In: Finance
In addition to the five factors, 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. The put-call parity condition is also altered when dividends are paid. The dividend-adjusted put-call parity formula is: S×e−dt+P=E×e−Rt+C where d is again the continuously compounded dividend yield. A stock is currently priced at $89 per share, the standard deviation of its return is 46 percent per year, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of a put option with a strike price of $85 and a maturity of six months if the stock has a dividend yield of 2 percent per year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)