Multivariate Binomial Approximations for Asset Prices with Non-Stationary Variance and Covariance Characteristics

In this paper, we suggest an efficient method of approximating a general, multivariate lognormal distribution by a multivariate binomial process. There are two features of such multivariate distributions that are of interest. First, the state variables may have volatilities that change over different time intervals. Second, the two or more relevant state variables involved may covary with each other in a specified manner, with a covariance structure that changes over time. Our method combines and extends previous work by Boyle (1988), Nelson and Ramaswamy (1990) and Amin (1991) who each deal with some aspects of the general problem. We discuss the asymptotic properties of the resulting processes and show how the methodology can be used to value a complex, multiple-exerciseable option whose payoff depends on the price of two assets