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Pricing Lookback and Barrier Options under the CEV Process

Published online by Cambridge University Press:  06 April 2009

Phelim P. Boyle  and
Yisong “Sam” Tian
Phelim P. Boyle
Affiliation:
Centre for Advanced Studies in Finance, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Yisong “Sam” Tian
Affiliation:
Department of Finance, College of Business Administration, University of Cincinnati, Cincinnati, OH 45221
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Abstract

This paper examines the pricing of lookback and barrier options when the underlying asset follows the constant elasticity of variance (CEV) process. We construct a trinomial method to approximate the CEV process and use it to price lookback and barrier options. For look-back options, we find that the technique proposed by Babbs for the lognormal case can be modified to value lookbacks when the asset price follows the CEV process. We demonstrate the accuracy of our approach for different parameter values of the CEV process. We find that the prices of barrier and lookback options for the CEV process deviate significantly from those for the lognormal process. For standard options, the corresponding differences between the CEV and Black-Scholes models are relatively small. Our results show that it is much more important to have the correct model specification for options that depend on extrema than for standard options.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 34 , Issue 2 , June 1999 , pp. 241 - 264
Copyright
Copyright © School of Business Administration, University of Washington 1999

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References

Andersen, L., and Andreasen, J.. “Volatility Skews and Extensions of the Libor Market Model.” Working Paper, General Re Financial Products (1998).Google Scholar
Babbs, S. “Binomial Valuation of Lookback Options.” Working Paper, Midland Global Markets (1992).Google Scholar
Black, F. and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–659.CrossRefGoogle Scholar
Boyle, P. P. “Option Valuation Using a Three-Jump Process.” International Options Journal, 3 (1986), 7–12.Google Scholar
Boyle, P. P. “A Lattice Framework for Option Pricing with Two State Variables.” Journal f Financial and Quantitative Analysis, 35 (1988), 1–12.Google Scholar
Boyle, P. P., and Lau, S. H.. “Bumping Up against the Barrier with the Binomial Method.” Journal of Derivatives, 2 (1994), 6–14.CrossRefGoogle Scholar
Cheuk, T. H. F., and Vorst, T. C. F.. “Real-Life Barrier Options.” Unpubl. Manuscript, Erasmus Univ., Rotterdam, the Netherlands (1994a).Google Scholar
Cheuk, T. H. F., and Vorst, T. C. F.. “Lookback Options and the Observation Frequency: A Binomial Approach.” Unpubl. Manuscript, Erasmus Univ., Rotterdam, the Netherlands (1994b).Google Scholar
Cheuk, T. H. F., and Vorst, T. C. F.. “Complex Barrier Options.” Journal of Derivatives, 4 (1996), 8–22.CrossRefGoogle Scholar
Cox, J. C. “Notes on Option Pricing I: Constant Elasticity of Variance Diffusions.” Unpubl. Note, Stanford Univ. (1975).Google Scholar
Cox, J. C. “The Constant Elasticity of Variance Option Pricing Model.” Journal of Portfolio Management, 22 (1996, special issue honoring Fischer Black), 15–17.Google Scholar
Cox, J. C., and Ross, S. A.. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, 3 (1976), 145–166.CrossRefGoogle Scholar
Cox, J. C.; Ross, S. A.; and Rubinstein, M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 1 (1979), 229–264.CrossRefGoogle Scholar
Derman, E.; Kani, I.; Ergener, D.; and Bardhan, I.. “Enhanced Numerical Methods for Options with Barriers.” Financial Analysts Journal, 51 (1995), 65–74.CrossRefGoogle Scholar
Duffie, D.Dynamic Asset Pricing Theory. Princeton, NJ: Princeton Univ. Press (1996).Google Scholar
Hull, J. C., and White, A.. “Efficient Procedures for Valuing European and American Path-Dependent Options.” Journal of Derivatives, 1 (1993), 21–31.CrossRefGoogle Scholar
Kamrad, B., and Ritchken, P.. “Multinomial Approximating Models for Options with k-State Variables.” Management Science, 37 (1991), 1640–1652.CrossRefGoogle Scholar
Karatzas, I., and Shreve, S.. Brownian Motion and Stochastic Calculus. New York, NY: Springer-Verlag (1994).Google Scholar
Li, A. “Using Stock Price as Numeraire in Option Pricing Models with Nonconstant Volatility.” Advances in Futures and Options Research, 9 (1997), 37–49.Google Scholar
MacBeth, J. D., and Merville, L. J.. “Tests of the Black-Scholes and Cox Call Option Valuation Models.” Journal of Finance, 35 (1980), 285–301.Google Scholar
Merton, R. C. “The Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Ritchken, P. “On Pricing Barrier Options.” Journal of Derivatives, 3 (1995), 19–28.Google Scholar
Tian, Y. “A Modified Lattice Approach to Option Pricing.” Journal of Futures Markets, 13 (1993), 563–577.CrossRefGoogle Scholar
Tian, Y. “A Re-Examination of Lattice Procedures for Interest Rate-Contingent Claims.” Advances in Futures and Options Research, 7 (1994), 87–111.Google Scholar