Lo, Chia Chun and Skindilias, Konstantinos (2014) An improved Markov Chain Approximation methodology: Derivatives pricing and model calibration. International Journal of Theoretical and Applied Finance, 17 (07):1450047. pp. 1-22. ISSN 0219-0249 (Print), 1793-6322 (Online) (doi:10.1142/S0219024914500472)

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Abstract

This paper presents an improved continuous-time Markov chain approximation (MCA) methodology for pricing derivatives and for calibrating model parameters. We propose a generalized nonequidistant grid model for a general stochastic differential equation, and extend the proposed model to accommodate a jump component. Because the prices of derivatives generated by the MCA models are sensitive to the setting of the chain's state space, we suggest a heuristic determination of the grid spacing such that the Kolmogorov-Smirnov distance between the underlying distribution and the MCA distribution is minimized. The continuous time setting allows us to introduce semi-analytical formulas for pricing European and American style options. The numerical examples demonstrate that the proposed model with a nonequidistant grid setting provides superior results over the equidistant grid setting. Finally, we present the MCA maximum likelihood estimator for a jump-diffusion process. The encouraging results from the simulation and empirical studies provide insight into calibration problems in finance where the density function of a jump-diffusion model is unknown.

Item Type:	Article
Uncontrolled Keywords:	Markov chain approximation, jump-diffusion, model calibration
Subjects:	Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS) Faculty of Engineering & Science
Related URLs:	Publisher
Last Modified:	04 Mar 2022 13:07
URI:	http://gala.gre.ac.uk/id/eprint/13660

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