Skip navigation

An improved Markov Chain Approximation methodology: Derivatives pricing and model calibration

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
Uncontrolled Keywords: Markov chain approximation, jump-diffusion, model calibration
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Related URLs:
Last Modified: 03 Nov 2016 16:38
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/13660

Actions (login required)

View Item View Item