Question

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)C=S×e−dt×N(d1)⁢−E×e−Rt×N(d2)

d1=[ln(S/E)+(R−d+σ2/2)×t](σ−t√)d1= [ln(S⁢  /E⁢ ) +(R⁢−d+σ2/2)×t ] (σ−t)

d2=d1−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+CS×e−dt+P=E×e−Rt+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?

Answer 1

Price of put is 7.0792