2. (a) Find a stock that pays a dividend and estimate the continuously compounded dividend payment rate (for example, .02). Using the Black/Scholes option pricing model (including dividends), estimate the price of an at the money call option and put option that have the same exercise price and maturity date. Assume r=.005 and use the appropriate S₀, t, K. For volatility, use 40%.

(b) Evaluate how well the Black/Scholes model worked by comparing the results to the midpoints of the bid-ask prices.

(c) Find (through trial and error using the Black/Scholes formula), the implied volatility of the (i) midpoint call price and (ii) midpoint put price.

(d) Are the results of (c) the same? In theory should they be the same? Explain.