Consider a one$-$step binomial model with underlying asset prices S$(0)=4,$ S$(1,)=8,$

S$(1,)=2$ and interest rate r $=0\mathrm{.}25.$ Suppose a European call option is written on

this underlying asset with strike K $=6$ and expiry T $=1.$

$($a$)$ Calculate the premium of the call by finding H$1$ and H$0$ of the replicating portfolio.

$($b$)$ Calculate the premium of the call using the one$-$step binomial asset pricing model.

$($c$)$ Calculate the premium of an otherwise identical put using the one$-$step