Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-27T00:08:48.468Z Has data issue: false hasContentIssue false
  • English
  • Français

Average Rate Claims with Emphasis on Catastrophe Loss Options

Published online by Cambridge University Press:  06 April 2009

Gurdip Bakshi  and
Dilip Madan
Gurdip Bakshi
Affiliation:
gbakshi@rhsmith.umd.edu, Department of Finance, Robert H. Smith School of Business, University of Maryland, College Park, MD 20742.
Dilip Madan
Affiliation:
dbm@rhsmith.umd.edu, Department of Finance, Robert H. Smith School of Business, University of Maryland, College Park, MD 20742.
Get access Rights & Permissions [Opens in a new window]

Abstract

This article studies the valuation of options written on the average level of a Markov process. The general properties of such options are examined. We propose a closed-form characterization in which the option payoff is contingent on cumulative catastrophe losses. In our framework, the loss rate is a mean-reverting Markov process, with no continuous martingale component. The model supposes that high loss levels have lower arrival rates. We analytically derive the cumulative loss process and its characteristic function. The resulting option model is promising.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 37 , Issue 1 , March 2002 , pp. 93 - 115
Copyright
Copyright © School of Business Administration, University of Washington 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 2003–2049.CrossRefGoogle Scholar
Bakshi, G., and Madan, D.. “Spanning and Derivative-Security Valuation.” Journal of Financial Economics, 55 (2000), 205–238.CrossRefGoogle Scholar
Bergman, Y.; Grundy, B.; and Wiener, Z. “General Properties of Option Prices.” Journal of Finance, 51 (1996), 1573–1610.CrossRefGoogle Scholar
Boyle, P. “New Life Forms on the Option Landscape.” Journal of Financial Engineering, 2 (1993), 217–252.Google Scholar
Chacko, G., and Das, S.. “Average Interest.” NBER # 6045 (1997).CrossRefGoogle Scholar
Chen, A; Chen, K. C.; and Laiss, B.. “Pricing Contingent Value Rights: Theory and Practice.” Journal of Financial Engineering, 2 (1995), 155–173.Google Scholar
Cox, J., and Ross, S.. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, 3 (1976), 145–166.CrossRefGoogle Scholar
Cummins, D., and Geman, H.. “Pricing Catastrophe Insurance Futures and Call Spread: An Arbitrage Approach.” Journal of Fixed Income, (03 1995), 46–57.CrossRefGoogle Scholar
Curran, M. “Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean.” Management Science, 40 (1994), 1705–1711.CrossRefGoogle Scholar
Dammon, R., and Spatt, C.. “An Option-Theoretic Approach to the Valuation of Dividend Reinvestment and Voluntary Purchase Plans.” Journal of Finance, 47 (1992), 331–347.Google Scholar
Fu, M.; Madan, D.; and Wang, T.. “Pricing Asian Options: A Comparison of Analytical and Monte Carlo Methods.” Journal of Computational Finance, 2 (1999), 49–74.CrossRefGoogle Scholar
Geman, H., and Yor, M.. “Bessel Processes, Asian Options and Perpetuities.” Mathematical Finance,(1993), 349–375.CrossRefGoogle Scholar
Hull, J., and White, A.. “Efficient Procedures for Valuing European and American Path Dependent Options.” Journal of Derivatives, 1 (1993), 21–31.CrossRefGoogle Scholar
Jacod, J., and Shiryaev, A.. Limit Theorems for Stochastic Processes. New York, NY: Springer-Verlag (1980).Google Scholar
Ju, N. “Fourier Transformation, Martingale, and the Pricing of Average-Rate Derivatives.” Mimeo, Univ. of Maryland (1997).CrossRefGoogle Scholar
Ju, N. “Pricing Asian and Basket Options via Taylor Expansion of the Underlying Volatility.” Mimeo, Univ. of Maryland (2000).Google Scholar
Kemna, A., and Vorst, A.. “A Pricing Method for Options Based on Average Asset Values.” Journal of Banking and Finance, (1990), 113–129.CrossRefGoogle Scholar
Levy, E. “The Valuation of Average Rate Currency Options.” Journal of International Money and Finance, 11 (1992), 474–491.CrossRefGoogle Scholar
Litzenberger, R.; Beaglehole, D.; and Reynolds, C.. “Assessing Catastrophe Reinsurance-Linked Securities as a New Asset Class.” Mimeo, Goldman Sachs (1996).Google Scholar
Merton, R. “Theory of Rational Option Pricing.” Bell Journal of Economics, 4 (1973), 141–183.Google Scholar
Milevsky, M., and Posner, S.. “Asian Options, the Sum of Lognormals and the Reciprocal Gamma Distribution.” Journal of Financial and Quantitative Analysis, 33 (1998), 409–422.CrossRefGoogle Scholar
Tilley, J. “The Latest in Financial Engineering: Structuring Catastrophe Reinsurance as a High-Yield Bond.” Mimeo, Morgan Stanley and Company (1995).Google Scholar
Turnbull, S., and Wakeman, L.. “A Quick Algorithm for Pricing European Average Options.” Journal of Financial and Quantitative Analysis, 26 (1991), 377–389.CrossRefGoogle Scholar