Let us consider a two$-$step binomial tree model with the following parameters:

$S_{t_0}=100,u=1\mathrm{.}1,d=0\mathrm{.}9,r=0\mathrm{.}03,t=1.$

Compute the price as well as the replication strategy of the American call with

strike $K=90.($For the American call, the option holder can exercise the option

at any time of $t_0,t_1,t_2,$ and the payoff of the option at the exercise time $t_k$ is

given by $(S_{t_k}-K{)}^{+}.)$