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Managing Catastrophic Risk by Alternative Risk Transfer Instruments University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations Summer 2010 MANAGING CATASTROPHIC RISK BY ALTERNATIVE RISK TRANSFER INSTRUMENTS Chieh Ou Yang University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Finance and Financial Management Commons, and the Insurance Commons Recommended Citation Ou Yang, Chieh, "MANAGING CATASTROPHIC RISK BY ALTERNATIVE RISK TRANSFER INSTRUMENTS" (2010). Publicly Accessible Penn Dissertations. 220. https://repository.upenn.edu/edissertations/220 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/220 For more information, please contact [email protected]. MANAGING CATASTROPHIC RISK BY ALTERNATIVE RISK TRANSFER INSTRUMENTS Abstract Chapter 1 analyzes hybrid-trigger CAT bonds, a new CAT bond deal that can reduce basis risk and eliminate moral hazard simultaneously. It is the first esearr ch that provides analytical evidence on the condition under which the hybrid trigger has lower basis risk. Simulation results support my analyses. Major findings in this study provide insights to insurers who would proactively manage the basis risk of CAT bonds. Chapter 2 examines whether the parimutuel mechanism can hedge risk-averse people against catastrophic losses. Two optimal stake choice models are constructed. In the first model where the stakes of other players are exogenous, the optimal stake can be obtained by equating the marginal cost of a net payoff with the ratio of the expected marginal utilities in the payoff state and the no payoff state. The dynamic optimal hedge can be achieved if the odds, and the conditional probability of a hurricane hitting the target area, are available. In the second model, an optimal equilibrium stake is derived by maximizing the representative agent’s expected utility. Given no transaction fee and tax, we show that parimutuel insurance intrinsically leads to participants being underinsured due to basis risk. Although participants will be underinsured, parimutuel insurance guarantees no underlying risk borne by the issuer. We also derive the equivalent transaction costs of traditional insurance relative to HuRLOs. The actual transaction cost for traditional insurance is found to be higher than the equivalent utility level implied by HuRLOs, suggesting that hedgers would be better off with HuRLOs than with traditional insurance. Chapter 3 analyzes the implications of climate change for catastrophic risk and examines the appropriateness of longer term insurance contracts to protect insurers against catastrophic losses and changes in risk estimates over time. Climate change essentially plays an important role in modeling catastrophic risks, especially in the tail of the loss distribution and for longer time scales. Mitigations can completely offset the impact of climate change. Longer term insurance contract may stimulate the incentive to invest on mitigation; however, risk capital required and annual premiums could increase significantly due ot the additional premium risk faced by the insurers. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Applied Economics First Advisor Howard Kunreuther Second Advisor Neil A. Doherty Third Advisor Gregory Nini Keywords risk management, insurance, insurance-link security, catastrophe bonds, parimutuel, climate change Subject Categories Finance and Financial Management | Insurance This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/220 MANAGING CATASTROPHIC RISK BY ALTERNATIVE RISK TRANSFER INSTRUMENTS Chieh Ou Yang A DISSERTATION in Insurance and Risk Management For the Graduate Group in Managerial Science and Applied Economics Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2010 Supervisor of Dissertation Howard Kunreuther Professor of Decision Sciences and Business and Public Policy Graduate Group Chairperson Eric Bradlow, Professor of Marketing, Statistics, and Education Dissertation Committee Neil A. Doherty, Professor of Insurance and Risk Management Gregory Nini, Assistant Professor of Insurance and Risk Management Omar Besbes, Assistant Professor, Decision, Risk & Operations Acknowledgements I am really grateful to my advisors, Neil A. Doherty and Howard Kunreuther, for their guidance, support, and encouragement. I also would like to thank my dissertation committee members: Gregory Nini, and Omar Besbes for their valuable comments and advice. I am also grateful to my wife, Yun-Sheng Chen, for her love and support, which helped me to concentrate on my studies. Financial support from Ministry of Education, Taiwan, Resource for the Future, and Wharton Risk Management and Decision Processes Center are gratefully acknowledged. ii ABSTRACT MANAGING CATASTROPHIC RISK BY ALTERNATIVE RISK TRANSFER INSTRUMENTS Chieh Ou Yang Howard Kunreuther Chapter 1 analyzes hybrid-trigger CAT bonds, a new CAT bond deal that can reduce basis risk and eliminate moral hazard simultaneously. It is the first research that provides analytical evidence on the condition under which the hybrid trigger has lower basis risk. Simulation results support my analyses. Major findings in this study provide insights to insurers who would proactively manage the basis risk of CAT bonds. Chapter 2 examines whether the parimutuel mechanism can hedge risk-averse people against catastrophic losses. Two optimal stake choice models are constructed. In the first model where the stakes of other players are exogenous, the optimal stake can be obtained by equating the marginal cost of a net payoff with the ratio of the expected marginal utilities in the payoff state and the no payoff state. The dynamic optimal hedge can be achieved if the odds, and the conditional probability of a hurricane hitting the target area, are available. In the second model, an optimal equilibrium stake is derived by maximizing the representative agent’s expected utility. Given no transaction fee and tax, we show that parimutuel insurance intrinsically leads to participants being underinsured due to basis risk. Although participants will be underinsured, parimutuel insurance guarantees no underlying risk borne by the issuer. We also derive the equivalent transaction costs of traditional insurance relative to HuRLOs. The actual transaction cost for traditional iii insurance is found to be higher than the equivalent utility level implied by HuRLOs, suggesting that hedgers would be better off with HuRLOs than with traditional insurance. Chapter 3 analyzes the implications of climate change for catastrophic risk and examines the appropriateness of longer term insurance contracts to protect insurers against catastrophic losses and changes in risk estimates over time. Climate change essentially plays an important role in modeling catastrophic risks, especially in the tail of the loss distribution and for longer time scales. Mitigations can completely offset the impact of climate change. Longer term insurance contract may stimulate the incentive to invest on mitigation; however, risk capital required and annual premiums could increase significantly due to the additional premium risk faced by the insurers. iv Contents Acknowledgements ii General Introduction 1 1 Managing Catastrophic Losses for Insurers: Hybrid-trigger CAT Bonds and Basis Risk Analysis 7 1.1 Introduction ..............................................................................................................7 1.1.1 Nature of CAT Bonds .....................................................................................7 1.1.2 Catastrophic Losses for Insurers .....................................................................8 1.1.3 Advantages and Disadvantages of CAT Bonds ..............................................9 1.1.4 Hybrid-trigger CAT Bonds ...........................................................................11 1.1.5 Basis Risk of Hybrid-trigger CAT Bonds .....................................................13 1.2 Basis Risk Analysis for an Individual Insurer .......................................................13 1.2.1 The Comparison of Basis Risk for the Hybrid Trigger and the PSC-index Trigger...........................................................................................................15 1.2.2 The Comparison of Basis Risk for the Hybrid Trigger and the Model-based Trigger...........................................................................................................17 1.2.3 Basis Risk Analysis for Public Insurance/Reinsurance Program .................20 1.3 Basis Risk and Fair Values of CAT Bonds ............................................................22 1.3.1 Loss Model....................................................................................................23 1.3.2 Payoff of CAT Bonds ...................................................................................24 1.3.3 Fair Values of CAT Bonds ...........................................................................25 1.3.4 Settings for Simulation .................................................................................27 1.3.5 Simulation Results ........................................................................................28 1.3.5.1 PCS-index CAT Bond and Hybrid-trigger CAT Bond .....................28 1.3.5.2 Model-based CAT Bond and Hybrid-trigger CAT Bond .................29
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