Department of Mathematics
Numerical methods for backward Markov chain driven Black-Scholes option pricing
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. © 2010 Higher Education Press and Springer-Verlag Berlin Heidelberg.
American option, backward Markov regime switching, European option, free boundary problem, method of fundamental solutions (MFS)
Source Publication Title
Frontiers of Mathematics in China
Au, Chi Yan, Eric S. Fung, and Leevan Ling. "Numerical methods for backward Markov chain driven Black-Scholes option pricing." Frontiers of Mathematics in China 6.1 (2011): 17-33.