$($a$)$ Compute the price of a European put option written on a non$-$dividend$-$payingstock. The current stock price is$$100$ and the volatility of the stock price is $30\%.$The maturity of the option is in three months and the strike price is$$105.$ The risk free interest rate with continuous compounding is $3\%$ per annum. You shoulduse a three step $($period$)$ binomial model to price the option.

$($b$)$ Use the same setup as in $($a$),$ except this time you should price an American put

option $($with strike $K=105).$