use the numeraire pricing

method outlined in the lecture instead of replication $($use the risk$-$free asset as the numeraire$)$:

A market has a risky binomial asset with parameters S$0=10,$ Su $=12,$ and Sd $=8,$ and a risk$-$free asset

that gains simple interest r $=0\mathrm{.}05$ over a single period $($the risk$-$free asset can be modelled as a binomial

asset with initial value $1$ and terminal value $1+$ r in all future states of the universe$).$ Find the value of

a call option in this market with strike price K $=10.$