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.

  

A stock is currently priced at $88 per share, the standard deviation of its return is 44 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 $84 and a maturity of six months if the stock has a dividend yield of 3 percent per year?

Answer 1

Price of call is 12.5594