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