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, 2006

                              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 - 3 October 2006 - Converium agrees a collateral reduction on
its letter of credit facility

Converium has reached an agreement with its counter-party banks to reduce the
level of collateral requirement on its USD 1.6 billion letter of credit
facility. As a result of the reduced level of collateral Converium will free up
around USD 110 million of assets on its balance sheet.

On 16 August 2006 Converium announced the conclusion of an agreement for an
uncollateralized USD 250 million letter of credit facility with a leading
European banking group.

Paolo De Martin, Chief Financial Officer, commented: "The reduced collateral
requirement is a considerable success for Converium. The agreement will provide
us with additional degrees of freedom in managing our assets."


                                  * * * * * * *


Enquiries:

Dr. Kai-Uwe Schanz Marco Circelli
Chief Communication &                        Head of Investor Relations &
Corporate Development Officer                Market Research
kai-uwe.schanz@converium.com                 marco.circelli@converium.com
----------------------------                 ----------------------------

Phone:         +41 (0) 44 639 90 35          Phone:         +41 (0) 44 639 91 31
Fax:           +41 (0) 44 639 70 35          Fax:           +41 (0) 44 639 71 31


About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs about 600
people in 18 offices around the globe and is organized into four business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance, which are based principally on ongoing global lines of
business, as well as the Run-Off segment, which primarily comprises the business
from Converium Reinsurance (North America) Inc., excluding the US originated
aviation business portfolio. Converium has a "BBB+" rating (outlook positive)
from Standard & Poor's and a "B++" rating (outlook positive) from A.M. Best
Company.



Important Disclaimer

This document contains forward-looking statements as defined in the US 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 'seek to', 'expects', 'should continue', 'believes',
'anticipates', 'estimates' and 'intends'. The specific forward-looking
statements cover, among other matters, the Company's internal review and related
restatement, the reinsurance market, the Company's operating results, certain
financial guidance such as the corporate tax rate, the reduction of CRNA net
liabilities , administration expense ratio and Corporate Center costs, the
rating environment, the prospect for improving results and expense reductions.
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 the impact of our
ratings downgrade or a further lowering or loss of one of our financial strength
ratings; the impact of the restatement on our ratings and client relationships;
uncertainties of assumptions used in our reserving process; risk associated with
implementing our business strategies and our capital improvement measures and
the run-off of our North American business; cyclicality of the reinsurance
industry; the occurrence of natural and man-made catastrophic events with a
frequency or severity exceeding our estimates; acts of terrorism and acts of
war; changes in economic conditions, including interest and currency rate
conditions that could affect our investment portfolio; actions of competitors,
including industry consolidation and development of competing financial
products; a decrease in the level of demand for our reinsurance or increased
competition in our industries or markets; a loss of our key employees or
executive officers without suitable replacements being recruited within a
suitable period of time; our ability to address material weaknesses we have
identified in our internal control environment; political risks in the countries
in which we operate or in which we reinsure risks; the passage of additional
legislation or the promulgation of new regulation in a jurisdiction in which we
or our clients operate or where our subsidiaries are organized; the effect on us
and the insurance industry as a result of the investigations being carried out
by the US Securities and Exchange Commission, New York's Attorney General and
other governmental authorities; changes in our investment results due to the
changed composition of our invested assets or changes in our investment policy;
failure of our retrocessional reinsurers to honor their obligations or changes
in the credit worthiness of our reinsurers; our failure to prevail in any
current or future arbitration or litigation; and extraordinary events affecting
our clients, such as bankruptcies and liquidations, and other risks and
uncertainties, including those detailed in the Company's filings with the US
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.

www.converium.com
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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.


                                               CONVERIUM HOLDING AG




                                               By:  /s/ Inga Beale
                                                    --------------
                                                    Name:  Inga Beale
                                                    Title: CEO




                                               By:  /s/ Christian Felderer
                                                    ----------------------
                                                    Name: Christian Felderer
                                                    Title: General Legal Counsel



Date: October 9, 2006