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

Baarerstrasse 8

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 þ          Form 40-F o

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 o          No þ

If “Yes” is marked, indicate the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-Not Applicable

On October 4, 2004, a securities class action lawsuit was filed against us and certain of our officers in the United States District Court for the Southern District of New York. The action is purportedly brought as a class action on behalf of persons who purchased our securities between December 11, 2001 and July 20, 2004. The complaint asserts claims for violations of Section 10(b) of the Securities Exchange Act of 1934 and Rule 10b-5 promulgated thereunder and Section 20(a) of the Securities Exchange Act of 1934, alleging we misrepresented or failed to disclose that we maintained inadequate loss reserves in our North American operations, that, contrary to representation, we did not establish adequate loss reserves to cover claims by policyholders of North American operations, that our announced reserve increases prior to July 20, 2004 were insufficient, and, as a result, our earnings and assets were material overstated. The plaintiffs are seeking unspecified compensatory damages, attorney’s fees and expert fees. Three other plaintiffs’ law firms have also announced that they have filed class action suits; however we have not yet received copies of these complaints. Based on our review of press releases issued by the plaintiffs’ attorneys, we believe these suits assert substantially similar claims. It is also possible that additional suits alleging similar claims may be filed in the future. We intend to defend the lawsuits vigorously. The actions are in the preliminary phases; thus, the timing and outcome of these matters are not currently predictable. An unfavorable outcome could have a material effect on our financial condition, results of operations and cash flows.

About Converium

Converium is an independent international multi-line reinsurer known for its innovation, professionalism and service. Today Converium employs approximately 850 people in 23 offices around the globe and is organized into three business segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance. Converium AG has a “BBB” rating (watch positive) from Standard & Poor’s and a “B++” (outlook stable) rating from A.M. Best Company.

Important Disclaimer

This document contains forward-looking statements as defined in the U.S. Private Securities Litigation Reform Act of 1995. It contains forward-looking statements and information relating to the Company’s financial condition, results of operations, business, strategy and plans, based on currently available information. These statements are often, but not always, made through the use of words or phrases such as ‘expects’, ‘should continue’, ‘believes’, ‘anticipates’, ‘estimates’ and ‘intends’. The specific forward-looking statements cover, among other matters, the reinsurance market, the outcome of insurance regulatory reviews, the Company’s operating results, the rating environment and the prospect for improving results, the amount of capital required and impact of its capital improvement measures, including the restructuring of our U.S. business and its reserve position. Such statements are inherently subject to certain risks and uncertainties. Actual future results and trends could differ materially from those set forth in such statements due to various factors. Such factors include general economic conditions, including in particular economic conditions; the frequency, severity and development of insured loss events arising out of catastrophes, as well as man-made disasters; the outcome of our regular quarterly reserve review, our ability to raise capital and the success of our capital improvement measures, the ability to obtain applicable regulatory approval for our capital improvement measures, the ability to exclude and to reinsure the risk of loss from terrorism; fluctuations in interest rates; returns on and fluctuations in the value of fixed-income investments, equity investments and properties; fluctuations in foreign currency exchange rates; rating agency actions; changes in laws and regulations and general competitive factors, and other risks and uncertainties, including those detailed in the Company’s filings with the U.S. Securities and Exchange Commission and the SWX Swiss Exchange. The Company does not assume any obligation to update any forward-looking statements, whether as a result of new information, future events or otherwise.

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