14. Note that the Black-Scholes formula gives the price of European call c given the time to expiration T, the strike price K, the stocks spot price S0, the stocks volatility , and the risk-free rate of return r : c = c(T, K, S0, , r). All the variables but one are observable, because an investor can quickly observe T, K, S0, r. The stock volatility, however, is not observable. Rather it relies on the choice of models the investor uses. The price of the option, c, if traded, is observable. So we can flip the problem around. Given observables T, K, S0, r and c, what volatility should the stock have in order for the Black-Scholes formula to be correct. This is called the implied volatility, BS. Some calculus, shows that BS exists and is unique.

The current spot price is $40, the expected rate of return of the stock is 8%, the risk-free rate is 3%. A European call option on the stock with strike price $40 expiring in 4 months is currently trading for $2. With trial and error, find a one-percentage point range which contains the implied volatility. So your answer should be of the form 14% BS 15%