In addition to the five factors, dividends also affect the price of an option. The BlackScholes Option Pricing Model with dividends is:

C=SedtN(d1)EeRtN(d2)C=SedtN(d1)EeRtN(d2)

d1=[ln(S/E)+(Rd+2/2)t](t)d1=[ln(S/E)+(Rd+2/2)t](t)

d2=d1td2=d1t

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.

The putcall parity condition is also altered when dividends are paid. The dividend-adjusted putcall parity formula is:

Sedt+P=EeRt+CSedt+P=EeRt+C

where d is again the continuously compounded dividend yield.

A stock is currently priced at $86 per share, the standard deviation of its return is 40 percent per year, and the risk-free rate is 5 percent per year, compounded continuously. What is the price of a put option with a strike price of $82 and a maturity of six months if the stock has a dividend yield of 3 percent per year?