In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The BlackScholes option pricing model with dividends is:

C = S e^dt N(d₁) E e^Rt N(d₂)

d₁ = [ln(S/E) + (R d + ² / 2) t] / ( tt)

d₂ = d₁ tt

All of the variables are the same as the BlackScholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock.

A stock is currently priced at $82 per share, the standard deviation of its return is 56 percent per year, and the risk-free rate is 3 percent per year, compounded continuously. What is the price of a call option with a strike price of $78 and a maturity of six months if the stock has a dividend yield of 3 percent per year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Price of call option

$