6-1 - Risk Management for Catastrophe Loss Jin-Ping Lee and...

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Unformatted text preview: Risk Management for Catastrophe Loss Jin-Ping Lee and Min-Teh Yu October 30, 2007 Abstract This study investigates the valuation models for three types of catastrophe-linked instruments: catastrophe bonds, catastrophe equity puts, and catastrophe futures and options. First, it looks into the pricing of catastrophe bonds under stochastic interest rates and examines how reinsurers can apply catastrophe bonds to reduce the default risk. Second, it models and values the catastrophe equity puts that give the (re)insurer the right to sell its stocks at a predetermined price if catastrophe losses surpass a trigger level. Third, this study models and prices catastrophe futures and catastrophe options contracts that are based on a catastrophe index. Key Words: Catastrophe Risk, Catastrophe Bond, Catastrophe Equity Put, Catastro- phe Futures Options, Contingent Claim Analysis. JEL classification: G20, G28, G21 Lee: Associate Professor, Department of Finance, Feng Chia University, Taichung, Taiwan. Fax: 886-4- 24513796, Email: jplee@fcu.edu.tw. Yu: Professor, Department of Finance, Providence University, Taichung 43301, Taiwan. Tel.: 886-4-26310631, Fax: 886-4-26311170, Email: mtyu@pu.edu.tw. 1 1 Introduction Catastrophic events having low frequency of occurrence but generally high loss severity can easily erode the underwriting capacity of property and casualty insurance and reinsur- ance companies (P&Cs, hereafter). P&Cs traditionally hedge catastrophe risks by buying catastrophe reinsurance contracts. Because of capacity shortage and constraints in the rein- surance markets, the capital markets develop alternative risk transfer instruments to provide (re)insurance companies with vehicles for hedging their catastrophe risk. These instruments can be broadly classi f ed into three categories: insurance-linked debt contracts (e.g. catastro- phe bonds), contingent capital f nancing instruments (e.g. catastrophe equity puts), and catastrophe derivatives (e.g. catastrophe futures and catastrophe options). The Chicago Board of Trade (CBOT) launched catastrophe (CAT) futures in 1992 and CAT futures call spreads in 1993 with contract values linked to the loss index compiled by the Insurance Services O ce. The CBOT switched to CAT options in 1995 to try to spur growth in the CAT derivatives market, but was unable to generate meaningful activity and ultimately abandoned it in 2000. The CAT bonds, however, have been quite successful with 89 transactions completed, representing $15.53 billion in issuance since the f rst issue in 1997. 1 Since 1996, several CAT equity put deals were negotiated usually with obligations to purchase stock of $100 million each. This study looks into the valuation models for these CAT-linked instruments and exam- ines how their values are related to catastrophe risk, terms of the contract, and other key elements of these instruments. The rest of this study is organized into four sections. Sec- tion II provides a model to value catastrophe bonds under stochastic interest rates. Sectiontion II provides a model to value catastrophe bonds under stochastic interest rates....
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6-1 - Risk Management for Catastrophe Loss Jin-Ping Lee and...

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