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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 June 2003

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

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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.

Date: June 4, 2003

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Converium Holding Ltd, Zug

Zug, Switzerland — June 4, 2003 — The United Kingdom Financial Services Authority (“FSA”) grants Converium Insurance (UK) Ltd permission to conduct the business of insurance in the class of general liability business in the United Kingdom.

Converium Insurance (UK) Ltd is a wholly owned subsidiary of Converium Holding (UK) Ltd, which in turn is a 100% subsidiary of Converium AG, Zurich. The company has been established for the purpose of supporting and strengthening Converium Group’s joint ventures and strategic business relationships, and will not operate as a general insurer.

Converium Insurance (UK) Ltd has had its application approved at an initial capitalization level of £ 50 million.

Dirk Lohmann, Group CEO Converium, said:

“Our core business is and remains reinsurance. Converium Insurance (UK) Ltd will allow us greater control over our destiny in conjunction with our existing joint ventures and strategic business relationships (e.g. The Medical Defence Union Ltd, London) where Converium requires direct insurance issuing capability.”

Converium is an independent top-ten reinsurance group. Converium Holding Ltd was listed on the SWX Swiss Exchange and the New York Stock Exchange on December 11, 2001. Converium’s 100% flotation was earmarked as the largest reinsurance IPO ever worldwide and the largest corporate IPO in Switzerland since 1998.

Today the Group ranks among the top ten professional reinsurers and employs more than 800 people in 22 offices around the globe. Converium has an “A” rating (stable outlook) both from Standard & Poor’s and A.M. Best Company.

Converium is organized around four business segments consisting of three non-life operations, Converium Zurich, Converium North America and Converium Cologne, as well as Converium Life.

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