Pricing European options on regime-switching assets: a comparative study of Monte Carlo and finite-difference approaches

Xiangchen Zeng, Ivan Guo, Song-Ping Zhu

Abstract


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.

doi:10.1017/S1446181117000335

Keywords


option pricing, regime-switching model, finite-difference method, Monte Carlo simulation, variance-reduction technique, simulating total occupation time.



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.10836



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.