Francesco Rotondi

Università Bocconi

Title

Effective binomial discretizations of bivariate diffusion processes

Author

Francesco Rotondi

Abstract

In this paper, we investigate the general conditions under which a bivariate continuous-time stochastic process can be approximated by a computationally feasible discrete-time bivariate binomial process. The key requirement is that two associated partial differential equations must be explicitly solvable. As a prominent application of this result, we construct a simple recombining bivariate binomial tree for the stochastic volatility model introduced by Heston (1993). We then use this discretized model to compute no-arbitrage prices for European call and put options, obtaining results consistent with those produced by other well-known numerical methods. Finally, we conduct an in-depth analysis of the two-dimensional free boundaries of American call and put options as functions of the spot price and spot volatility.