In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black-Scholes option pricing model with dividends is:
C = S × e-dt × N(d1) – E × e-Rt × N(d2)d1 = [ln(S/E) + (R – d + σ2 / 2) × t] / (σ × t√t)d2 = d1 – σ × t√t
All of the variables are the same as the Black-Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock.
A stock is currently priced at $85 per share, the standard deviation of its return is 62 percent per year, and the risk-free rate is 6 percent per year, compounded continuously. What is the price of a call option with a strike price of $81 and a maturity of six months if the stock has a dividend yield of 2 percent per year?