Question

What is the price of a European call option that is expected to pay a dividend of $1 in three months with the following parameters? s0 = $40 d = $1 in 3 months k = $40 r = 10% sigma = 20% T = 0.5 years (required precision 0.01 +/- 0.01) black scholes equation.PNG As a reminder, the cumulative probability function is calculated in Excel as follows: N(d1) = NORM.S.DIST(d1,TRUE) N(d2) = NORM.S.DIST(d2,TRUE) If the above equations don't load for whatever reason, here are the text versions of the equations as a back-up: c = So*N(d1) - K*e^(-rT)*N(d2) p = K*e^(-rT)*N(-d2) - So*N(-d1) d1 = [ln(So/K) + (r + 0.5*(sigma^2))*T] / [sigma * sqrt(T)] d2 = d1 - sigma*sqrt(T) To validate your equations, you may use the following information to ensure you have it coded correctly: s0 = 22 k = 25 r = 0.1 sigma = 0.2 T = 0.75 d1 = -0.2184 d2 = -0.3916 c = 1.03446 p = 2.22805

Answer 1

So current stock price = 40

dividend = 1 (in 3 months or 0.25 years)

risk free rate = 10%

Present value of dividend = 1*e^(-10%*0.25) = 0.9753

So (adjusted for dividend) = 40-0.9753 = 39.0247

K strike price = 40

r risk free rate = 10% = 0.1

s: standard deviation = 20% = 0.2

t: time to maturity = 6month = 0.5 year

d1 = 0.2497

d2 = 0.1083

N(d1) = normsdist(d1) = 0.5986

N(d2) = normsdist(d2) = 0.5431

C: value of call option

e: natural exponent

c = $2.695 (price of european call option)