Consider a non$-$dividend paying stock whose initial stock price is $62$ and has a $log-$

volatility of $=0\mathrm{.}20.$ The interest rate $r=10\%,$ compounded monthly. Consider a

$5-$month option with a strike price of $60$ in which after exactly $3$ months the purchaser

may declare this option a $($European$)$ call or put option.

Assume $u=1\mathrm{.}05943$ and $d=\frac{1}{u}=0\mathrm{.}94390$

$($a$)$ Compute the values of the binomial lattice for $51$ month period.

$($b$)$ Compute the appropriate risk$-$free rate.

$($c$)$ Find the risk$-$neutral probability tilde$(p)$ of going up$?$

$($d$)$ Find the values of call option and put option along this lattice: