AN IMPROVED MARKOV CHAIN APPROXIMATION METHODOLOGY: DERIVATIVES PRICING AND MODEL CALIBRATION

Chia Chun Lo () and Konstantinos Skindilias ()
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Chia Chun Lo: Faculty of Business Administration, University of Macau, Avenida Padre Toms Pereira, Taipa, Macau, China
Konstantinos Skindilias: Department of Mathematics, School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, London, SE10 9LS, United Kingdom

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 07, 1-22

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.

Keywords: Markov chain approximation; jump-diffusion; model calibration (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (19)

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DOI: 10.1142/S0219024914500472

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