A Markov Chain Approximation Scheme for Option Pricing Under Skew Diffusions

31 Pages Posted: 25 Jun 2019

See all articles by Kailin Ding

Kailin Ding

Nankai University - School of Mathematical Sciences

Zhenyu Cui

Stevens Institute of Technology - School of Business

Yongjin Wang

Nankai University - Business School

Date Written: June 18, 2019

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

Suggested Citation

Ding, Kailin and Cui, Zhenyu and Wang, Yongjin, A Markov Chain Approximation Scheme for Option Pricing Under Skew Diffusions (June 18, 2019). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=3406811 or http://dx.doi.org/10.2139/ssrn.3406811

Kailin Ding

Nankai University - School of Mathematical Sciences ( email )

Weijin Road #94
Tianjin, 300071
China

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Yongjin Wang

Nankai University - Business School ( email )

94 Weijin Road, Nankai District
Tianjin, 300071
China

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