Use the following inputs to compute the price of a European call option: S = $100, K = $50, r = 0.06, σ = 0.30, T = 0.01, δ = 0.
a. Verify that the Black-Scholes price is $50.0299.
b. Verify that the vega for this option is almost zero. Why is this so?
c. Verify that if you compute the option price with volatilities ranging from 0.05 to 1.00, you get essentially the same option price and vega remains about zero. Why is this so? What happens if you set σ = 5.00 (i.e., 500%)?
d. What can you conclude about difficulties in computing implied volatility for very short-term, deep in-the-money options?