A Simplified Approach to Approximate Diffusion Processes Widely Used in Finance

We propose a simplified approach to approximate a variety of heteroskedastic diffusions widely used in finance to describe the evolution of state variables such as equity prices, short interest rates, and others. In contrast to the common approach based on the approximating a new homoskedastic process obtained by transforming the original heteroskedastic one, we build up binomial and trinomial trees that directly discretize the initial process. Despite this, the proposed approximation models are based on recombining lattices that converge weakly to the corresponding limiting diffusion. Numerical results show that the proposed algorithms are efficent and that they compute accurate prices.