scholarly journals A numerical study for optimal portfolio regime-switching model I. 2D Black–Scholes equation with an exponential non-linear term

2017 ◽  
Vol 318 ◽  
pp. 538-549 ◽  
Author(s):  
Miglena N. Koleva ◽  
Lubin G. Vulkov
Keyword(s):  
Regime Switching ◽  
Numerical Study ◽  
Optimal Portfolio ◽  
Linear Term ◽  
Regime Switching Model ◽  
Switching Model ◽  
Black Scholes ◽  
Non Linear

scholarly journals Option pricing in a regime-switching model using the fast Fourier transform

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
R. H. Liu ◽  
Q. Zhang ◽  
G. Yin
Keyword(s):  
Fourier Transform ◽  
Markov Chain ◽  
Fast Fourier Transform ◽  
Regime Switching ◽  
Asset Price ◽  
Sample Path ◽  
Regime Switching Model ◽  
Switching Model ◽  
Large State Space ◽  
Black Scholes

This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black-Scholes formula. Finally, numerical results are reported.

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