An improved Markov Chain Approximation methodology: Derivatives pricing and model calibration
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:https://doi.org/10.1142/S0219024914500472)
Full text not available from this repository.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 |
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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: | |
Last Modified: | 04 Mar 2022 13:07 |
URI: | http://gala.gre.ac.uk/id/eprint/13660 |
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