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 .
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are 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 option by BTM and EDS have the monotonic property on time variable are found. Using convergence of EDS for variational inequality model of American options to viscosity solution the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied .
R
Convergence of binomial tree method
Binomial tree methods (BTM)
A
(EDS)
D
put
R
is
are
D
put
R
explicit difference scheme
EDS
R
Convergence of BTM and explicit difference schemes for the
Using convergence of EDS for
D
put
R
is proved
the decreasing property of the price of American put options and increasing property of the optimal exercise boundary on time variable are proved. First, put options are considered. Then the linear homogeneity and call-put symmetry of the price functions in the BTM and the EDS for the variational inequality model of American options with time dependent coefficients are studied and using them call options are studied