Suppose the 180-day futures price on crude oil is $110.00 per barrel and the volatility is 20.0%.Assume interest rates are 3.5%.What is the price of a $120 strike call futures option that expires in 180 days?

Question

Quizplus · Accepted Answer

We can use the Black-Scholes model to calculate the price of the call option:
d1 = [ln(S/X) + (r + σ^2/2)t]/(σ√t)
d2 = d1 - σ√t
where S = 110 (futures price), X = 120 (strike price), r = 0.035 (interest rate), σ = 0.20 (volatility), and t = 180/365 (time to expiration in years).
Plugging in the values, we get:
d1 = [ln(110/120) + (0.035 + 0.20^2/2) × 180/365]/(0.20 √180/365) = -0.0473
d2 = -0.0473 - 0.20 √180/365 = -0.3649
N(d1) = 0.4878 (from standard normal distribution table)
N(d2) = 0.3560 (from standard normal distribution table)
The price of the call option is:
C = S N(d1) - X e^(-rt) N(d2)
C = 110 × 0.4878 - 120 e^(-0.035×180/365) × 0.3560 = $2.59 (rounded to two decimal places)

Suppose the 180-Day Futures Price on Crude Oil Is $110