Pricing Barrier Options with Time-Dependent Parameters and Curved Boundaries

The major purpose of this paper is to discuss the valuation of barrier option with time-dependent parameters: risk-free rate, dividend yield, instantaneous volatility and curved boundaries. Applying the non-uniform space grid approach, we extend the Crank-Nicolson method, and use the generalized method to solve the numerical experiments for our barrier option problem. Furthermore, corresponding to explicit time dependent parameters and curved boundary function, we give some numerical examples.