Efficient finite difference method for optimal portfolio in a power utility regime-switching model

2018 ◽  
Vol 96 (11) ◽  
pp. 2115-2134 ◽  
Author(s):  
Tihomir B. Gyulov ◽  
Miglena N. Koleva ◽  
Lubin G. Vulkov
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Regime Switching ◽  
Optimal Portfolio ◽  
Power Utility ◽  
Regime Switching Model ◽  
Switching Model

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

2017 ◽  
Vol 59 (2) ◽  
pp. 183-199 ◽  
Author(s):  
X. C. ZENG ◽  
I. GUO ◽  
S. P. ZHU
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Regime Switching ◽  
Computational Time ◽  
Switching Frequency ◽  
Numerical Comparison ◽  
European Options ◽  
Mc Simulation

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.

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