Consider a non$-$dividend$-$paying stock whose current price is $$100.$ Using a two$-$period binomial tree and assuming that the risk$-$free rate is $0\mathrm{.}30\%$ per month and that $u=1\mathrm{.}05$ and $d=0\mathrm{.}95.$

$($a$)(2$ points$)$ What is the current $($i$.$e$.,$ time$-0)$ price of a $2-$month European call on the stock whose exercise price is $$99?$ What is its price at the end of the first month $($i$.$e$.,$ the start of the second month$)$ in the up state? What is its price at the end of the first month in the down state?

$($b$)(2$ points$)$ Suppose that you have just written the above call. What is the starting hedge ratio? What is the hedge ratio for the second period in the up state? What is the hedge ratio for the second period in the down state?

$($c$)(2$ point$)$ Use the binomial model to find the current $($i$.$e$.,$ time$-0)$ price of a $2-$month European put on the stock with the same exercise price. Then, verify that Put Call Parity holds.