On binomial discretizations of correlated skew Brownian motions: Applications to option pricing

In this article, we establish binomial lattices for discretizing the dynamics of two correlated skew Brownian motions, each one defined as the combination of two independent processes, i.e., a standard Brownian motion and a reflecting Brownian motion. The skew Brownian motions share the reflecting component, while the two standard components show a constant correlation $\rho$. The intent is to provide an option pricing framework that can overcome the shortcomings of Black-Scholes and is useful for evaluating not only European options but also their American counterparts. Numerical experiments are performed to evaluate the accuracy of the proposed method in pricing vulnerable, spread, and exchange options. To the best of the authors' knowledge, the proposed algorithm is the first method presented in the financial literature allowing for the pricing of American-style contingent claims under correlated skew Brownian motions.