Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T12:07:00.119Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Black, F. and Scholes, M., “The pricing of options and corporate liabilities”, J. Polit. Econ. 81 (1973) 637–654; doi:10.1086/260062.CrossRefGoogle Scholar
Bollen, N. P. B., “Valuing options in regime-switching models”, J. Deriv. 6 (1998) 38–49; doi:10.3905/jod.1998.408011.CrossRefGoogle Scholar
Brandimarte, P., Numerical methods in finance and economics: a MATLAB-based introduction, 2nd edn (John Wiley, Hoboken, NJ, 2006).CrossRefGoogle Scholar
Buffington, J. and Elliott, R. J., “Regime switching and European options”, in: Stochastic theory control, Volume 280 of Lect. Notes in Control and Information Sciences (ed. Pasik-Duncan, B.), (Springer, Berlin–Heidelberg, 2002) 73–82.Google Scholar
Detemple, J., American-style derivatives: valuation and computation (CRC Press, Boca Raton, FL, 2005).CrossRefGoogle Scholar
Elliott, R. J., Chan, L. and Siu, T. K., “Option pricing and Esscher transform under regime switching”, Ann. Finance 1 (2005) 423–432; doi:10.1007/s10436-005-0013-z.CrossRefGoogle Scholar
Fang, F. and Oosterlee, C. W., “A novel pricing method for European options based on Fourier-cosine series expansions”, SIAM J. Sci. Comput. 31 (2009) 826–848; doi:10.1137/080718061.CrossRefGoogle Scholar
Fuh, C. D., Wang, R. H. and Cheng, J. C., “Option pricing in a Black–Scholes model with Markov switching”, 2002, working paper, https://www.researchgate.net/publication/2880608_Option_Pricing_in_a_Black-Scholes_Model_with_Markov_Switching.Google Scholar
Glasserman, P., Monte Carlo methods in financial engineering (Springer, New York, 2004).Google Scholar
Guo, X., “Information and option pricings”, Quant. Finance 1 (2001) 38–44; doi:10.1080/713665550.CrossRefGoogle Scholar
Hamilton, J. D., “A new approach to the economic analysis of nonstationary time series and the business cycle”, Econometrica 57 (1989) 357–384; doi:10.2307/1912559.CrossRefGoogle Scholar
Hieber, P. and Scherer, M., “Efficiently pricing barrier options in a Markov-switching framework”, J. Comput. Appl. Math. 235 (2010) 679–685; doi:10.1016/j.cam.2010.06.021.CrossRefGoogle Scholar
Lemieux, C., Monte Carlo and quasi-Monte Carlo sampling, Springer Ser. Statist. (Springer, New York, 2009).Google Scholar
Mielkie, M. A., “Options pricing and hedging in a regime-switching volatility model”, Ph.D. Thesis, The University of Western Ontario, 2014;http://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=3581&context=etd.Google Scholar
Mielkie, M. and Davison, M., “Investigating the market price of volatility risk for options in a regime-switching market”, SSRN Electron. J. (2013) doi:10.2139/ssrn.2326534.CrossRefGoogle Scholar
Yuen, F. L. and Yang, H., “Option pricing with regime switching by trinomial tree method”, J. Comput. Appl. Math. 233 (2010) 1821–1833; doi:10.1016/j.cam.2009.09.019.CrossRefGoogle Scholar
Zhu, S. P., Badran, A. and Lu, X., “A new exact solution for pricing European options in a two-state regime-switching economy”, Comput. Math. Appl. 64 (2012) 2744–2755; doi:10.1016/j.camwa.2012.08.005.CrossRefGoogle Scholar