Multivariate Binomial Approximations to the Valuation of Exotic Options

10.6985/TBFQ.200306.0001

張森林

binomial option ； pricing model ； multivariate binomial tree ； American option ； exotic option

台灣金融財務季刊

4卷2期（2003 / 06 / 01）

1 - 16

英文

Ho, Stapleton and Subrahmanyam (1995, hereafter HSS) propose an efficient method of approximating a general, multivariate and/or multiperiod lognormal distribution by a multivariate binomial process. Their method is general for the valuation of many kinds of exotic options, such as an option with n exercise dates, an outperformance option, and a quanto option, whose payoff depends on multiple variables and/or dates. This paper makes further contributions to improve their method. Firstly, this paper shows the efficient way to construct HSS's binomial tree to enhance the convergence performance. We give an example of applying their method to value an option on the minimum of two assets. Secondly, the conditional probabilities for multiperiod cases are generalized such that their method is applicable to more general stochastic processes. Thirdly, the conditional probabilities and up and down movements for the multiperiod and multivariate cases are corrected to be applicable to general processes. The error concerning the required inputs for their method is also discussed. Finally, we extend HSS's method to a general, multivariate normal distribution process.

1. Chang, C. C.(1995).Lancaster University.
2. Cheuk, T.,T. Vorst(1996).Complex Barrier Options.Journal of Derivatives,4,8-22.
3. Geske, R.,H. E. Johnson(1984).The American Put Option Valued Analytically.Journal of Finance,39,1511-1524.
4. Greene, W. H.(1993).Econometric Analysis.New York:Macmillan Publishing Company.
5. Ho, T.S.(1997).The Valuation of American Options on Bonds.Journal of Banking and Finance,21,1487-1513.
6. Ho, T.S.,R. C. Stapleton,M. G. Subrahmanyam(1995).Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics.The Review of Financial Studies,8,1125-1152.
7. Ho, T.S.,R. C. Stapleton,M. G. Subrahmanyam(1997).The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique.Journal of Finance,52,827-840.
8. Hull, J.,A. White(1993).Efficient Procedures for Valuing European and American Path-dependent Options.Journal of Derivatives,3,21-31.
9. Hull, J.,A. White(1988).The Use of the Control Variate Technique in Option Pricing.Journal of Financial and Quantitative Analysis,23,237-251.
10. Johnson, H.(1987).Options on the Maximum or the Minimum of Several Assets.Journal of Financial and Quantitative Analysis,22,277-283.
11. Kat, H.(1995).Pricing Lookback Options using Binomial Trees: An Evaluation.Journal of Financial Engineering,4,375-397.
12. Stulz, R. M(1982).Options on the Minimum or the Maximum of Two Risky Assets.Journal of Financial Economics,10,161-185.