A call option with a time to maturity of nine months and an exercise price of $$28$ is

written on a stock whose current price is $$30.$ The stock distributes a dividend of $1\mathrm{.}0\%$

everyone quarter, and last one was distributed one month ago. The risk$-$free interest rate

is $4\mathrm{.}8\%$ p$.$a$.($compounded continuously$)$ and the stock's volatility is $38\%$ p$.$a$..$

a$.$ Please use a four$-$step binomial tree to estimate the option value and delta for both

the European and American cases. $($Note: please estimate delta using the next two

nodes as shown in class $-$ you only have to estimate the current delta, not for the

future nodes$).$

b$.$ Now, assume instead that the third dividend distribution is $3\%.$ Recalculate the

European and American call values and compare them. What can you conclude?