OUESTION TWO $[20$ marks$]$

Consider a one$-$year European stock put option. The current stock price is Sh $\mathrm{.}50$ and the exercise price is Sh$.54.$ The risk$-$free rate is $6\%$ and the size of the up move is $1\mathrm{.}25$ per year. Required.

Using binomial model

a$)$ Calculate the put price today $(5$ marks$)$

$\frac{1}{2}$ b$)$ Suppose the available$-$cat, price is Sh$.3,$ determine the arbitrage strategy assume you tra $1,000$ options. $(8$ marks$)$

c$)$ What would be the put price today if it were a $2-$year American option? $(7$ marks$)$