Valuation of Catastrophe Equity Puts With Markov-Modulated Poisson Processes

Chia‐Chien Chang · Shih‐Kuei Lin · Min‐Teh Yu

42 citations0/0 files storedJournal of Risk & Insurance

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Stochastic processes and financial applications Insurance and Financial Risk Management Probability and Risk Models

Abstract

We derive the pricing formula for catastrophe equity put options (CatEPuts) by assuming catastrophic events follow a Markov Modulated Poisson process (MMPP) whose intensity varies according to the change of the Atlantic Multidecadal Oscillation (AMO) signal. U.S. hurricanes events from 1960 to 2007 show that the CatEPuts pricing errors under the MMPP(2) are smaller than the PP by 30 percent to 66 percent. The scenario analysis indicates that the MMPP outperforms the exponential growth pattern (EG) if the hurricane intensity is the AMO signal, whereas the EG may outperform the MMPP if the future climate is warming rapidly.

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References

1976Option pricing when underlying stock returns are discontinuous 2009Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk‐Transfer Solutions 1999The Financing of Catastrophe Risk 2002Pricing Default‐Risky CAT Bonds With Moral Hazard and Basis Risk 1995Pricing Catastrophe Insurance Futures and Call Spreads 2006Catastrophe options with stochastic interest rates and compound Poisson losses 2006Valuation of catastrophe reinsurance with catastrophe bonds

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