Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days.

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Table of Contents

TABLE OF CONTENTS

(Please Note: Table of Contents not converted due to Hot Links in HTML.)

PRESENTATION OF INFORMATION

In this annual report on Form 20-F, unless the context otherwise requires, “Converium,” “we,” “us,” and “our” refer to Converium Holding AG and our consolidated entities. Please refer to the glossary beginning on page G-1 for definitions of selected insurance and reinsurance terms.

We publish our financial statements in US dollars, and unless we note otherwise, all amounts in this annual report are expressed in US dollars. As used herein, references to “US dollars,” “dollars” or “$” and “cents” are to US currency, references to “Swiss francs” or “CHF” are to Swiss currency, references to “yen” or “Japanese yen” are to Japanese currency, references to “British pounds” or “£” are to British currency and references to “euro” or “€” are to the single European currency of the member states of the European Monetary Union at the relevant time.

CAUTIONARY NOTE REGARDING FORWARD-LOOKING STATEMENTS

This annual report contains certain forward-looking statements. Forward-looking statements are necessarily based on estimates and assumptions that are inherently subject to significant business, economic and competitive uncertainties and contingencies, many of which, with respect to future business decisions, are subject to change. These uncertainties and contingencies can affect actual results and could cause actual results to differ materially from those expressed in any forward-looking statements.

In particular, statements using words such as “expect,” “anticipate,” “intend,” “believe” or words of similar import generally involve forward-looking statements. This annual report includes a number of forward-looking statements, including the following:

In light of the risks and uncertainties inherent in all future projections, the inclusion of forward-looking statements should not be considered a representation by us that our objectives or plans will be achieved. Numerous factors could cause our actual results to differ materially from those in the forward-looking statements, including factors set forth in “Item 3. — Key Information — D. Risk Factors” and the following:

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The factors listed above should not be construed as exhaustive. We cannot assess the impact of each factor on our business or the extent to which any factor, or combination of factors, may cause actual results to differ materially from those described in any forward-looking statements. Except as otherwise required by law, we undertake no obligation to publicly release any future revisions we may make to forward-looking statements to reflect subsequent events or circumstances or to reflect the occurrence of unanticipated events.

We have made it a policy not to provide any quarterly or annual earnings guidance and we will not update any past outlook for full year earnings. We will, however, provide investors with a perspective on our value drivers, our strategic initiatives and those factors critical to understanding our business and operating environment.

PART I

ITEM 1. IDENTITY OF DIRECTORS, SENIOR MANAGEMENT AND ADVISERS

     Not applicable.

ITEM 2. OFFER STATISTICS AND EXPECTED TIMETABLE

     Not applicable.

ITEM 3. KEY INFORMATION

A. SELECTED FINANCIAL AND OTHER DATA

We have prepared our financial statements included in this annual report in accordance with accounting principles generally accepted in the United States, or US GAAP. The following financial data highlights selected information that is derived from our financial statements as of and for the years ended December 31, 2004, 2003, 2002, 2001 and 2000.

Converium was formed as a result of the divestiture of the former “Zurich Re” business of Zurich Financial Services in December 2001. For a description of the transactions that led to the divestiture, which we refer to herein as the “Formation Transactions,” see “Item 4. — Information on the Company — A. History and Development of the Company”. The financial statements are presented as if we had been a separate entity for all periods presented and include estimates related to the

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allocation to Converium of costs of Zurich Financial Services’ corporate infrastructure prior to the Formation Transactions. We believe that these allocations are reasonable. However, this financial information may not be indicative of our future performance and does not necessarily reflect what our financial position and results of operations would have been had we operated as a stand-alone entity during the periods covered.

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Dividends

For a discussion of our dividend policy, see “Item 8. — Financial Information — A. Consolidated Statements and Other Financial Information — Dividends and Dividend Policy”.

B. CAPITALIZATION AND INDEBTEDNESS

     Not applicable.

C. REASONS FOR THE OFFER AND USE OF PROCEEDS

     Not applicable.

D. RISK FACTORS

Risks relating to Converium and the reinsurance industry

If we do not successfully implement our new strategy or if such strategy is not effective, it could have a material adverse effect on our business, financial condition, results of operations and cash flows

Early in 2004 Converium adopted a comprehensive corporate strategy intended to build on its accomplishments since the Company was formed in 2001. Later in the year the Global Executive Committee adjusted the business model in response to adverse developments with respect to our reserves, which led to the decision to cease underwriting in North America, and to the subsequent downgrading by Standard & Poor’s and A.M. Best Company of Converium AG’s insurer financial strength ratings to “BBB+” and “B++”, respectively, and the downgrading of certain of our subsidiaries. See “Item 4. Business Overview – Overview” and “– Our Strategy”

There can be no assurance, however, that we will be able to successfully implement our new strategy or that such strategy will be effective. The implementation and the effectiveness of this strategy are based on a certain number of assumptions (including continued client acceptance outside the United States) and factors that are not under our control. If economic conditions, our competitive position, our rating level or our financial condition are not consistent with these assumptions or our objectives, or if the measures envisaged by the new strategy are insufficient, it is possible that our strategy would fail and

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that we would not achieve our objectives. In this case, our business and financial condition could deteriorate and new measures would need to be devised.

The run-off of our North American business subjects us to particular risks

We have ceased the writing of substa;ntially all new business in North America and have decided to take the following additional steps with respect to our North American business:

By placing CRNA into run-off, it became subject to increased regulatory scrutiny and our plans are subject to the approval of state insurance regulators in the United States. Although we cannot predict the effect of any future regulatory orders or proceedings, state insurance regulatory agencies in the United States have broad power to institute proceedings and seek consensual orders to, among other things, take possession of the property of an insurer and to conduct the business of such insurer under rehabilitation and liquidation statutes. On September 7, 2004, we entered into a voluntary letter of understanding with the Connecticut Department of Insurance (the “Department”) pursuant to which CRNA is prevented from taking a number of actions, including the payment of any dividends, without the approval of the Department. The requirements stated in this letter will remain in effect until March 15, 2006, at which time the Department will reassess the financial condition of CRNA. Other insurance regulators may seek similar agreements or initiate other proceedings or actions. See Note 22 to our 2004 consolidated financial statements.

The ratings downgrades as well as our decision to place CRNA into runoff have triggered “special funding” clauses in CRNA’s and CINA’s reinsurance and insurance contracts. These clauses require CRNA and CINA to provide collateral for their payment obligations under those contracts. In addition, state insurance regulators may request that CRNA and CINA make special deposits in their states or provide collateral for contracts issued to residents of their states. The approval of the Department is required before we provide collateral that is not contractually required. If the Department withholds its approval, state insurance regulators that requested special deposits or collateral not contractually required, could seek to revoke CRNA’s or CINA’s licenses or initiate proceedings to take possession of the property, business and affairs of CRNA or CINA in the respective states.

Additionally, there can be no assurances that commutations may be available on terms that are appropriate to our decision to run-off our North American business or that are economically acceptable.

The run-off of our North American business could ultimately have a negative impact on the perception of our franchise in the reinsurance market. As a result, we may not be able to retain personnel with the appropriate skill sets for the tasks associated with our run-off.

There also can be no assurance that we will be able to successfully write the lines that we currently contemplate from our operation in Zurich using Converium AG. Although we believe that Converium AG holds the necessary licenses to write these lines of business as a non-admitted reinsurer, Converium AG may require increased capitalization to successfully do so and we may in the future be unable to provide the necessary capitalization.

Our ratings downgrades during 2004, and any further downgrades, of our ratings could have a material adverse effect on our business, financial condition, result of operations or cash flows

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Based on the developments of the latter part of 2004, both Standard & Poor’s Ratings Services and A.M. Best lowered their respective ratings of Converium, including its subsidiaries. Following Converium Holding AG’s successful 2004 rights offering, some of the ratings were subsequently raised, although not to the levels preceding the reserving action.

Currently, Standard & Poor’s long-term counterparty credit and insurer financial strength rating of Converium AG is “BBB+” (downgraded from a rating of “A”). For Converium Rückversicherung (Deutschland) AG and Converium Insurance (UK) Ltd., the insurer financial strength rating is currently “BBB+” (downgraded from a rating of “A”). Based on our announcement to place CRNA into run-off, the long-term counterparty credit and insurer financial strength ratings were downgraded to “R” (downgraded from a rating of “A”). In addition, Standard & Poor’s issued a long-term counterparty credit and senior unsecured debt ratings of “BB+” for Converium Holdings (North America) Inc. (downgraded from a rating of “BBB”). The current junior subordinated debt rating on Converium Finance S.A. is “BBB-” (downgraded from a rating of “BBB+”). All ratings have been assigned a stable outlook by Standard and Poor’s.

Currently, A.M. Best’s financial strength rating of Converium AG, Converium Rückversicherung (Deutschland) AG and Converium Insurance (UK) Ltd. is “B++” (downgraded from a rating of “A”) and its issuer credit rating for all three entities is “bbb+” (downgraded from a rating of “a”). CINA is currently assigned a financial strength rating of “B” (downgraded from a rating of “A”) and an issuer credit rating of “bb” (downgraded from a rating of “a” ). For Converium Finance S.A. the current issuer credit rating is “bb+” (downgraded from a rating of “bbb”) and the junior subordinated debt rating is “bbb-” (downgraded from a rating of “bbb+”). All ratings have been assigned a stable outlook by A.M. Best. Following our announcement of our intention to place CRNA into run-off, the financial strength rating was downgraded to “B-” from “A” and the issuer credit rating to “bb-” from “a”. For Converium Holdings (North America) Inc. the issuer credit as well as the senior unsecured debt ratings were lowered to “b-” from “bbb-”.

Claims-paying ability and financial strength ratings are a key factor in establishing the competitive position of reinsurers. Given that our main competitors hold higher ratings than us, our current ratings may significantly hinder our competitive position. Our ratings may not satisfy the criteria required by some of our clients and brokers or the requirements under our existing reinsurance contracts, which would negatively impact new business and adversely affect our ability to compete in our markets. The reduction in our ratings might result in a significant decline in our premium volume in 2005.

Additionally, contracts representing approximately one-third of our total ultimate premiums with our cedents contain termination provisions relating to a downgrade of our ratings. As a result of recent downgrades, the termination provisions of many of our contracts have been triggered giving rise to a right of termination in favor of the cedent that allows the cedent to terminate the contract on a prospective basis from the date of termination. Alternatively, the cedent and the reinsurer may renegotiate the terms of the contract. In renegotiating the contract terms, the cedent will usually require the reinsurer to post collateral to secure the obligations under the contract, which would have negative financial implications for us, as reinsurer. Moreover, limitations on our ability to post collateral could force us to renegotiate the contracts on significantly less favorable terms than if we were able to post collateral or lead to the termination of the contracts by cedents. Our recent ratings downgrades may make cedents less inclined to renegotiate the contracts at all, and has led to an increased rate of terminations.

The ratings downgrades in 2004 have also made it more difficult to renew our existing contracts, without regards to whether or not the existing contract contains a ratings trigger. We expect approximately one third of our existing Non-Life contracts not to be renewed in 2005 which is partially attributable to the ratings downgrade in 2004. This will, in turn, lead to a corresponding reduction our premiums written.

The pool members’ agreement with respect to GAUM provides that if a member of the pool has its financial strength rating downgraded below BBB+ by Standard & Poor’s Rating Service it may be served with a notice terminating its membership in the pool upon approval by the committee of representatives of the pool. Converium believes that no formal action was taken by the pool membership committee to serve a notice terminating Converium’s pool membership. However, the committee has discussed Converium’s downgrade and sought to take action to limit its rights to dispute the validity of any notice served on Converium. The continuation of Converium’s membership at its current rating was likely to be conditional upon its entering fronting arrangements acceptable to other pool members in a timely fashion and thereafter maintaining such arrangements. Converium entered into formal written fronting arrangements, preventing the termination of its membership in the pool. The fronting arrangements require Converium to post collateral to secure its reinsurance obligations under the fronting arrangements. If Converium’s membership were to be reduced to less than a 5% share, it would not be permitted to participate in future pool business and would have to collateralize by way of a letter of credit its obligations under the business written by the pool in its name prior to its termination. If Converium’s membership were terminated, it also may be required to sell its shares in GAUM at an amount less than its carrying value. In 2004, this business generated $289.0 million of gross premiums written. See Notes 3, 8 and 18 to our 2004 consolidated financial statements for additional information on GAUM.

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There can be no assurance that our responses to the adverse developments of 2004 will enable us to improve or maintain our ratings.

Our loss reserves may not adequately cover future losses and benefits

Our loss reserves may prove to be inadequate to cover our actual losses and benefits experience. To the extent loss reserves are insufficient to cover actual losses, loss adjustment expenses or future life benefits, we would have to add to these loss reserves and incur a charge to our earnings which could have a material adverse effect on our financial condition, results of operations or cash flows.

As of December 31, 2004 we had $8,776.9 million of gross reserves and $7,641.5 million of net reserves for losses and loss adjustment expenses. If we underestimated these net reserves by 5%, this would have resulted in an additional $382.1 million of incurred losses and loss adjustment expenses, before income taxes, for the year ended December 31, 2004.

Loss reserves do not represent an exact calculation of liability, but rather are estimates of the expected cost of the ultimate settlement of losses. All of our loss reserve estimates are based on actuarial and statistical projections at a given time, facts and circumstances known at that time and estimates of trends in loss severity and other variable factors, including new concepts of liability and general economic conditions. Changes in these trends or other variable factors could result in claims in excess of our loss reserves.

Unforeseen losses, the type or magnitude of which we cannot predict, may emerge in the future. These additional losses could arise from newly acquired lines of business, changes in the legal environment, or extraordinary events affecting our clients such as reorganizations and liquidations or changes in general economic conditions. We continue to conduct pricing, loss reserving, claims and underwriting studies for many casualty lines of business, including those in which preliminary loss trends are noted. Converium has experienced significant adverse development, predominantly in its US casualty reinsurance lines, for the last several years. Since 2000, Converium has recorded a total of $868.2 million of additional net provisions on prior years’ non-life business (2000: $65.4 million: 2001: $123.6 million; 2002: $148.5 million; 2003: $(31.3) million; and 2004: $562.0 million).

During early 2004, Converium announced that reported losses from prior year US casualty business had exceeded expected loss emergence and that the volatility of longer-tail risks was likely to persist for some time. This adverse loss-reporting trend continued and accelerated into mid-2004 and prompted Converium to initiate additional reviews of its US business from an integrated underwriting, claims and actuarial perspective in order to examine the adequacy of prior years’ provisions. In addition, in order to obtain an external review of our overall reserve position, we commissioned the actuarial consulting firm Tillinghast-Towers Perrin to perform an independent actuarial review of our non-life loss and allocated loss adjustment expense reserves as of June 30, 2004 in respect of the Zurich and New York originated businesses. The outcome of these in-depth internal and external reviews resulted in an aggregate strengthening of prior years’ non-life loss reserves by $562.0 million for the year ended December 31, 2004. This action was taken in response to the continued adverse loss emergence due to increased claims reporting activity from clients relating to US Casualty business written from 1997 to 2001 as well as deterioration from European non-proportional motor business written in recent years. While we believe that we have sought to fully address this issue through our reserving actions, volatility is nonetheless expected to persist for some time.

In addition, because we, like other reinsurers, do not separately evaluate each of the individual risks assumed under reinsurance treaties, we are largely dependent on the original underwriting decisions made by ceding companies. We are subject to the risk that our ceding companies may not have adequately evaluated the risks to be reinsured and that the premiums ceded to us may not adequately compensate us for the risks we assume.

We may be unable to meet the collateral requirements necessary for our business

As a result of the 2004 downgrades of our ratings, we have been and may continue to be required to post additional collateral in order to be accepted as sufficiently secure to write certain business. In addition, there has been a trend in our industry for a ceding company to require reinsurers to post collateral in excess of applicable regulatory collateral requirements in order to secure the reinsurers’ obligation to pay claims. We may have greater limitation on our ability to post collateral than some of our competitors. If we are unable to meet the collateral requirements of ceding companies, we would be limited in our business opportunities, which could have a material adverse effect on our financial condition, results of operations or cash flows.

In November 2004, Converium AG obtained a $1.6 billion, three-year syndicated letter of credit facility (the “Syndicated Letter of Credit Facility”) from various banks. The facility provides Converium’s non-US operating companies with a $1.5 billion capacity for issuing letters of credit and a $100.0 million liquidity reserve. It replaces the existing $900.0 million letter of credit facility that was signed in July 2003. As of December 31, 2004, Converium had outstanding letters of credit of

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$955.7 million under the facility. Investments of $1,060.8 million are pledged as collateral related to the Syndicated Letter of Credit Facility. However, Converium must comply with various financial covenants in order to avoid default under the agreement. In an event of default the majority lenders may cancel the total commitment and/or may declare that all amounts outstanding may be immediately due and payable and that full cash cover in respect of each letter of credit is immediately due and payable.

In addition to the Syndicated Letter of Credit Facility, other irrevocable letters of credit of $639.1 million were outstanding at December 31, 2004 to secure certain assumed reinsurance contracts. Investments of $704.7 million are pledged as collateral related to certain of these letters of credit.

See “Item 3. — Key information — D. Risk factors – Ratings changes” for information on collateral requirements related to GAUM and Notes 3, 8 and 18 to our 2004 consolidated financial statements. See “Item 3. — Key information — D. Risk factors – Run-off of our North American business” for information on collateral requirements related to our North American operations.

We are subject to the cyclicality of the reinsurance industry

The insurance and reinsurance industries, particularly the non-life market, are cyclical. Historically, operating results of reinsurers have fluctuated significantly because of volatile and sometimes unpredictable developments, many of which are beyond their direct control. These developments include:

As a result, the reinsurance business historically has been characterized by periods of intense price competition due to excessive underwriting capacity as well as periods when shortages of underwriting capacity permitted attractive premium levels. We expect to continue to experience the effects of cyclicality, which could have a material adverse effect on our business, financial condition, results of operations or cash flows.

As a result of ongoing investigations of the insurance and reinsurance industry and non-traditional insurance products, we are conducting an internal review and analysis of certain of our reinsurance transactions.

Ongoing investigations of the insurance and reinsurance industry and non-traditional insurance and reinsurance products are being conducted by U.S. regulators and governmental authorities, including the Securities and Exchange Commission and the New York Attorney General.

On March 8, 2005, MBIA Inc. (“MBIA”) issued a press release stating that MBIA’s audit committee undertook an investigation to determine whether there was an oral agreement with MBIA under which MBIA would replace Axa Re Finance as a reinsurer to CRNA by no later than October 2005. The press release stated that it appears likely that such an agreement or understanding with Axa Re Finance was made in 1998. Thereafter, on April 19, 2005, CRNA received subpoenas from the U.S. Securities and Exchange Commission and the Office of the New York Attorney General seeking documents related to certain transactions between CRNA and MBIA.

In view of the industry investigations and the events relating to MBIA described above, we have engaged counsel to assist us in a review and analysis of certain of our reinsurance transactions, including the MBIA transactions. We are fully cooperating with the governmental authorities in connection with their investigation. The impact of our ongoing review and analysis and the ongoing regulatory investigations on us is uncertain, and there can be no assurance as to whether or not the outcome of such investigations will have a material impact on Converium.

Our exposure to catastrophic events, both natural and man-made, may cause large losses

A catastrophic event or multiple catastrophic events may cause large losses and could have a material adverse effect on our business, financial condition, and results of operations or cash flows. Natural catastrophic events to which we are exposed include windstorms, hurricanes, earthquakes, tornadoes, severe hail, severe winter weather, floods and fires, and are inherently unpredictable in terms of both their occurrence and severity. For example, in 1999 and 2002, the reinsurance industry suffered losses from unusually strong and widespread windstorms and flooding in Europe. These events adversely affected our results. In 2004, the reinsurance industry suffered losses from hurricanes in the United States and the Caribbean, the Japanese typhoons and the tsunami in the Indian Ocean.

We are also exposed to man-made catastrophic events, which may have a significant adverse impact on our industry and on us. It is possible that both the frequency and severity of man-made catastrophic events will increase.

As a result, claims from natural or man-made catastrophic events could cause substantial volatility in our financial results for any period and adversely affect our financial condition, results of operations or cash flows. Our ability to write new business could also be impacted. We believe that increases in the value and geographic concentration of insured property and the effects of inflation will increase the severity of claims from catastrophic events in the future.

The extent of our losses from catastrophic occurrences is a function of the total insured amount of losses our clients incur, the number of our clients affected, and the frequency and severity of the events. In addition, depending on the nature of the loss, the speed with which claims are made and settled, and the terms of the policies affected, we may be required to make large claims payments upon short notice. We may be forced to fund these obligations by liquidating investments unexpectedly and in unfavorable market conditions, or by raising funds at unfavorable costs, both of which could adversely affect the results of our operations.

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Our efforts to protect ourselves against catastrophic losses, such as the use of selective underwriting practices, the purchasing of reinsurance (which, when bought by a reinsurer such as Converium, is known as retrocessional reinsurance) and the monitoring of risk accumulations may not prevent such occurrences from adversely affecting our profitability or financial condition.

The majority of the natural catastrophe reinsurance we write relates to exposures within the United States, Europe and Japan. Accordingly, we are exposed to natural catastrophic events, which affect these regions, such as US hurricane, California earthquake, European windstorm and Japanese earthquake events. Our estimated potential losses, on a probable maximum loss basis, before giving effect to our retrocessional protection, for 2004, were managed to a self- imposed maximum gross event limit of $500 million for a 250-year return period loss. See “Item 9. — The Offer and Listing — D. Material Contracts”.

Terrorist attacks, national security threats, military initiatives and political unrest could result in the payment of material insurance claims and may have a negative effect on our business

Threats of terrorist attacks, national security threats, military initiatives and political unrest have had and may continue to have a significant adverse effect on general economic, market and political conditions, increasing many of the risks in our businesses. We cannot predict the long-term effects of terrorist attacks, threats to national security, military initiatives and political unrest on our businesses at this time.

Although Zurich Financial Services, through its subsidiaries, has agreed to arrangements that cap our exposure for losses and loss adjustment expenses arising out of the September 11th terrorist attacks at $289.2 million, net of retrocessional reinsurance recoveries, terrorist attacks and other man-made catastrophic events may have a material adverse effect on our business, financial condition or results of operations. For a discussion of the impact of the September 11th terrorist attacks on our business, see Note 9 to our 2004 consolidated financial statements.

If we are unable to achieve our investment objectives, our investment results may be adversely affected

Investment returns are an important part of our overall profitability, and fluctuations in the fixed income or equity markets could have a material adverse effect on our financial condition, results of operations or cash flows. For the years ended December 31, 2004 and 2003, net investment income and net realized capital gains accounted for 8.9% and 6.4% of our revenues, respectively. Our capital levels, ability to pay claims and our operating results substantially depend on our ability to achieve our investment objectives, which may be affected by general political and economic conditions that are beyond our control.

Fluctuations in interest rates affect our returns on fixed income investments, as well as the market values of, and corresponding levels of capital gains or losses on, the fixed income securities in our investment portfolio. Generally, investment income will be reduced during sustained periods of lower interest rates as higher yielding fixed income securities are called, mature or are sold and the proceeds reinvested at lower rates. During periods of rising interest rates, prices of fixed income securities tend to fall and realized gains upon their sale are reduced.

In addition, as described under “Formation transactions and relationship with Zurich Financial Services,” under the Quota Share Retrocession Agreement, the Funds Withheld Asset may be prepaid to us, in whole or in part, as of the end of any calendar quarter. In the event that the Funds Withheld Asset is prepaid, we would have to reinvest these assets in investments and we may not be able to invest them at yields comparable to those payable under the Quota Share Retrocession Agreement. To the extent we are not able to invest these funds at comparable yields, our investment income could be adversely affected.

Capital market fluctuations may adversely impact the value of our investments

We had a cash and investments portfolio of $8.5 billion as of December 31, 2004. As with any institutional investor with a similarly sized portfolio, Converium is exposed to the financial markets; in particular, an increase in interest rates, and a resulting decline in the market value of our fixed income securities, would adversely impact our shareholders’ equity.

General economic conditions can adversely affect the markets for interest-rate-sensitive securities, including the extent and timing of investor participation in such markets, the level and volatility of interest rates and, consequently, the value of fixed income securities. Interest rates are highly sensitive to many factors, including governmental monetary policies, domestic and international economic political conditions and other factors beyond our control.

We have historically invested and may continue to invest a portion of our assets globally in equity securities, which are generally subject to greater risks and more volatility than fixed income securities. General economic conditions, stock market

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conditions and many other factors beyond our control can adversely affect the equity markets and, consequently, the value of the equity securities we own.

Foreign exchange rate fluctuations may impact our financial condition, results of operation and cash flows

We publish our financial statements in US dollars. Therefore, fluctuations in exchange rates used to translate other currencies, particularly European currencies including the Euro, British pound and Swiss franc, into US dollars will impact our reported financial condition, results of operations and cash flows from year to year. These fluctuations in exchange rates will also impact the US dollar value of our investments and the return on our investments. For 2004, approximately:

were denominated in currencies other than the US dollar. For a discussion of the impact of material changes in foreign exchange rates on our shareholders’ equity, see “Item 11. — Quantitative and Qualitative Disclosures About Market Risk”.

As we will no longer be writing business from the United States, a smaller proportion of our business will be denominated in US dollars in the future. For a discussion of the impact of material changes in foreign exchange rates on our shareholders’ equity, see “Item 11. — Quantitative and Qualitative Disclosures About Market Risk”.

We may face competitive disadvantages in the reinsurance industry

The reinsurance industry is highly competitive. Some of our competitors may have greater financial or operating resources or offer a broader range of products or more competitive pricing than we do. Our ability to compete is based on many factors, including our overall financial strength and rating, geographic scope of business, client relationships, premiums charged, contract terms and conditions, products and services offered, speed of claims payment, reputation, experience and qualifications of employees and local presence. As a result of the recent ratings downgrades we expect to be in a less competitive position than we have been historically. We compete for reinsurance business in international reinsurance markets with numerous reinsurance and insurance companies, some of which have greater financial or other resources and most of which have higher financial strength ratings. We believe that our largest competitors include:

In addition, new companies have entered the reinsurance market and existing companies have raised additional capital to increase their underwriting capacity. Other financial institutions, such as banks, are also able to offer services similar to our

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own. We have also recently seen the creation of alternative products from capital market participants that are intended to compete with reinsurance products. We are unable to predict the extent to which these new, proposed or potential initiatives may affect the demand for our products or the supply and terms of risks that may be available for us to consider underwriting.

The loss of key employees and executive officers without suitable replacements being recruited within a suitable period of time could adversely affect us

Our ability to execute our business strategy is dependent on our ability to attract, develop and retain a staff of qualified underwriters and other key employees. Our senior management team includes a number of key personnel whose skills, experience and knowledge of the reinsurance industry constitute important elements of Converium’s competitive strengths. Certain of our key employees and executive officers have recently resigned. If additional executive officers or key employees leave their positions at Converium, even if we were able to find persons with suitable skills to replace them, our operations could be adversely affected. In addition, a strong financial position is important to us in order to retain and attract skilled personnel in the industry, especially underwriters with specific expertise in high-margin, non-commoditized specialty lines of business. If our current or future financial position does not allow us to do so, our operations could be adversely affected. See “Item 6. — Directors, Senior Management and Employees — A. Directors and Senior Management”.

In addition, one of the two material weaknesses identified within Converium’s internal control environment was the need to train or recruit suitably qualified individuals to fill the knowledge and experience gaps that have been identified within the financial accounting and reporting function. Although we are actively undertaking a recruitment search to identify and hire additional qualified staff and providing further training to existing staff to fill the knowledge and experience gaps within financial accounting and reporting, there can be no assurance that we will be able to do so. If we are unable to successfully recruit and train such staff we will be unable to remedy the material weakness.

We have identified two material weaknesses in our internal control environments; investor confidence and our share value may be adversely impacted if we are unable to remedy the material weaknesses.

As a foreign private issuer we are not currently subject to Section 404 of the Sarbanes-Oxley Act. However, in connection with our year-end audit and our Sarbanes-Oxley implementation project two ‘material weaknesses’ were identified within Converium’s internal control environment as at December 31, 2004. For purposes of Section 404 of the Sarbanes-Oxley Act, a ‘material weakness’ is a significant deficiency, or combination of significant deficiencies, that results in more than a remote likelihood that a material misstatement of the annual or interim financial statements will not be prevented or detected.

Two material weaknesses were identified within Converium’s financial accounting and reporting function. The first weakness identified was the need to train or recruit suitably qualified individuals to fill the knowledge and experience gaps caused by the departure of various key finance employees. The second weakness identified was the failure in the operation of key internal controls over the initiation of reinsurance and financial accounting data.

Converium is in the process of addressing these weaknesses by actively undertaking a recruitment search to identify and hire additional suitably qualified staff and by providing further training to existing staff in order to address the current knowledge and experience gaps within the financial accounting and reporting function. In addition, Converium is actively addressing the key internal control weaknesses identified over the initiation of reinsurance and financial accounting data by committing both internal and third-party consulting resources to address this issue and to further enhance our overall control environment. However, if our remedial measures are not successful in addressing these material weaknesses, our ability to report our future financial results on a timely and accurate basis may be adversely affected.

The SEC, as directed by Section 404 of the Sarbanes-Oxley Act, adopted rules requiring public companies to include a report of management on the company’s internal control over financial reporting in its Annual Report on Form 20-F that contains an assessment by management of the effectiveness of the company’s internal control over financial reporting. In addition, our principal independent auditor must attest to and report on management’s assessment of the effectiveness of the company’s internal control over financial reporting. As a foreign private issuer, these requirements will first apply to our Annual Report on Form 20-F for the fiscal year ending December 31, 2006. If we are unable to remedy the material weaknesses we have identified by that time, or if new material weaknesses come to our attention and remain unremedied at that time, management will not be permitted to conclude that our internal control over financial reporting is effective. Moreover, even if management does conclude that our internal control over financial reporting is effective, if our principal independent auditor is not satisfied with our internal control over financial reporting or the level at which controls are documented, designed, operated or reviewed, or if the independent registered public accounting firm interprets the requirements, rules or regulations differently from us, then they may decline to attest to management’s assessment or may issue a report that is qualified.

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Any of these possible outcomes could result in an adverse reaction in the financial marketplace due to a loss of investor confidence in the reliability of our financial statements, which ultimately could negatively impact the market price of our securities.

Consolidation in the insurance industry could lead to lower margins for us and less demand for our reinsurance products and services

The insurance industry overall is undergoing a process of consolidation as industry participants seek to enhance their product and geographic reach, client base, operating efficiency and general market power through merger and acquisition activities. These larger entities may seek to use the benefits of consolidation to, among other things, implement price reductions for the products and services they purchase. If competitive pressures compel us to reduce our prices, our operating margins would decrease.

As the insurance industry consolidates, competition for customers may become more intense and the importance of acquiring and properly servicing each customer will become greater. We could incur greater expenses relating to customer acquisition and retention, which could reduce our operating margins. In addition, insurance companies that merge may be able to enhance their negotiating position when buying reinsurance and may be able to spread their risks across a larger capital base so that they require less reinsurance.

Regulatory or legal changes could adversely affect our business

Insurance laws, regulations and policies currently governing our clients and us may change at any time in ways which may adversely affect our business. Furthermore, we cannot predict the timing or form of any future regulatory initiatives. We are subject to applicable government regulation in each of the jurisdictions in which we conduct business, particularly in Switzerland, the United States, the United Kingdom and Germany. Regulatory agencies have broad administrative power over many aspects of the insurance and reinsurance industries. Government regulators are concerned primarily with the protection of policyholders rather than shareholders or creditors.

Recently, the insurance and reinsurance regulatory framework has been subject to increased scrutiny in many jurisdictions. Changes in current insurance regulation may include increased governmental involvement in the insurance industry, initiatives aimed at premium controls, requirements for participation in guaranty associations or other industry pools and other changes which could adversely affect the reinsurance business and economic environment. Such changes could impose new financial obligations on us, require us to make unplanned modifications of our products and services, or result in delays or cancellations of sales of our products and services.

The reinsurance industry is also affected by political, judicial, regulatory and other legal developments, which have at times in the past resulted in new or expanded theories of liability. We cannot predict the future impact of changing law or regulation on our business.

In addition the reinsurance industry may also be impacted by the New York Attorney General’s investigations of the insurance industry. See “Item 4. — B. Business Overview — Regulation”.

We purchase retrocessional reinsurance, which may become unavailable on acceptable terms and subjects us to credit risk

In order to limit the effect on our financial condition of large and multiple losses, we buy retrocessional reinsurance. From time to time, market conditions have limited, and in some cases have prevented, insurers and reinsurers from obtaining the types and amounts of reinsurance which they consider adequate for their business needs. There can be no assurance that we will be able to obtain our desired amounts of retrocessional reinsurance. There is also no assurance that, if we are able to obtain such retrocessional reinsurance, we will be able to negotiate terms as favorable to us as in prior years.

A retrocessionaire’s insolvency or its inability or unwillingness to make payments under the terms of its reinsurance treaty with us could have a material adverse effect on our business, financial condition, results of operations or cash flows. Therefore, our retrocessions subject us to credit risk because the ceding of risk to retrocessionaires does not relieve us of our liability to our ceding companies. See “Item 4. — B. Business Overview — Retrocessional reinsurance” and Note 27 to our 2004 consolidated financial statements.

Because we depend on a small number of reinsurance brokers for a large portion of our revenue, loss of business written through them could adversely affect our financial condition, results of operations or cash flows

We market our reinsurance products worldwide in substantial part through reinsurance brokers. In some markets we principally write through reinsurance brokers. In 2004, two reinsurance intermediaries produced approximately 12.0% and

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9.0% of our gross premiums written, respectively. Loss of all or a substantial portion of the business written through brokers could have a material adverse effect on our financial condition, results of operations or cash flows.

Our reliance on reinsurance brokers exposes us to their credit risk

In 2004, approximately 49.0% of our gross premiums written were written through brokers. In accordance with industry practice, we frequently pay amounts owed on claims under our policies to reinsurance brokers, and these brokers, in turn, pay these amounts over to the insurers that have reinsured a portion of their liabilities with us. We refer to these insurers as ceding insurers. In some jurisdictions, or pursuant to some contractual arrangements, if a broker fails to make such a payment, we may remain liable to the ceding insurer for the deficiency. Conversely, in certain jurisdictions, when the ceding insurer pays premiums for these policies to reinsurance brokers for payment over to us, these premiums are considered to have been paid and the ceding insurer will no longer be liable to us for those amounts, whether or not we have actually received the premiums. Consequently, in connection with the settlement of reinsurance balances, we assume a degree of credit risk associated with reinsurance brokers around the world.

We may be adversely affected if Zurich Financial Services or its subsidiaries fail to honor their obligations to us or our clients

As part of the Formation Transactions described under “Formation transactions and relationship with Zurich Financial Services,” we entered into a number of contractual agreements with Zurich Financial Services and its affiliates including the Master Agreement, the Quota Share Retrocession Agreement, the Master Novation and Indemnity Reinsurance Agreement, service agreements, lease agreements and certain indemnity agreements. Among other things, under the Quota Share Retrocession Agreement, Zurich Financial Services, through its subsidiaries, provides us with a substantial amount of our investment returns. Additionally, Zurich Financial Services, through its subsidiaries, has agreed to arrangements that cap our exposure, net of retrocessional reinsurance recoveries, for losses and loss adjustment expenses arising out of the September 11th terrorist attacks at $289.2 million, the amount of loss and loss adjustment expenses we recorded as of September 30, 2001. In addition, subsidiaries of Zurich Financial Services have provided us with retrocessional reinsurance protection, provided coverage for certain workers’ compensation exposure, indemnified us for specified taxes and other matters and agreed to lease or sublease office space to us. Therefore, we are exposed to credit risk from Zurich Financial Services with respect to these obligations.

In addition, Zurich Financial Services subsidiaries remain the legal counterparty for many of our assumed reinsurance contracts. Although we do not have credit risk exposure with respect to these contracts, if these Zurich Financial Services subsidiaries do not honor their commitments efficiently and effectively to these clients, we might bear reputational risk. See “Item 4. – Information on the Company – A. History and Development of the Company”.

We may be restricted from consummating a change of control transaction, disposing of assets or entering new lines of business

Certain tax considerations and contractual arrangements with Zurich Financial Services may make an acquisition of Converium less likely and limit our ability to dispose of assets or enter into new lines of business. See “Formation transactions and relationship with Zurich Financial Services”.

We are also restricted from disposing of assets under the terms of our indenture relating to the $200 million principal amount of 7.125% Senior Notes due 2023.

Our inability to dispose of assets or enter new lines of business may render us less able to respond to changing market and competitive conditions, which could have a material adverse effect on our financial condition, results of operations or cash flows.

European Reinsurance Directive may disadvantage companies like us which are not established within the European Union

In June 2005, the European Parliament adopted a proposal for a directive (the “Directive”) on reinsurance for consideration. The Directive, when implemented, will establish the principles applicable to the operation of reinsurance business in a Member State and rules regarding technical provisions and the solvency requirements applicable to reinsurance companies. The Directive is based largely on solvency related concepts stipulated in the prior directive adopted by the European Union (the “EU”) for insurance companies. The Directive does not provide for any discrimination of non-EU based reinsurance companies. However, if the final implementation Directive should bring about such discriminatory regulations, this could be a disadvantage for Converium AG in its doing business in the EU, as Converium AG derives a substantial proportion of its revenues within the EU and any competitive disadvantage we face there could have an adverse effect on our financial

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condition, results of operations or cash flows.

ITEM 4. INFORMATION ON THE COMPANY

Converium Holding AG was incorporated in Switzerland on June 19, 2001 as a joint stock company as defined in article 620 et seq. of the Swiss Code of Obligations. We were registered on June 21, 2001 in the Commercial Register of the Canton of Zug with registered number CH-170.3.024.827-8. Our registered office is Baarerstrasse 8, CH-6300 Zug, Switzerland.

A. HISTORY AND DEVELOPMENT OF THE COMPANY

On March 22, 2001, Zurich Financial Services announced its intention to divest substantially all of its third-party reinsurance business historically operated under the “Zurich Re” brand name. This business had been managed and operated as a global operation since 1998. We refer to our initial public offering and the associated transactions described below in this offering memorandum as the “Formation Transactions”. As part of the Formation Transactions, ownership of this business was consolidated under Converium Holding AG, a newly incorporated Swiss company.

The Formation Transactions consisted of the following principal steps:

As part of the Formation Transactions, Zurich Financial Services and its subsidiaries transferred cash and other assets and liabilities to Converium. The assets transferred to us included:

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For a description of the agreements and transactions involved in the Formation Transactions and our divestiture from Zurich Financial Services, including certain ongoing contractual arrangements with Zurich Financial Services, see “Item 10. — Additional Information — C. Material Contracts”.

For description of our capital raising activities that occurred in October 2004, see “Item 10. — Additional Information — B. Memorandum and Articles of Incorporation”.

Converium Finance S.A. is a company incorporated for unlimited duration under the laws of Luxembourg on October 7, 2002. It has authorized share capital of €31,000 divided into 3,100 shares with a par value of €10 per share, 3,099 of which are owned by Converium AG and one of which is held by BAC Management S.a.r.l., a director of Converium Finance S.A., and all of which are fully paid. Converium Finance S.A.’s registered office is 54, boulevard Napoleon Ier, L-2210 Luxembourg. The objective of Converium Finance S.A., as stated in its Articles of Incorporation, is the acquisition, the management, the enhancement and the disposal of participations in whichever form in domestic and foreign companies.

Converium Insurance (UK) Ltd is an insurance company that incorporated for unlimited duration in the United Kingdom on November 11, 2002. It holds a license as an insurer from the United Kingdom Financial Services Authority dated May 27, 2003. Converium Insurance (UK) Ltd engages in issuing insurance policies in conjunction with selected cases, currently comprising of our business relating to GAUM, MDU and SATEC. It has authorized share capital of GBP 60,000,000 divided into 60,000,000 shares with a par value of GBP 1 per share, all of which are owned by Converium Holdings (UK) Ltd.

Converium PCC Ltd, Guernsey, is a company incorporated for an unlimited time in Guernsey/United Kingdom on October 31, 2000, which was set up in conjunction with the Formation Transactions of the IPO. The company holds a reinsurance license from the Guernsey Financial Services Commission dated October 12, 2001,and its purpose is to facilitate the intra-group reinsurance between certain branch offices of Converium AG and the parent.

In 2004 we formed Converium Finance (Bermuda) Ltd, as well as Converium IP Management Ltd, both of which were incorporated in Bermuda on December 17, 2004. As part of the formation process, Converium Holding AG has contributed the rights to commercially exploit the Converium brand to Converium Finance (Bermuda) Ltd, which in turn has entered into a license agreement with Converium IP Management Ltd allowing the latter to commercially exploit the Converium brand with respect to our operating insurance respectively, reinsurance branch offices and subsidiaries. We implemented this corporate change mainly to comply with relevant tax rules applicable to holding companies in the Canton of Zug, Switzerland in order to protect the current tax status of Converium Holding AG as a holding company.

B. BUSINESS OVERVIEW

Overview

We are an international reinsurer whose business operations are recognized for innovation, professionalism and service. We believe we are accepted as a professional reinsurer for all major lines of non-life and life reinsurance mainly in Europe, Asia-Pacific and Latin America. We actively seek to create innovative and efficient reinsurance solutions to complement our target clients’ business plans and needs. We focus on core underwriting skills and on developing close client relationships while honoring our and our clients’ relationships with intermediaries.

We offer a broad range of mostly traditional non-life and life reinsurance solutions to help our target clients to efficiently manage capital and risks. In non-life reinsurance, our lines of business are General Third Party Liability, Motor, Personal Accident (assumed from non-life insurers), Property, Agribusiness, Aviation & Space, Credit & Surety, Engineering, Marine & Energy, Professional Liability and other Special Liability and Workers’ Compensation. In Life & Health Reinsurance, our lines of business are Life and Disability reinsurance, including quota share, surplus coverage and financing contracts, and Accident and Health.

We underwrite reinsurance both directly with ceding companies and through intermediaries, giving us the flexibility to pursue business in accordance with our ceding companies’ preferred reinsurance purchasing method. In 2004, 49% of our gross premiums written were written through intermediaries and 51% were written on a direct basis.

During 2004, our business was organized around three operating segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance; which are based principally on lines of business. The business segments are supported by global business support functions such as Actuarial & Risk Management and Underwriting Technical Services, and by global services such as Human Resources, Finance and IT. We believe that this structure provides a higher degree of transparency, accountability and management control. Unless otherwise stated, the information presented in this Annual Report on Form 20-F is presented on the basis of these business segments as organized during 2004.

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In the first quarter of 2005, Converium formally adopted a change to the reporting line of the management of its North American operations. This change was introduced to reflect the placement of CRNA into orderly run-off and management’s desire to monitor this business on a stand-alone basis. Therefore, Converium’s business will be organized around three ongoing operating segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance, which are based principally on global lines of business, in addition to a Run-Off segment. The Run-Off segment includes all business, both life and non-life, originating from CRNA and CINA, excluding the US originated aviation business. Unless otherwise stated, the information included in this Annual Report on Form 20-F is presented in on the basis of the three business segments organized during 2004 and the Run-Off segment is included within these three segments as appropriate. In addition to the four segments’ financial results, the Corporate Center carries certain administration expenses, such as costs of the Board of Directors, the Global Executive Committee, and other corporate functions.

There are types of business which we historically participated in that we will no longer be able to write or will write at a significantly reduced level due to the placement of our US operations into run-off. We have discontinued the writing of reinsurance from offices located in North America. However, we will offer reinsurance for attractive US originated business to a limited number of select accounts. This business will be underwritten and managed through Converium AG, Zurich.

Our Strategy

Early in 2004 Converium adopted a comprehensive corporate strategy intended to build on its accomplishments since the Company was formed in 2001. Later in the year the Global Executive Committee adjusted the business model in response to developments which led to the decision to cease underwriting in North America, and in response to the subsequent downgrading by Standard & Poor’s and A.M. Best Company of Converium AG’s insurer financial strength rating to “BBB+” and “B++”, respectively.

Certain key elements of Converium’s post-IPO strategy have remained both profitable and tactically sound. Business underwritten outside the United States, since the IPO, has met or exceeded financial targets based on current estimates. Converium continued to attract business in targeted lines and regions during the January 1, 2005 renewal period. This success underlines market appetite for a mid-sized, independent reinsurer, and justifies shareholders’ decision at the Extraordinary General Meeting in late September 2004 to support Converium as a stand-alone entity delivering consistency and continuity under its existing business model. Current strengths arising from recent strategic positioning and development include the decision to continue to build direct client relationships in Continental Europe and elsewhere. In general, such relationships have proven more enduring than broker channels in the current business environment. In the specific case of Converium’s contract renewals for January 1, 2005, the greatest business continuity achievements were made among clients with whom Converium has direct personal relationships at all levels, with or without the involvement of intermediaries. In addition, the strategic diversification of Converium’s income streams has created a more robust organization by gaining access to business at its source. These steps include the development of strategic partnerships such as that with the Medical Defence Union (“MDU”) in the United Kingdom, participation in GAUM, and the formation of Converium’s corporate name at Lloyd’s to support clients operating in that market by providing capital to them directly. Other successful strategic initiatives include expansion in the Asia-Pacific region, and refocusing and expanding of Converium’s Life & Health Reinsurance segment in Europe. Strategic decisions to increase activity supported by knowledge-based underwriting in certain specialty lines markets and to maintain a thoroughly technical and profitability focused approach to all aspects of Converium’s business have also contributed to the Company’s resilience.

Looking ahead

Despite the strength of Converium’s strategic business model, changes lie ahead. The Company will continue to adjust its client base to concentrate on partnership-focused professional reinsurance buyers within client segments dependent on reinsurance. This move is supported by Converium’s value proposition, built around comprehensive client services such as underwriting support and financial and natural-hazard modeling. Geographically, Converium now focuses its local presence and underwriting on clients located in Europe, Asia-Pacific, and Latin America. The Company will continue to serve North American customers selectively from Zurich, following the decision to place CRNA into an orderly run-off, which will be accompanied by an active commutation strategy. A restructuring process is now underway to ensure that Converium’s physical presence matches its strategic outlook. Converium will continue to serve and develop clients that will benefit from its strong capitalization following the 2004 rights offering. Converium’s existing targeting of strategic partnerships will continue, especially for rating-sensitive specialty lines underwriting. Although 2004 was a challenging year for Converium, the validity of its incumbent strategic path outside the United States has been clearly endorsed. Converium’s business model will be further enhanced in 2005, with a clear line-of-business and geographical focus, an emphasis on expertise and service, and a rigorous technical approach.

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Our vision

We aim to be a core competitor in the international reinsurance industry, contributing to the evolution of the sector with forward-thinking and innovative solutions that enable our clients to efficiently manage their risk. We aspire to be recognized as an agile, credible and interactive organization that provides a model to a new generation of reinsurers.

Our mission

We are an international multi-line reinsurer that satisfies our clients’ business needs by excelling at analyzing, assuming and managing risks. In an ethical and responsible manner we aspire to provide:

Our core business

Our core business is to analyze, assume and manage portfolios of insurance risks, and to invest our assets so that they support the insurance risks we assume. Our strategy for each of our business segments is as follows:

Standard Property & Casualty Reinsurance

The Standard Property & Casualty Reinsurance segment is comprised of the General Third Party Liability, Motor, Personal Accident (assumed from non-life insurers) and Property lines of business. The Standard Property & Casualty Reinsurance segment’s strategy is to continue as a stand-alone, multi-line competitor in the international reinsurance marketplace. The strategy was redefined following the latest rating agencies’ downgrading in the second half of 2004 and now focuses on partnership-oriented professional reinsurance buyers in the markets Europe, Latin America, Asia and Australia. Our long-term client relationships are based on our capabilities, e.g. natural hazard expertise, financial modeling capabilities, structuring advice and claims and underwriting audits, contributing to earnings and cash flows. We remain committed to underwriting discipline to achieve the best possible shareholder return, which is only possible through cycle management.

Specialty Lines

The Specialty Lines segment includes the Agribusiness, Aviation & Space, Credit & Surety, Engineering, Marine & Energy, Professional Liability and other Specialty Liability and Workers’ Compensation lines of business. The Specialty Lines segment’s strategy is to develop specialty businesses in which Converium can position itself as a market leader and effectively leverage its intellectual assets in risk analysis, structuring, product design and risk modeling. We focus on specialty businesses because we believe that Converium possesses superior underwriting and structuring capabilities in certain areas, which is both a key driver of profitability as well as an effective barrier to entry in certain business lines.

Wherever possible, Converium seeks to develop preferred access to specialty lines through strong relationships, strategic partnerships or participations in entities that enjoy a unique position, such as strong control over the origination of their business, which prevent them from having to compete in annual insurance or reinsurance auctions. Examples of the approach by which we seek to develop preferred access to these businesses are our strategic partnership with MDU in the U.K., our participation in GAUM and our shares in its pools and our participation in SATEC and our share in its pool, as well as many strong relationships with specialized mono-line insurers.

Also, Converium Underwriting Ltd, a Lloyd’s Corporate Member, has successfully provided third-party capacity to certain specialist Lloyd’s syndicates.

Some specialty lines are subject to cyclical pricing fluctuations. Converium remains committed to underwriting discipline to achieve the best possible shareholder return, which is only possible through cycle management.

Life & Health Reinsurance

The Life & Health Reinsurance segment comprises the Life and Disability and Accident and Health lines of business. The Life & Health Reinsurance segment’s strategy is to increase the stability of Converium’s income. Traditional life reinsurance

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has a low correlation to property and casualty risks and can therefore improve our risk diversification. Our Life & Health Reinsurance segment will continue to grow its activities in its existing key markets, which are Germany, Italy and France; markets with significant potential for future opportunities for us include Switzerland, Austria, Denmark, Poland and the Czech Republic.

The business segments are supported by global business support functions such as Actuarial & Risk Management and Underwriting Technical Services, and by global services such as Human Resources, Finance and IT.

Guiding principles for our business

We have established the following guiding principles for the development of our business:

In addition, we have established the following guiding principles to manage our business:

Cycle management. We have a systematic approach to the allocation of capital and resources to those lines of business and markets that meet our profitability standards, and to withdraw from businesses that do not meet our performance thresholds. Historically, the reinsurance cycles in different lines of business and markets have not moved simultaneously. Our strong international franchise and our distribution and servicing platform provide broad access to an international reinsurance market, and enable the flexible allocation of resources to those lines of business or markets in which profitability prospects are most favorable at any point in time. Our well established relationships with clients and intermediaries, as well as our transparent pricing approach, allow us to manage the cycle by moving in and out of lines of business or markets without putting long-term business relationships at risk.

Risk management. We continue to maintain, develop and implement an enterprise risk management culture, including underwriting, pricing, reserving, asset & liability management and operational risk management, by balancing upside potential and downside risk, based on appropriate capital allocation and relevant risk migration measures.

Operational efficiency. We manage our expense base effectively through continuous analysis of business processes and operational structures, with a view to enhancing business integration and achieving synergies and efficiencies.

Retention management. We manage our gross and net risk positions on a legal entity basis and on a group-wide basis, through global risk pooling and the limited use of retrocession.

Investment policy. We allocate capital primarily to support underwriting risks with the aim of optimizing the after-tax risk-return characteristics of our investment portfolio. Our asset allocation focuses on core portfolios of high-quality bonds and equities, generally managed passively. Further diversification is achieved through complementary portfolios in other asset classes, such as real estate, credit portfolios and non-traditional or alternative investments; these portfolios are generally actively managed. The acquisition of minority stakes in insurance or reinsurance companies remains outside of our strategic scope.

Capital management. We are committed to strengthening our capitalization in order to ensure that clients, intermediaries and

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rating agencies regard us as a credible reinsurer for short-, medium- and long-tail business. At the same time, we remain committed to returning capital to shareholders if such capital cannot be fully deployed to support reinsurance underwriting at adequate returns and it does not jeopardize the perception of our financial strength.

Our business

We are an international professional reinsurer, which offers a broad range of non-life and life reinsurance to help our clients manage capital and risk. Our principal lines of non-life reinsurance include General Third Party Liability, Motor, Personal Accident (assumed from non-life insurers), Property, Agribusiness, Aviation & Space, Credit & Surety, Engineering, Marine & Energy, Professional Liability and other Special Liability and Workers’ Compensation. The principal life reinsurance products are Life and Disability reinsurance, including quota share, surplus coverage and financing contracts, and Accident and Health.

In addition to our offices in Cologne, New York, Zug and Zurich, we have branch offices in Bermuda, Labuan, London, Milan, Paris, Singapore and Sydney, as well as marketing offices in Buenos Aires, Kuala Lumpur, London, Mexico City (to be closed in 2006), Sao Paulo and Tokyo. In addition, we have administrative offices in Stamford, Connecticut. We have a sub-holding company in London and finance subsidiaries in Luxembourg and Bermuda, an IP company in Bermuda (to be transferred to Zug, Switzerland in 2005) and a licensed reinsurance company, Guernsey, facilitating intra-group reinsurance within Converium.

During 2004 our business was organized around three operating segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance; which are based principally on lines of business. The business segments are supported by global business support functions such as Actuarial & Risk Management and Underwriting Technical Services, and by global services such as Human Resources, Finance and IT. We believe that this structure provides a higher degree of transparency, accountability and management control. See “Item 4. — Information on the Company — B. Business Overview” for discussion regarding the reorganization of our segment structure in the first quarter of 2005.

The table below presents, by segment, the distribution of our premiums written and (loss) income for the year ended December 31, 2004. For additional information regarding the results of our operating segments, see “Item 5– Operating and Financial Review and Prospects – A. Operating Results” and the Schedule of Segment Data on pages F-7 and F-8 of the financial statements. As a result of the ratings downgrades and the run-off of our North American business, we expect a significant decline in the amount of premiums as well as significant shifts in the geographic and line of business distributions of premiums that we write going forward as compared to our historical performance.

The table below presents the geographic distribution of our gross premiums written for the years ended December 31, 2004, 2003 and 2002, based on the location of the ceding companies.

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The table below presents the distribution of our net premiums written by line of business for the years ended December 31, 2004, 2003 and 2002.

Types of Reinsurance

Both non-life reinsurance and life reinsurance can be written on either a proportional basis or a non-proportional basis. Proportional reinsurance is also known as pro rata reinsurance. Quota share reinsurance and surplus reinsurance are types of proportional reinsurance. Some non-proportional reinsurance takes the form of excess of loss reinsurance in which the reinsurer’s obligations are only triggered after covered losses exceed a specified attachment point. In the case of proportional reinsurance, the reinsurer assumes a predetermined portion of the ceding company’s risks under the covered insurance contract or contracts. In the case of non-proportional reinsurance, the reinsurer assumes all or a specified portion of the ceding company’s risks in excess of a specified amount, known as the ceding company’s retention or the reinsurer’s attachment point, subject to a negotiated reinsurance contract limit.

Premiums that the ceding company pays to a reinsurer for proportional reinsurance are a predetermined portion of the premiums that the ceding company receives from its insured, consistent with the proportional sharing of risk. In addition, in proportional reinsurance, the reinsurer generally pays the ceding company a ceding commission. The ceding commission is usually based on the ceding company’s cost of generating the business being reinsured, which includes commissions, premium taxes, assessments and miscellaneous administrative expenses and a profit participation for originating the business, the amount of which is based on the claims experience. The ceding commission may also be affected by competitive factors. Premiums that the ceding company pays to a reinsurer for non-proportional reinsurance are not directly proportional to the premiums that the ceding company receives because the reinsurer does not assume a direct proportion of the ceding company’s risk. The frequency of claims under a proportional reinsurance contract is usually greater than under a non-proportional contract, and therefore the claims experience with proportional reinsurance contracts is generally more predictable.

Non-proportional non-life reinsurance is often written in layers. One or a group of reinsurers accepts the risk just above the ceding company’s retention up to a specified amount, at which point another reinsurer or a group of reinsurers accepts the excess liability up to an additional specified limit or the excess liability reverts to the ceding company. The reinsurer taking on

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the risk just above the ceding company’s retention is typically said to write lower layer excess reinsurance. A claim that reaches just beyond the ceding company’s retention will create a claims payment for the lower layer reinsurer, but not for the reinsurers of any higher layers. Claims activity in lower layer reinsurance tends to be more predictable than in higher layers due to greater frequency and availability of historical data, and therefore, like proportional reinsurance, better enables underwriters and actuaries to more accurately price the underlying risks. In a limited number of cases, reinsurance is also written on an aggregate stop-loss basis to protect the ceding company’s total portfolio from extraordinary losses resulting from the aggregation of individual risks.

Both non-life reinsurance and life reinsurance can be written either through treaty or facultative reinsurance arrangements. In treaty reinsurance, the ceding company cedes, and the reinsurer assumes, a specified portion of a type or category of risks insured by the ceding company. Generally in the industry, treaty reinsurers do not separately evaluate each of the individual risks assumed under their treaties and are largely dependent on the original risk underwriting decisions made by the ceding company’s underwriters. This dependence subjects reinsurers to the possibility that the ceding company has not adequately evaluated the risks to be reinsured and, therefore, that the premiums ceded to the reinsurer may not adequately compensate the reinsurer for the risk assumed. Accordingly, the reinsurer’s evaluation of the ceding company’s risk management and underwriting practices, as well as claims settlement practices and procedures, will usually impact the pricing of the treaty.

In facultative reinsurance, the ceding company cedes, and the reinsurer assumes, all or part of a specific risk or risks. Facultative reinsurance normally is purchased by ceding companies for risks not covered by their reinsurance treaties, for amounts in excess of the monetary limits of their reinsurance treaties and for unusual and complex risks. In addition, facultative risks often provide coverages for relatively severe exposures, which results in greater volatility. The ability to evaluate separately each risk reinsured, however, increases the probability that the reinsurance underwriter can price the contract to reflect more accurately the risks involved.

Non-traditional reinsurance involves structured reinsurance solutions tailored to meet individual client strategic and financial objectives. Both non-life reinsurance and life reinsurance can be written on a structured/finite basis. Often these reinsurance solutions provide reinsurance protection across a company’s entire insurance portfolio. Because of the constantly changing industry and regulatory framework, as well as the changing market demands facing insurance companies, the approaches utilized in structured/finite programs are constantly evolving and will continue to do so.

We underwrite our product lines on a non-proportional and proportional basis, as well as on a structured/finite basis. We integrate our facultative specialists with our underwriting professionals with treaty expertise, organizing them as focused teams around client relationship management and lines of business. We do not distinguish between treaty and facultative reinsurance, but rather between proportional and non-proportional underwriting and lines of business.

In 2004, $2.9 billion or approximately 75.2% of our gross premiums written were written on a proportional treaty basis, $0.6 billion or approximately 15.5% of our gross premiums written were written on a non-proportional basis, and $0.4 million or approximately 9.3% of our net premiums written were written on a structured/finite basis.

The table below presents the distribution of our gross premiums written by type of reinsurance for the years ended December 31, 2004, 2003 and 2002.

Proportional and Non-proportional

We offer traditional reinsurance products on both a proportional and non-proportional basis in all our lines of business. Our non-proportional business includes Property, Motor, Aviation & Space and Professional Liability and other Special Liability lines, to complement our established market position in non-proportional liability. The growth in our proportional business has been mainly due to an increase in proportional Property, Aviation & Space and Motor as well as opportunities in proportional Agribusiness. In 2004, we saw increased premium writings from proportional business, especially in General Third Party Liability and Professional Liability and other Special Liability.

We believe that clients and brokers actively seek our input in the evaluation and structuring of businesses with unique or difficult risk characteristics. We believe this is a result of our innovative approach, organizational resources and financial

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strength. We have developed integrated teams of professionals with significant treaty and individual risk, or facultative, expertise which support the professionals we have in our branch network. We offer facultative products to a limited extent and only to a selected number of clients on a proportional and non-proportional basis. We deploy our international specialty lines experts and local specialists to design solutions to address our clients’ risk management needs.

Structured/finite

Structured/finite reinsurance solutions are marketed by our Standard Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance segments. Our structured/finite specialists focus on providing clients with innovative financial solutions for their risk management and other financial needs, primarily through reinsurance products. Whether working directly with the client or through a broker, we seek to develop client-specific solutions after spending time with the client to understand its business needs.

We believe that to succeed in providing our clients with the solutions they need, we must take a comprehensive, iterative approach in our analysis. To accomplish this goal, we deploy teams that include underwriting, tax, accounting, actuarial and banking experts who can effectively address all aspects of the solution composed of internal and external resources. We believe this multi-disciplinary approach provides an efficient way to address the respective issues.

Some structured/finite reinsurance markets are rating-sensitive, and due to our recent downgrades we expect written premium volume in this area to reduce significantly.

Non-Life Operations

Overview

We operate our non-life reinsurance business through our two non-life segments: Standard Property & Casualty Reinsurance and Specialty Lines. Our non-life operations had gross premiums written of $3,394.9 million for the year ended December 31, 2004, representing 88.4% of our total gross premiums written.

The following table sets forth our non-life reinsurance gross premiums written by type and line of business for the years ended December 31, 2004, 2003 and 2002:

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The table below presents the loss, underwriting expense and combined ratios of our non-life reinsurance business both by line of business and type of reinsurance for the years ended December 31, 2004, 2003 and 2002. This table represents an aggregation of line of business ratios for our two non-life segments. Subsequent tables present ratios for each non-life segment by line of business and type of reinsurance. Any prior underwriting year development (positive or negative) will affect the ratios of the calendar year in which the activity is recorded.

Loss, Expense and Combined Ratios
Year Ended December 31,

For an explanation of ratio calculations, please refer to the Schedule of Segment Data on pages F-7 and F-8 of our 2004 consolidated financial statements.

For an explanation of significant loss activity, see “Item 5– Operating and Financial Review and Prospects – A. Operating Results”.

Standard Property & Casualty Reinsurance

The Standard Property & Casualty Reinsurance segment’s strategy is to continue as a stand-alone, multi-line competitor in the international reinsurance marketplace. The strategy was redefined following the latest rating agencies’ downgrading in the second half of 2004 and now focuses on partnership-oriented professional reinsurance buyers in the markets Europe, Latin America, Asia and Australia. Our long-term client relationships are based on our capabilities, e.g. natural hazard expertise, financial modeling capabilities, structuring advice and claims and underwriting audits, contributing to earnings and cash flows. We remain committed to underwriting discipline to achieve the best possible shareholder return, which is only possible through cycle management.

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The lines of business of the Standard Property & Casualty Reinsurance segment are as follows:

General Third Party Liability

We provide a broad range of coverage for reinsurance of industrial, manufacturer, operational, environmental, product and general third-party liability. We provide liability coverage on both a proportional and non-proportional basis.

Motor

Motor insurance can include coverage in three major areas — liability, physical damage and accident benefits, for all of which we provide reinsurance coverage. Liability insurance provides coverage payment for injuries and for property damage to third parties. Physical damage provides for payment of damages to an insured automobile arising from a collision with another object or from other risks such as fire or theft. Accident benefits provide coverage for loss of income and medical and rehabilitation expenses for insured persons who are injured in an automobile accident, regardless of fault.

Personal Accident (assumed from non-life insurers)

We provide accident coverages for various business lines, including personal accident and travel accident.

Property

We reinsure liability for physical damage caused by fire and allied perils such as explosion, lightning, storm, flood, earthquake and for costs of debris removal, as well as coverage of business interruption and loss of rent as a result of an insured loss. Other sub-lines of Property reinsurance include cover for hail, burglary, water damage and glass breakage.

The following table presents the distribution of net premiums written by our Standard Property & Casualty Reinsurance segment for the years ended December 31, 2004, 2003 and 2002.

The following table presents the loss, underwriting expense and combined ratios of our Standard Property & Casualty Reinsurance segment by line of business and type of reinsurance for the years ended December 31, 2004, 2003 and 2002.

Loss, Expense and Combined Ratios
Year Ended December 31,