Question

What is the price of an American 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 = $41 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

Dividend yield is calculated as: (dividend/stock price)12/no. of months - 1

Price of call option is $2.613.

Call Option input data	Output data
Stock price	$40.00	d1	-0.1174
Strike price	$41.00	d2	-0.2588
Time (in years)	0.5000	N(d1)	0.4533
Interest rate	10.00%	N(d2)	0.3979
Volatility	20.00%
Dividend yield	10.38%
Call option value	$2.613

Calculations