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 behaviors, e.g. in 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, zero-coupon bonds, and arithmetic Asian options. 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. The framework is shown to be able to also handle the case of skew jump diffusions. Numerical results demonstrate that our approach is accurate and efficient, and recover various benchmark results in the literature in a unified fashion.

Keywords: Skew diffusion, local time, continuous-time Markov chain, option pricing, target zone,psychological barriers

JEL Classification: G12, G13