Suppose the 120-day futures price on crude oil is $115.00 per barrel and the volatility is 20.0%.Assume interest rates are 3.5%.What is the price of a $110 strike call futures option that expires in 120 days?

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula, 
d1 = (ln(S0/K) + (r + (sigma^2/2))(T-t)) / (sigma*sqrt(T-t)) 
= (ln(115/110) + (0.035 + (0.20^2/2))(120/365)) / (0.20*sqrt(120/365)) 
= 0.7201 
d2 = d1 - (sigma*sqrt(T-t))
= 0.3263 
N(d1) = 0.7665 
N(d2) = 0.3700 
Using the formula for a call option, 
C = S0*N(d1) - Ke^(-r(T-t))*N(d2) 
= 115*0.7665 - 110*e^(-0.035*(120/365))*0.3700 
= $2.99, rounded to the nearest cent.

Therefore, the correct answer is B.

Suppose the 120-Day Futures Price on Crude Oil Is $115