Numerical method for discrete double barrier option pricing with time-dependent parameters

In this paper, the main purpose is pricing of discrete double barrier option under Black-Scholes framework with time dependent parameters. By some conventional transforms, in each monitoring interval, the problem is reduced to well-known Black-Scholes partial differential equations with convenient constant coefficient such that the solution can be expressed recursively upon the heat equation solution. Finally a numerical method is proposed to compute the obtained recursive formula efficiently. Also, the Greeks of contract are calculated.