Pricing catastrophe options with stochastic claim arrival intensity in claim time
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Banking & Finance.
Volume (Year): 34 (2010)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jbf
Catastrophe insurance derivatives Stochastic claim arrival Operational time Trinomial tree Stochastic time change Binomial tree with random time steps Option pricing;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2551-2569, August.
- Jaimungal, Sebastian & Wang, Tao, 2006. "Catastrophe options with stochastic interest rates and compound Poisson losses," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 469-483, June.
- Robert E. Hoyt & Kathleen A. McCullough, 1999. "Catastrophe Insurance Options: Are They Zero-Beta Assets?," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 22(2), pages 147-163.
- Gerber, Hans U., 1984. "Error bounds for the compound poisson approximation," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 191-194, July.
- Henri Louberge & Evis Kellezi & Manfred Gilli, 1999.
"Using Catastrophe-Linked Securities to Diversity Insurance Risk: A Financial Analysis of Cat Bonds,"
Journal of Insurance Issues,
Western Risk and Insurance Association, vol. 22(2), pages 125-146.
- Louberge, H. & Kellezi, E. & Gilli, M., 1999. "Using Catastrophe-Linked Securities to Diversify Insurance Risk: a Financial Analysis of Cat Bonds," Research Papers by the Department of Economics, University of Geneva 99.04, Département des Sciences Économiques, Université de Genève.
- Froot, Kenneth A. & O'Connell, Paul G.J., 2008.
"On the pricing of intermediated risks: Theory and application to catastrophe reinsurance,"
Journal of Banking & Finance,
Elsevier, vol. 32(1), pages 69-85, January.
- Kenneth A. Froot & Paul G. J. O'Connell, 1997. "On The Pricing of Intermediated Risks: Theory and Application to Catastrophe Reinsurance," NBER Working Papers 6011, National Bureau of Economic Research, Inc.
- Kenneth A. Froot & Paul G.J. O'Connell, . "On the Pricing of Intermediated Risks: Theory and Application to Catastrophe Reinsurance," Center for Financial Institutions Working Papers 97-24, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Chernobai, Anna & Yildirim, Yildiray, 2008. "The dynamics of operational loss clustering," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2655-2666, December.
- Bakshi, Gurdip & Madan, Dilip, 2002. "Average Rate Claims with Emphasis on Catastrophe Loss Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 93-115, March.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Lee, Jin-Ping & Yu, Min-Teh, 2007. "Valuation of catastrophe reinsurance with catastrophe bonds," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 264-278, September.
- Walden, Johan & Ibragimov, Rustam, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
- Geman, Hélyette, 2005. "From Measure Changes to Time Changes in Asset Pricing," Economics Papers from University Paris Dauphine 123456789/1388, Paris Dauphine University.
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
- Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
- Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
- Knut Aase, 1999. "An Equilibrium Model of Catastrophe Insurance Futures and Spreads," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 24(1), pages 69-96, June.
- 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.
- Li, Junye, 2011. "Volatility components, leverage effects, and the return-volatility relations," Journal of Banking & Finance, Elsevier, vol. 35(6), pages 1530-1540, June.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.