusted book value per share11 (US$)                                               11.52
  ---------------------------------------------------------------------------- ------------- ------------ -------------
  Adjusted book value per share11 (CHF)                                               14.39
  ---------------------------------------------------------------------------- ------------- ------------ -------------


-------------

11   Adjusted for the new shares issued based on a rights offering that occurred
     in October 2004.

12   Return on equity is defined as net income or loss (after-tax) divided by
     shareholders' equity at the beginning of the period, annualized.

13   Claims supporting capital is defined as total equity plus debt.

14   Total tangible equity is defined as shareholders' equity less net deferred
     tax assets/liabilities, goodwill and other intangible assets.


                                       5




  ------------------------------------------------------------ ---------------------------- ---------------------------
  Financial highlights: Investment results                          Three months ended           Nine months ended
                                                                       September 30                 September 30
  in US$ million, unless noted
  ------------------------------------------------------------
                                                                          2004         2003          2004         2003
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
                                                                                                      
  Investment income - Fixed maturities                                    52.3         26.3         146.3         92.2
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Investment income - Equity securities                                    1.0          1.7          10.2          9.5
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Investment income - Funds Withheld Asset                                18.2         20.5          57.5         64.3
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Other investment income, net                                             5.5          5.7          10.8         11.2
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Net investment income                                                   77.0         54.2         224.8        177.2
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Average annualized net investment income yield (pre-tax)                3.9%         3.0%          3.8%         3.4%
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Net realized capital gains (losses)                                     20.3         -1.3          42.0          6.2
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Total investment results                                                97.3         52.9         266.8        183.4
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Average annualized total investment income yield (pre-tax)              4.9%         2.9%          4.5%         3.5%
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Change in net unrealized gains (pre-tax)                                30.9         10.9         -46.0        115.9
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Total investment return (pre-tax)                                      128.2         63.8         220.8        299.3
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Average annualized total investment return (pre-tax)                    6.4%         3.5%          3.7%         5.7%
  ------------------------------------------------------------ --------------- ------------ ------------- -------------
  Average total invested assets (including cash and cash               7,945.8      7,245.4       7,887.3      6,938.1
  equivalents)
  ------------------------------------------------------------ --------------- ------------ ------------- -------------



Business Development

The following are comments on the development of Converium's three main
business segments and the Corporate Center. Reference is made to the tables
attached to this press release.

Standard Property & Casualty Reinsurance represented approximately 38.7% of
total net premiums written in the third quarter of 2004. For this period of time
Converium's Standard Property & Casualty Reinsurance segment reported a segment
income of US$ 18.9 million, a decline of US$ 31.9 million compared to the same
period of the previous year.

In the third quarter of 2004 gross premiums written increased by 6.3% to
US$ 407.4 million, net premiums written increased by 6.6% to US$ 361.2 million,
and net premiums earned decreased by 0.2% to US$ 422.1 million. The Standard
Property & Casualty Reinsurance segment's non-life combined ratio was 105.0% for
the third quarter of 2004 (compared to 93.7% for the third quarter of 2003). The
results were substantially influenced by hurricanes Charley, Frances, Ivan and
Jeanne and Japanese typhoons which generated losses of US$ 95.8 million and
added 22.7 percentage points to the segment's third quarter loss ratio.

For the third quarter of 2004, the Standard Property & Casualty Reinsurance
segment recorded a positive reserve development of US$ 31.8 million. This
favorable development primarily related to property (US$ 31.5 million) and
general third party liability (US$ 45.6 million) and was partially offset by
reserve strengthening, mainly for motor outside the United States (US$ 45.8
million).

For the nine months ended September 30, 2004, gross premiums written
increased 7.2% to US$ 1,483.5 million, net premiums written increased 5.5% to
US$ 1,349.7 million and net premiums earned increased 6.0% to US$ 1,282.3
million.

For the nine months ended September 30, 2004, net premiums written growth
in the Standard Property & Casualty Reinsurance segment by lines of business
included:


                                       6



o    Motor (increased by 17.1% or US$ 66.3 million to US$ 454.0 million), which
     grew as a result of the expansion of motor business in Western Europe;

o    Personal accident non-life (increased by 15.5% or US$ 4.1 million to US$
     30.7 million), which expanded on the back of new or extended relationships
     with cedents in Italy and a number of other European countries; and

o    General third party liability (increased by 18.1% or US$ 48.8 million to
     US$ 317.9 million), which grew mainly due to continuing rate increases and
     new business.

These increases were partially offset by a decrease in net premiums written
within the property line of business. Property contracted by 8.3% or US$ 49.3
million to US$ 547.1 million, which was primarily driven by the softening of
property rates and a consequent non-renewal of several large contracts in North
America, and by reduced premium writings with cedents in Asia and Latin America.

Specialty Lines represented approximately 49.1% of total net premiums
written in the third quarter of 2004. For this period of time Converium's
Specialty Lines segment reported a segment loss of US$ 81.2 million. In the
third quarter of 2004, gross premiums written decreased by 6.7% to US$ 506.9
million, and net premiums written decreased by 3.5% to US$ 458.3 million; net
premiums earned increased by 17.2% to US$ 478.3 million. These developments
reflect the strict underwriting discipline and cycle management applied by
Converium. The Specialty Lines segment's non-life combined ratio was 128.2% for
the third quarter of 2004.

Specialty Lines reported a segment loss which was primarily attributable to
reserve additions. In the third quarter of 2004, US$ 128.2 million of reserve
strengthening were recorded, which added 26.8 percentage points to the segment's
loss ratio. The strengthening arose mainly from workers' compensation (US$ 26.9
million) and from the professional liability & other special liability lines, in
particular umbrella, professional liability and excess & surplus lines of
business in the United States (US$ 101.9 million).

For the nine months ended September 30, 2004, gross premiums written
increased 2.9% to US$ 1,577.3 million, net premiums written increased 4.9% to
US$ 1,473.9 million and net premiums earned increased 13.3% to US$ 1,395.2
million.

For the nine months ended September 30, 2004, the Specialty Lines segment
exhibited the following growth dynamics:

o    Professional liability and other special liability (increased by 7.0% or
     US$ 34.4 million to US$ 528.6 million), which grew as a result of new
     business written and an increase in premium volume for Converium's Medical
     Defence Union (MDU) business;

o    Agribusiness (increased by 34.2% or US$ 22.4 million to US$ 88.0 million),
     which expanded as new business was written as well as return premium
     received on a specific contract due to favorable technical results; and

o    Aviation & space (increased by 8.6% or US$ 23.0 million to US$ 289.7
     million), which grew as a result of an increased net retention in the
     business underwritten by Global Aerospace Underwriting Managers Ltd.

Life & Health Reinsurance represented approximately 12.2% of total net
premiums written in the third quarter of 2004. For this period of time
Converium's Life & Health Reinsurance segment reported a segment income of US$
5.7 million, an increase of US$ 20.5 million compared to the same period of the
previous year.

In the third quarter of 2004 gross premiums written increased by 43.9% to
US$ 119.0 million, net premiums written increased by 54.9% to US$ 114.3 million,
and net premiums earned increased by 29.7% to US$ 113.5 million.

Life & Health Reinsurance reported a segment income for the nine months
ended September 30, 2004 as compared to a segment loss for the same period in
2003. The technical result increased from minus US$ 12.6 million to US$ 5.2
million for the same period. The increases in 2004 were primarily attributable
to:

o    Strong growth in premium volume driven by the expansion of existing
     financing reinsurance transactions in Continental Europe and increased
     shares of current business; and

o    The development of Converium's GMDB book during the first nine months of
     2004 as compared to 2003. Whereas in the first nine months of 2003 reserves
     were strengthened by US$ 22.6 million, no actions were required in 2004.


                                       7



For the nine months ended September 30, 2004, gross premiums written
increased 25.6% to US$ 383.7 million, net premiums written increased 25.0% to
US$ 357.6 million and net premiums earned increased 24.0% to US$ 339.3 million.
Converium continues to build its Life & Health Reinsurance operations in order
to further reduce the volatility of the Company's net income, because life and
health reinsurance has a low correlation to property and casualty risk and can
therefore improve risk diversification.

The Corporate Center carries certain administration expenses such as the
costs of the Board of Directors, the Global Executive Committee, and other
global functions. In the third quarter of 2004 other operating and
administration expenses were US$ 8.2 million (an increase of 1.2% as compared to
the same period in 2003).


Rights Offering

In October 2004, Converium's share capital was increased by CHF 533,416,225
by issuing 106,683,245 shares at CHF 5.00 each. The capital increase (and
reduction of the nominal value) was recorded, in the Commercial Register of the
Canton of Zug (Switzerland) on October 12, 2004. After the registration of the
share capital increase in the Commercial Register of the Canton of Zug,
Converium's issued outstanding share capital is now CHF 733,447,310, divided
into 146,689,462 shares with a nominal value of CHF 5.00. The capital increase
brings Converium's total tangible capital close to the level of December 31,
2003.

After the reduction of the nominal value from CHF 10 to CHF 5 for each of
Converium's shares, its conditional capital is now CHF 20,000,000 pursuant to
which up to 4,000,000 shares can be issued upon exercise of conversion or option
rights allotted in connection with bonds and other financial market instruments.
Similarly, Converium's authorized capital is now CHF 20,000,000 pursuant to
which the Board is authorized to issue up to 4,000,000 shares.




                                  * * * * * * *



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 perspectives on its value
drivers, its strategic initiatives and those factors critical to understanding
its business and operating environment.



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
800 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 Ltd, Converium Ruckversicherung (Deutschland) AG
and Converium Insurance (UK) Ltd. have a "BBB+" rating (outlook stable) from
Standard & Poor's. Converium Ltd. has a "B++" (outlook stable) rating from A.M.
Best Company.

                                       8


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.

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.

www.converium.com

                                       9




  -----------------------------------------------------------------------------------------------------------------------
   Consolidated statements of income                Three months ended     Change      Nine months ended       Change
   (Unaudited)                                        September 30,                      September 30,
   In US$ million, unless noted                       2004        2003       (%)        2004        2003         (%)
  -----------------------------------------------------------------------------------------------------------------------
  Revenues
  -----------------------------------------------------------------------------------------------------------------------
                                                                                                 
  Gross premiums written                              1,033.3    1,009.6      +2.3%     3,444.5     3,222.1       +6.9%
  -----------------------------------------------------------------------------------------------------------------------
  Less ceded premiums written                           -99.5     -122.2     -18.6%      -263.3      -250.8       +5.0%
  -----------------------------------------------------------------------------------------------------------------------
  Net premiums written                                  933.8      887.4      +5.2%     3,181.2     2,971.3       +7.1%
  -----------------------------------------------------------------------------------------------------------------------
  Net change in unearned premiums                        80.1       31.2       n.m.      -164.4      -255.9      -35.8%
  -----------------------------------------------------------------------------------------------------------------------
  Net premiums earned                                 1,013.9      918.6     +10.4%     3,016.8     2,715.4      +11.1%
  -----------------------------------------------------------------------------------------------------------------------
  Net investment income                                  77.0       54.2     +42.1%       224.8       177.2      +26.9%
  -----------------------------------------------------------------------------------------------------------------------
  Net realized capital gains (losses)                    20.3       -1.3       n.m.        42.0         6.2        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Other (loss) income                                   -31.7          -       n.m.       -28.8        -4.4        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Total revenues                                      1,079.5      971.5     +11.1%     3,254.8     2,894.4        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Benefits, losses and expenses
  -----------------------------------------------------------------------------------------------------------------------
  Losses, loss adjustment expenses and life            -914.2     -662.2     +38.1%    -2,738.9    -1,994.9      +37.3%
  benefits
  -----------------------------------------------------------------------------------------------------------------------
  Underwriting acquisition costs                       -211.2     -201.8      +4.7%      -642.4      -582.3      +10.3%
  -----------------------------------------------------------------------------------------------------------------------
  Other operating and administration expenses           -50.6      -45.5     +11.2%      -154.9      -142.4       +8.8%
  -----------------------------------------------------------------------------------------------------------------------
  Interest expense                                       -8.2       -6.9     +18.8%       -24.8       -23.9       +3.8%
  -----------------------------------------------------------------------------------------------------------------------
  Impairment of goodwill                                    -          -       n.m.       -94.0           -        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Restructuring costs                                    -3.4          -       n.m.        -3.4           -        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Total benefits, losses and expenses                -1,187.6     -916.4     +29.6%    -3,658.4    -2,743.5       33.3%
  -----------------------------------------------------------------------------------------------------------------------
  (Loss) Income before taxes                           -108.1       55.1       n.m.      -403.6       150.9        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  (Loss) income tax (expense)                            -8.2      -10.8     -24.1%      -307.0       -22.0        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Net (loss) income                                    -116.3       44.3       n.m.      -710.6       128.9        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Basic (loss) earnings per share (US$)                 -2.91       1.12       n.m.      -17.83        3.24        n.m.
  -----------------------------------------------------------------------------------------------------------------------
  Diluted (loss) earnings per share (US$)               -2.87       1.10       n.m.      -17.56        3.20        n.m.
  -----------------------------------------------------------------------------------------------------------------------


                                       10





  ---------------------------------------------------------------------------------------------------------------------
  Consolidated balance sheets                                                              September 30,  December 31,
  In US$ million, unless noted                                                                 2004          2003
                                                                                            (unaudited)
  ---------------------------------------------------------------------------------------------------------------------
  Invested assets
  ---------------------------------------------------------------------------------------------------------------------
  Held-to-maturity securities:
                                                                                                          
             Fixed maturities                                                                     851.8         500.4
  ---------------------------------------------------------------------------------------------------------------------
  Available-for-sale securities:
         Fixed maturities                                                                       4,724.6       4,428.2
         Equity securities                                                                        372.2         840.2
  ---------------------------------------------------------------------------------------------------------------------
  Other investments                                                                               259.4         173.5
  ---------------------------------------------------------------------------------------------------------------------
  Short-term investments                                                                          144.0          55.8
  ---------------------------------------------------------------------------------------------------------------------
  Total investments                                                                             6,352.0       5,998.1
  ---------------------------------------------------------------------------------------------------------------------
  Funds Withheld Asset                                                                          1,314.5       1,530.6
  ---------------------------------------------------------------------------------------------------------------------
  Total invested assets                                                                         7,666.5       7,528.7
  ---------------------------------------------------------------------------------------------------------------------
  Other assets
  ---------------------------------------------------------------------------------------------------------------------
  Cash and cash equivalents                                                                       298.6         280.8
  ---------------------------------------------------------------------------------------------------------------------
  Premiums receivables:
         Current                                                                                  221.7         182.8
         Accrued                                                                                1,989.9       1,825.5
  ---------------------------------------------------------------------------------------------------------------------
  Reinsurance assets:
         Underwriting reserves                                                                  1,593.1       1,718.6
         Insurance balances receivable, net                                                       232.8         224.0
  ---------------------------------------------------------------------------------------------------------------------
  Funds held by reinsureds                                                                      1,608.2       1,374.0
  ---------------------------------------------------------------------------------------------------------------------
  Deferred policy acquisition costs                                                               415.1         380.1
  ---------------------------------------------------------------------------------------------------------------------
  Deferred income taxes                                                                            90.9         345.1
  ---------------------------------------------------------------------------------------------------------------------
  Other assets                                                                                    460.6         495.0
  ---------------------------------------------------------------------------------------------------------------------
  Total assets                                                                                 14,577.4      14,354.6
  ---------------------------------------------------------------------------------------------------------------------
  ---------------------------------------------------------------------------------------------------------------------
  Liabilities
  ---------------------------------------------------------------------------------------------------------------------
  Losses and loss adjustment expenses, gross                                                    8,809.0       7,842.8
  ---------------------------------------------------------------------------------------------------------------------
  Unearned premiums, gross                                                                      1,594.8       1,467.4
  ---------------------------------------------------------------------------------------------------------------------
  Future life benefits, gross                                                                     518.8         483.5
  ---------------------------------------------------------------------------------------------------------------------
  Other reinsurance liabilities                                                                 1,154.2       1,087.3
  ---------------------------------------------------------------------------------------------------------------------
  Funds held under reinsurance contracts                                                          459.6         529.8
  ---------------------------------------------------------------------------------------------------------------------
  Deferred income taxes                                                                           137.8         158.3
  ---------------------------------------------------------------------------------------------------------------------
  Accrued expenses and other liabilities                                                          237.3         311.6
  ---------------------------------------------------------------------------------------------------------------------
  Debt                                                                                            390.8         390.6
  ---------------------------------------------------------------------------------------------------------------------
  Total liabilities                                                                            13,302.3      12,271.3
  ---------------------------------------------------------------------------------------------------------------------
  Equity
  ---------------------------------------------------------------------------------------------------------------------
  Common stock                                                                                    253.0         253.0
  ---------------------------------------------------------------------------------------------------------------------
  Additional paid-in capital                                                                    1,330.8       1,326.7
  ---------------------------------------------------------------------------------------------------------------------
  Treasury stock                                                                                   -6.5         -10.0
  ---------------------------------------------------------------------------------------------------------------------
  Unearned stock compensation                                                                      -6.6          -6.1
  ---------------------------------------------------------------------------------------------------------------------
  Accumulated other comprehensive income:
         Net unrealized gains on investments, net of taxes                                         94.3         145.3
  ---------------------------------------------------------------------------------------------------------------------
  ---------------------------------------------------------------------------------------------------------------------
         Cumulative translation adjustments                                                       114.1         116.1
  ---------------------------------------------------------------------------------------------------------------------
  ---------------------------------------------------------------------------------------------------------------------
  Total accumulated other comprehensive income                                                    208.4         261.4
  ---------------------------------------------------------------------------------------------------------------------
  Retained (deficit) earnings                                                                    -504.0         258.3
  ---------------------------------------------------------------------------------------------------------------------
  Total equity                                                                                  1,275.1       2,083.3
  ---------------------------------------------------------------------------------------------------------------------
  Total liabilities and equity                                                                 14,577.4      14,354.6
  ---------------------------------------------------------------------------------------------------------------------


                                       11





  ---------------------------------------------------------------------------------------------------------------------
  Consolidated statements of cash flows                                                        Nine months ended
  (Unaudited)                                                                                    September 30,
  In US$ million, unless noted                                                                  2004           2003
  ---------------------------------------------------------------------------------------------------------------------
                                                                                                            
  Net income                                                                                    -710.6            128.9
  ---------------------------------------------------------------------------------------------------------------------
         Net realized capital gains on investments                                               -42.0             -6.2
         Amortization of premium/discount                                                         43.5             32.2
         Depreciation and amortization                                                            18.7             22.5
         Impairment of goodwill and deferred tax assets                                          363.8                -
  ---------------------------------------------------------------------------------------------------------------------
  Total adjustments                                                                              384.0             48.5
  ---------------------------------------------------------------------------------------------------------------------
         Deferred policy acquisition costs                                                       -36.0            -87.6
         Reinsurance assets                                                                      117.8            -11.7
         Funds held by reinsureds                                                               -238.1           -162.9
         Funds Withheld Asset                                                                    218.4            116.6
         Premiums receivables                                                                   -195.2           -446.3
         Unearned premiums, gross                                                                127.9            267.4
         Losses and loss adjustment expenses, gross                                              958.5            502.4
         Future life benefits, gross                                                              36.4             95.1
         Funds held under reinsurance contracts                                                  -71.9             68.1
         Other reinsurance liabilities                                                            71.7            316.8
         Income taxes, net                                                                        26.0             24.9
         Net change in all other operational assets and liabilities                             -267.5             43.8
  ---------------------------------------------------------------------------------------------------------------------
  Total changes in operational assets and liabilities                                            748.0            726.6
  ---------------------------------------------------------------------------------------------------------------------
  Cash provided by operating activities                                                          421.4            904.0
  ---------------------------------------------------------------------------------------------------------------------
         Purchases of fixed maturities held-to-maturity                                         -212.1           -108.9
         Proceeds from sales and maturities of fixed maturities available-for-sale             2,679.5          2,786.1
         Purchases of fixed maturities available-for-sale                                     -3,106.8         -3,553.3
  ---------------------------------------------------------------------------------------------------------------------
  Cash flows from investing activities (fixed maturities)                                       -639.4           -876.1
  ---------------------------------------------------------------------------------------------------------------------
         Proceeds from sales of equity securities                                                958.8             41.0
         Purchases of equity securities                                                         -537.5           -182.0
  ---------------------------------------------------------------------------------------------------------------------
  Cash flows from investing activities (equity securities)                                       421.3           -141.0
  ---------------------------------------------------------------------------------------------------------------------
         Net (increase) decrease in short-term investments                                       -88.2            108.3
         Proceeds from sales of other assets                                                      65.1             25.1
         Purchases of other assets                                                              -100.4            -62.7
  ---------------------------------------------------------------------------------------------------------------------
  Cash flows from investing activities (other)                                                  -123.5             70.7
  ---------------------------------------------------------------------------------------------------------------------
  Net cash used in investing activities                                                         -341.6           -946.4
  ---------------------------------------------------------------------------------------------------------------------
         Net purchases of common shares                                                           -4.9             -5.4
  ---------------------------------------------------------------------------------------------------------------------
         Dividends to shareholders                                                               -47.9            -29.2
  ---------------------------------------------------------------------------------------------------------------------
  Net cash used in financing activities                                                          -52.8            -34.6
  ---------------------------------------------------------------------------------------------------------------------
  Effect of exchange rate changes on cash and cash equivalents                                    -9.2              9.8
  ---------------------------------------------------------------------------------------------------------------------
  Change in cash and cash equivalents                                                             17.8            -67.2
  ---------------------------------------------------------------------------------------------------------------------
  Cash and cash equivalents as of January 1                                                      280.8            361.5
  ---------------------------------------------------------------------------------------------------------------------
  Cash and cash equivalents as of September 30                                                   298.6            294.3
  ---------------------------------------------------------------------------------------------------------------------


                                       12





   ---------------------------------------------------------------------------------------------------------------------
    Segments                                   Three months ended       Change       Nine months ended        Change
    (Unaudited)                                  September 30,                         September 30,
    In US$ million, unless noted                2004        2003         (%)          2004        2003         (%)
   ---------------------------------------------------------------------------------------------------------------------
    Standard Property & Casualty Reinsurance
   ---------------------------------------------------------------------------------------------------------------------
                                                                                                 
    Gross premiums written                         407.4       383.4        +6.3%      1,483.5    1,384.3         +7.2%
    Net premiums written                           361.2       338.9        +6.6%      1,349.7    1,279.6         +5.5%
    Net premiums earned                            422.1       422.9        -0.2%      1,282.3    1,210.1         +6.0%
    Non-life loss ratio15                          76.5%       66.2%     +10.3pts        78.6%      66.0%      +12.6pts
    Non-life underwriting expense ratio16          23.2%       23.5%      -0.3pts        22.6%      22.6%             -
    Non-life administration expense ratio17         5.3%        4.0%      +1.3pts         4.5%       4.0%       +0.5pts
    Non-life combined ratio18                     105.0%       93.7%     +11.3pts       105.7%      92.6%      +13.1pts
    Total investment results19                      37.0        20.9       +77.0%        104.2       73.1        +42.5%
    Segment income                                  18.9        50.8       -62.8%         27.8      160.6        -82.7%
    Retention ratio20                              88.7%       88.4%      +0.3pts        91.0%      92.4%       -1.4pts
   ---------------------------------------------------------------------------------------------------------------------

    Specialty Lines
   ---------------------------------------------------------------------------------------------------------------------
    Gross premiums written                         506.9       543.5        -6.7%      1,577.3    1,532.3         +2.9%
    Net premiums written                           458.3       474.7        -3.5%      1,473.9    1,405.6         +4.9%
    Net premiums earned                            478.3       408.2       +17.2%      1,395.2    1,231.7        +13.3%
    Non-life loss ratio15                         105.4%       72.3%     +33.1pts       105.7%      78.0%      +27.7pts
    Non-life underwriting expense ratio16          18.9%       21.5%      -2.6pts        20.0%      20.7%       -0.7pts
    Non-life administration expense ratio17         3.9%        4.0%      -0.1pts         3.5%       4.0%       -0.5pts
    Non-life combined ratio18                     128.2%       97.8%     +30.4pts       129.2%     102.7%      +26.5pts
    Total investment results19                      52.7        28.0       +88.2%        142.8       96.5        +48.0%
    Segment (loss) income                          -81.2        34.1         n.m.       -266.9       56.3          n.m.
    Retention ratio20                              90.4%       87.3%      +3.1pts        93.4%      91.7%       +1.7pts
   ---------------------------------------------------------------------------------------------------------------------

    Life & Health Reinsurance
   ---------------------------------------------------------------------------------------------------------------------
    Gross premiums written                         119.0        82.7       +43.9%        383.7      305.5        +25.6%
    Net premiums written                           114.3        73.8       +54.9%        357.6      286.1        +25.0%
    Net premiums earned                            113.5        87.5       +29.7%        339.3      273.6        +24.0%
    Underwriting expense ratio Life &              20.1%       16.8%      +3.3pts        21.9%      19.9%       +2.0pts
    Health21
    Administration expense ratio Life &             4.9%        6.4%      -1.5pts         4.6%       3.9%       +0.7pts
    Health22
    Total investment results19                       7.6         4.0       +90.0%         19.8       13.8        +43.5%
    Segment income (loss)                            5.7       -14.8         n.m.         11.6      -13.4          n.m.
    Retention ratio20                              96.1%       89.2%      +6.9pts        93.2%      93.6%       -0.4pts
   ---------------------------------------------------------------------------------------------------------------------
    Corporate Center
   ---------------------------------------------------------------------------------------------------------------------
    Operating and administration expenses           -8.2       -8.1        +1.2%         -25.1      -24.3         +3.3%
   ---------------------------------------------------------------------------------------------------------------------


---------------

15   Non-life loss ratio is defined as losses and loss adjustment expenses
     divided by net premiums earned.

16   Non-life underwriting expense ratio is defined as underwriting acquisition
     costs divided by net premiums earned.

17   Non-life administration expense ratio is defined as other operating and
     administration expenses divided by net premiums written.

18   The non-life combined ratio is defined as non-life loss ratio (to premiums
     earned) plus non-life underwriting expense ratio (to premiums earned) plus
     non-life administration expense ratio (to premiums written).

19   Total investment results are defined as net investment income plus net
     realized capital gains (losses).

20   Retention ratio is defined as net premiums written divided by gross
     premiums written.

21   Life & Health underwriting expense ratio is defined as underwriting
     acquisition costs divided by net premiums earned.

22   Life & Health administration expense ratio is defined as other operating
     and administration expenses divided by net premiums written.

                                       13




                                   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 29, 2004

                                       14