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)
d2 = d1 – σ × √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. What effect do you think the dividend yield will have on the price of a call option? Explain.
b. A stock is currently priced at $83 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 5 percent per year compounded continuously. What is the price of a call option with a strike price of $85 and a maturity of 6 months if the stock has a dividend yield of 2 percent per year?