Problem $2.$ Consider a one$-$period binomial model, where $S_0=4,u=2,d=\frac{1}{2},$ and $r=25\%.$ Also,

consider a European call option with strike price $$5.$

$10($a$)$ By using the risk$-$neutral pricing formula, calculate the option value at each node.

$10($b$)$ If the option is traded at $$1\mathrm{.}5$ at time $0,$ then show explicitly how you can make an arbitrage profit.

$($c$)$ If the option is traded at $$1$ at time $0,$ then show explicitly how you can make an arbitrage profit.