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 $87 per share, the standard deviation of its return is 42 percent per year, and the risk-free rate is 6 percent per year, compounded continuously. What is the price of a call option with a strike price of $83 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.)

  

Price of call option

$

Answer 1

Please refer to the screenshot below showing all the calculations:

(I have used symbol 'K' for strike price & 'y' for dividend yield. These are same as 'E' & 'd' in the formula included in your question)

The following screenshot shows the formula view of calculations:

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