Convergence of binomial tree method and explicit difference scheme for American put options with time dependent coefficients

Convergence of binomial tree method and explicit difference schemes for the variational inequality model of American put options with time dependent coefficients is studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partition of time interval with equal parts is used. A time interval partition method that allows binomial tree dynamics of the underlying asset's price is provided. Conditions under which the prices of American put option by BTM and explicit difference scheme have the monotonic property on time variable are found. Convergence of BTM and explicit difference schemes for the variational inequality model of American put options to viscosity solution is proved.