Derivatives Pricing and Model Calibration Using Continuous Time Markov Chain Approximation Model

43 Pages Posted: 28 Aug 2012

See all articles by Chia Lo

Chia Lo

University of Macau - Department of Finance and Business Economics

Konstantinos Skindilias

University of Greenwich, CMS

Date Written: August 27, 2012

Abstract

We propose a non-equidistant Q rate matrix setting formula such that a well-defined continuous time Markov chain can lead to excellent approximations to jump-diffusions with affine or non-affine functional specifications. This approach also accommodates state-dependent jump intensity and jump distribution, a fexibility that is very hard to achieve with traditional numerical methods. Our approach not only satisfies Kushner (1990) local consistency conditions but also resolves the approximation errors induced by Piccioni (1987) scheme. European stock option pricing examples based on jump-diffusions illustrate the ease of implementation of our model. The proposed algorithm for pricing American options highlights the speed and accuracy. Finally the empirical analysis using daily VIX data shows that the maximum likelihood estimates of the underlying jump-diffusions can be efficiently computed by the model proposed in this article.

Keywords: continuous time Markov chain, diffusion approximation, local consistency, option pricing

JEL Classification: C60, G10, G12, G13

Suggested Citation

Lo, Chia and Skindilias, Konstantinos, Derivatives Pricing and Model Calibration Using Continuous Time Markov Chain Approximation Model (August 27, 2012). Available at SSRN: https://ssrn.com/abstract=2136822 or http://dx.doi.org/10.2139/ssrn.2136822

Chia Lo (Contact Author)

University of Macau - Department of Finance and Business Economics ( email )

Macau

Konstantinos Skindilias

University of Greenwich, CMS ( email )

30 Park Row
Greenwich
London, SE10 9LS
United Kingdom

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