Skip to main content
placeholder image

Pricing European Options On Regime-switching Assets: A Comparative Study Of Monte Carlo And Finite-difference Approaches

Journal Article


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.

Authors


  •   Zeng, Xiangchen (external author)
  •   Guo, Ivan W. (external author)
  •   Zhu , Song-Ping

Publication Date


  • 2017

Citation


  • Zeng, X. C., Guo, I. & Zhu , S. P. (2017). Pricing European Options On Regime-switching Assets: A Comparative Study Of Monte Carlo And Finite-difference Approaches. ANZIAM Journal, 59 (2), 183-199.

Scopus Eid


  • 2-s2.0-85032178292

Number Of Pages


  • 16

Start Page


  • 183

End Page


  • 199

Volume


  • 59

Issue


  • 2

Place Of Publication


  • United Kingdom

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.

Authors


  •   Zeng, Xiangchen (external author)
  •   Guo, Ivan W. (external author)
  •   Zhu , Song-Ping

Publication Date


  • 2017

Citation


  • Zeng, X. C., Guo, I. & Zhu , S. P. (2017). Pricing European Options On Regime-switching Assets: A Comparative Study Of Monte Carlo And Finite-difference Approaches. ANZIAM Journal, 59 (2), 183-199.

Scopus Eid


  • 2-s2.0-85032178292

Number Of Pages


  • 16

Start Page


  • 183

End Page


  • 199

Volume


  • 59

Issue


  • 2

Place Of Publication


  • United Kingdom