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 important features of such multivariate distributions. First, the state variables may have volatilities that change over time. Second, the two or more relevant state variables involved may covary with each other in a specified manner, with a time-varying covariance structure. We discuss the asymptotic properties of the resulting processes and show how the mothodology can be used to value a complex, multiple-exerciseable option whose payoff depends on the prices of two assets