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

$S_{t_0}=100,u=1\mathrm{.}1,d=0\mathrm{.}9,r=0\mathrm{.}05,t=1.$

Compute the price as well as the replication strategy of the European knock$-$out

call option with strike price $K=95$ and barrier $H=90.($The knock$-$out option

is a path$-$dependent option, such that the payoff becomes $0$ if the underlying

asset's price hits or falls below barrier $H$ during the option's lifetime.$)$