Numerical methods for backward Markov chain driven Black-Scholes option pricing

doi:10.1007/s11464-010-0089-2

Front Math Chin

2011, Vol. 6

Issue (1) : 17-33 https://doi.org/10.1007/s11464-010-0089-2

RESEARCH ARTICLE

Numerical methods for backward Markov chain driven Black-Scholes option pricing

Chi Yan AU, Eric S. FUNG, Leevan LING(

)

Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

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Abstract

The drift, the risk-free interest rate, and the volatility change over time horizon in realistic financial world. These frustrations break the necessary assumptions in the Black-Scholes model (BSM) in which all parameters are assumed to be constant. To better model the real markets, a modified BSM is proposed for numerically evaluating options price–changeable parameters are allowed through the backward Markov regime switching. The method of fundamental solutions (MFS) is applied to solve the modified model and price a given option. A series of numerical simulations are provided to illustrate the effect of the changing market on option pricing.

Keywords backward Markov regime switching method of fundamental solutions (MFS) free boundary problem American option European option

Corresponding Author(s): LING Leevan,Email:lling@hkbu.edu.hk

Issue Date: 01 February 2011

Cite this article:

Chi Yan AU,Eric S. FUNG,Leevan LING. Numerical methods for backward Markov chain driven Black-Scholes option pricing[J]. Front Math Chin, 2011, 6(1): 17-33.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0089-2
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I1/17

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[1]	Ran ZHANG,Haiming SONG,Nana LUAN. Weak Galerkin finite element method for valuation of American options[J]. Front. Math. China, 2014, 9(2): 455-476.
[2]	LIN Jianwei, LIANG Jin. Pricing of perpetual American and Bermudan options by binomial tree method[J]. Front. Math. China, 2007, 2(2): 243-256.

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