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In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black - Scholes option pricing model

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\times edt\times N(d1)E\times eRt\times N(d2)
d1=[ln(S/E)+(Rd+\sigma 2/2)\times t](\sigma t)
d2=d1\sigma \times 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.
The put-call parity condition is altered when dividends are paid. The dividend-adjusted put-call parity formula is:
S\times edt+P=E\times eRt+C
where d is the continuously compounded dividend yield.
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 put 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.)

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