The setting for this problem is the multi$-$period binomial model with T $=2,$ S$0=$ $$100,$

u $=2,$ d $=1/2,$ r $=0\mathrm{.}1.$ Consider an American put option with strike price K $=$ $$120.$

$($a$)$ Use a binary tree to compute the no$-$arbitrage initial price of the American put

option.

$($b$)$ Determine an explicit superhedging strategy $$ for this option.

$($c$)$ Suppose that you can buy the American put option at time zero for $$1$ less than its

no$-$arbitrage price. Describe an investment strategy that yields an arbitrage opportunity

for a buyer of the American put option. In particular, you need to describe the stopping

time at which the buyer will exercise the option.