A Markov chain approximation scheme for option pricing under skew diffusions

Abstract

In this paper, we propose a general valuation framework for option pricing problems related to skew diffusions based on a continuous-time Markov chain approximation to the underlying stochastic process. We obtain an explicit closed-form approximation of the transition density of a general skew diffusion process, which facilitates the unified valuation of various financial contracts written on assets with natural boundary behavior, e.g. in the foreign exchange market with target zones, and equity markets with psychological barriers. Applications include valuation of European call and put options, barrier and Bermudan options, and zero-coupon bonds. Motivated by the presence of psychological barriers in the market volatility, we also propose a novel ‘skew stochastic volatility’ model, in which the latent stochastic variance follows a skew diffusion process. Numerical results demonstrate that our approach is accurate and efficient, and recovers various benchmark results in the literature in a unified fashion.