On the Computation of Continuous Time Option Prices Using Discrete Approximations

We develop a class of discrete, path-independent models to compute prices of American options within the Black-Scholes (1973) framework, including models in which state variables have time-varying volatility functions and models with multiple state variables. Time-varying volatility functions are illustrated with applications to term structure models developed by Vasicek (1977) and Heath, Jarrow, and Morton (1988), (1990). Distinct from previous work in the literature, the multivariate models suggested in this paper are consistent with arbitrarily large, though constant, covariance functions. Finally, we compare and contrast the numerical accuracy of a large number of models with simulation results.