Let us consider a two$-$step binomial tree model with interest rate $r=$

$0\mathrm{.}05,S_{t_0}=100,u=1\mathrm{.}1,d=0\mathrm{.}9,t=1.$ The option we consider has ma$-$

turity time $T=t_2=2t,$ and payoff $S_T^2{1}_{\{S_T)}>90.$

Compute the price and the replication strategy of the option.