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

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.