Question

# Using the Black Scholes model. If the current price of oil is \$20.86 per barrel, the...

Using the Black Scholes model. If the current price of oil is \$20.86 per barrel, the risk free interest rate is 2.0%, the cost to store oil for one year is 10% of the price and the standard deviation of oil prices is 0.6255, what is the price of a 1-year call option on oil with a strike price of \$34.15 per barrel?

The value of a call option is given by the Black Scholes model

where S is the storing cost adjusted current price = 20.86*1.1 = \$22.946

K is the strike price = 34.15

Risk free rate r = 0.02

Volatility = 0.6255

d1 = (ln(22.946/34.15) + (0.02+ (0.6255*0.6255/2)))/(0.6255*1) = -0.291

d2 = -0.291 - 0.6255*1 = -0.9165

N(d1) = 0.3855

N(d2) = 0.1797

Substituting, we get

c = 22.946*0.3855 - (34.15*0.1797*e^(-0.02)) = 2.83

Hence the price of a 1 year call option c = \$2.83

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