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Pricing and Hedging Path-Dependent Options Under the CEV Process

  • Dmitry Davydov

    ()

    (Equities Quantitative Strategies, UBS Warburg, 677 Washington Boulevard, Stamford, Connecticut 06901)

  • Vadim Linetsky

    ()

    (Department of Industrial Engineering and Management Sciences, McCormick School of Engineering and Applied Sciences, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208)

Registered author(s):

    Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance (CEV) diffusion model where the volatility is a function of the underlying asset price. We derive analytical formulae for the prices of important types of path-dependent options under this assumption. We demonstrate that the prices of options, which depend on extrema, such as barrier and lookback options, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.

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    File URL: http://dx.doi.org/10.1287/mnsc.47.7.949.9804
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 47 (2001)
    Issue (Month): 7 (July)
    Pages: 949-965

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    Handle: RePEc:inm:ormnsc:v:47:y:2001:i:7:p:949-965
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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    2. Antoon Pelsser, 1997. "Pricing Double Barrier Options: An Analytical Approach," Tinbergen Institute Discussion Papers 97-015/2, Tinbergen Institute.
    3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    4. Goldenberg, David H., 1991. "A unified method for pricing options on diffusion processes," Journal of Financial Economics, Elsevier, vol. 29(1), pages 3-34, March.
    5. Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 241-264, June.
    6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    7. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
    8. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(04), pages 533-554, November.
    9. Conze, Antoine & Viswanathan, 1991. " Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-907, December.
    10. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
    11. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-91.
    12. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298.
    13. Goldman, M Barry & Sosin, Howard B & Shepp, Lawrence A, 1979. "On Contingent Claims That Insure Ex-post Optimal Stock Market Timing," Journal of Finance, American Finance Association, vol. 34(2), pages 401-13, May.
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