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PRICING EUROPEAN OPTIONS ON REGIME-SWITCHING ASSETS: A COMPARATIVE STUDY OF MONTE CARLO AND FINITE-DIFFERENCE APPROACHES

Part of: Probabilistic methods, simulation and stochastic differential equations Partial differential equations, boundary value problems

Published online by Cambridge University Press:  23 October 2017

X. C. ZENG Open the ORCID record for X. C. ZENG [Opens in a new window] ,
I. GUO  and
S. P. ZHU
X. C. ZENG*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email xz379@uowmail.edu.au, spz@uow.edu.au
I. GUO
Affiliation:
School of Mathematical Sciences, Clayton Campus, Monash University, VIC 3800, Australia email ivan.guo@monash.edu.au
S. P. ZHU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email xz379@uowmail.edu.au, spz@uow.edu.au
*
✉xz379@uowmail.edu.au
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Abstract

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A numerical comparison of the Monte Carlo (MC) simulation and the finite-difference method for pricing European options under a regime-switching framework is presented in this paper. We consider pricing options on stocks having two to four volatility regimes. Numerical results show that the MC simulation outperforms the Crank–Nicolson (CN) finite-difference method in both the low-frequency case and the high-frequency case. Even though both methods have linear growth, as the number of regimes increases, the computational time of CN grows much faster than that of MC. In addition, for the two-state case, we propose a much faster simulation algorithm whose computational time is almost independent of the switching frequency. We also investigate the performances of two variance-reduction techniques: antithetic variates and control variates, to further improve the efficiency of the simulation.

Keywords

option pricingregime-switching modelfinite-difference methodMonte Carlo simulationvariance-reduction techniquesimulating total occupation time

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 65N06: Finite difference methods
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 183 - 199
Copyright
© 2017 Australian Mathematical Society 

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