Problem $3$

Consider a binomial model with $=0\mathrm{.}24,=0\mathrm{.}06$ and interest rate $r=5\%$ annual, both

compounded continuously. Using $T=1$ maturity of one year, initial stock price $S_0=100$

and $N=4$ periods, consider the American Call $C^{Am}$ with strike $K=95.$

In which scenarios is early exercise rational?

Find the premium of this Call today $C_0^{Am}.$

Suppose the stock moves are $U\frac{p}{U}\frac{p}{D}ow\frac{n}{D}$own. Compute the replicating port$-$

folio and the exercise strategy along that scenario.