Consider a stock with a current price of $$100.$ A $6-$month European call option with a strike price 

of $$102$ costs $$5.$ Assume all assumptions of the Black$-$Scholes model are satisfied.

 A$)$ Using a trial$-$and$-$error method, find the annual volatility of the stock return up to $6$ decimal digits 

 

B$)$ Find the price of a $3-$month European put option with a strike price of $$97.$