Exhibit 13.1

CERTIFICATION OF TERRY G. CLARKE, CHIEF EXECUTIVE OFFICER OF CONVERIUM
HOLDING AG, PURSUANT TO SECTION 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT
TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Converium Holding AG (the “Company”) on Form 20-F for the period ending December 31, 2004, as filed with the Securities and Exchange Commission on the date here of (the “Report”), the undersigned hereby certifies that to the best of my knowledge:

1.	The Report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934; and
2.	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: June • , 2005

By:	/s/ Terry G. Clarke
Terry G. Clarke Chief Executive Officer, Converium Holding AG