Consider a two step binomial tree with the following parameters: $S_{t_0}=$

$100,u=1\mathrm{.}2,d=0\mathrm{.}8,r=0\mathrm{.}05,t=1.$ Find the European knock$-$out call

option with a strike price of $95$ and a barrier of $90$ and the corresponding

replication strategy. $($The payout of the knockout call option at time $t_2$ is given

by

$(S_{t_2}-K{)}_{+}*1_{\{mi{n}_{\text{k}\text{i}\text{n}\{0,1,2\}}{S}_{t_k})}>H$

where $K$ is the strike price and $H$ is the barrier price.$)$