Multivariate Binomial Approximations to the Valuation of Exotic Options

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.