Consider a European Call option with the strike price K=100 with the underlying trading at S=100.

It is given that the risk free rate r=0.05. Using the Black Scholes formula

a) Fix the time to expiry at 3 months. Plot the value of the option vs. volatility for = 0.1, 0.15, 0.2, 0.25, ...0.8. Comment on your observations

b) Fix the volatility at = 0.2. Plot the value of the option vs. time to expiry t =1, 2, 3, ...12 months. Comment your observations