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 April, 2007

                              CONVERIUM HOLDING AG
                 (Translation of registrant's name into English)

                                 Dammstrasse 19
                                   CH-6301 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






Alert
Converium Holding Ltd, Zug



Zug, Switzerland - 4 April 2007 - Converium informs its shareholders of
incorrect information regarding Converium in today's SCOR presentation

Today's presentation by SCOR included information which could lead Converium's
shareholders to false conclusions. Some of Converium's financial targets
presented in the SCOR communication were factually incorrect or incomplete.

Paolo De Martin, Chief Financial Officer of Converium, comments: "We urge our
shareholders to carefully review SCOR's analysis concerning Converium. Our
return on equity target is 14% over the cycle, for the full year and beyond
2009, and not just for 2009, as erroneously stated by SCOR. We target a long
term S&P capital adequacy ratio of 140%, which is well above the minimum
security level required for an A- rating. This target already includes the
anticipated USD 300 million of funds to be returned to shareholders in 2007. In
addition, Converium intends to achieve a dividend payout-ratio of 25%-35%, and
not 0%-35% as suggested by SCOR."

Paolo De Martin added: "We would like to reiterate the hostile nature of SCOR's
actions. The hostility of the bid has the potential to destroy substantial
value."

Converium recommends that shareholders consult Converium's documentation for
Converium related details.



Enquiries





Beat W. Werder                       Marco Circelli                       Inken Ehrich

Head of Public Relations             Head of Investor Relations           Investor Relations Specialist



                                                                    
beat.werder@converium.com            marco.circelli@converium.com         inken.ehrich@converium.com

Phone:  +41 (0) 44 639 90 22         Phone:  +41 (0) 44 639 91 31         Phone:  +41 (0) 44 639 90 94

Fax:    +41 (0) 44 639 70 22         Fax:    +41 (0) 44 639 71 31         Fax:    +41 (0) 44 639 70 94




About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs about 500
people in 15 offices around the globe and is organized into three business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance. Converium has an "A-" ("strong") financial strength rating
(outlook stable) from Standard & Poor's and a "B++" financial strength rating
(outlook positive) from A.M. Best Company.




Important Disclaimers

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 `seek to', `expects', `aims' `should continue',
`believes', `anticipates', `estimates' and `intends'. The specific
forward-looking statements cover, among other matters, our combined ratio,
return on equity and premium volume and expense reduction targets, our plans to
use capital more efficiently and to return capital to shareholders, the
reinsurance market, the Company's operating results, the Company's dividend
policy, the prospects for improving our results, investment yield and market
share. 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
whether we are able to secure an upgrade of our financial strength ratings; our
ability to refinance our outstanding indebtedness and increase our use of hybrid
capital; uncertainties of assumptions used in our reserving process; risk
associated with implementing our business strategies and our capital improvement
measures; 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; our
ability to expand into emerging markets; our ability to enter into strategic
investment partnerships; 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; our ability to regain past customers following any
rating upgrades and the resolution 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 U.S.
Securities and Exchange Commission (including, but not limited to, our Annual
Report on Form 20-F filed 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.




Additional information and where to find it:

In connection with the offer by SCOR, Converium expects to file a
solicitation/recommendation statement with the Securities and Exchange
Commission (the "SEC"). Investors and security holders are strongly advised to
read these documents when they become available because they will contain
important information about the tender offer and the proposed merger. Copies of
the solicitation/recommendation statement will be available free of charge at
the SEC's web site at www.sec.gov, or at Converium's website at
www.converium.com.











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: March 6, 2007