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Pricing catastrophe options with stochastic claim arrival intensity in claim time

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  • Chang, Carolyn W.
  • Chang, Jack S.K.
  • Lu, WeLi
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    Abstract

    We model claim arrival and loss uncertainties jointly in a doubly-binomial framework to price an Asian-style catastrophe (CAT) option with a non-traded underlying loss index using the no-arbitrage martingale pricing methodology. We span these uncertainties by benchmarking to the shadow price of a one-claim bond and the premium of a reinsurance contract. We implement a stochastic time change from calendar time to claim time to more efficiently price the CAT option as a random sum - a binomial sum of claim time binomial Asian option prices. This choice of the operational time dimension allows us to incorporate different patterns of catastrophe arrivals by adjusting the claim arrival probability. We demonstrate this versatility by incorporating a mean-reverting Ornstein-Uhlenbeck intensity arrival process. Simulation results verify our model predictions and demonstrate how the claim arrival probability varies with the expected claim arrival intensity.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 34 (2010)
    Issue (Month): 1 (January)
    Pages: 24-32

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    Handle: RePEc:eee:jbfina:v:34:y:2010:i:1:p:24-32

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: Catastrophe insurance derivatives Stochastic claim arrival Operational time Trinomial tree Stochastic time change Binomial tree with random time steps Option pricing;

    References

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    Cited by:
    1. Li, Junye, 2011. "Volatility components, leverage effects, and the return-volatility relations," Journal of Banking & Finance, Elsevier, vol. 35(6), pages 1530-1540, June.
    2. Wu, Yang-Che & Chung, San-Lin, 2010. "Catastrophe risk management with counterparty risk using alternative instruments," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 234-245, October.
    3. Perrakis, Stylianos & Boloorforoosh, Ali, 2013. "Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3157-3168.
    4. Lo, Chien-Ling & Lee, Jin-Ping & Yu, Min-Teh, 2013. "Valuation of insurers’ contingent capital with counterparty risk and price endogeneity," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5025-5035.

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