Question

Gasworks, Inc., has been approached to sell up to 3.4 million gallons of gasoline in three months at a price of $2.80 per gallon. Gasoline is currently selling on the wholesale market at $2.70 per gallon and has a standard deviation of 59 percent.

If the risk-free rate is 5 percent per year, what is the value of this option? Use the two-state model to value the real option. (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

It is assumed that the underlying asset in this case is Gasoline and the firm gets the option to sell the underlying asset after a fixed amount of time, the underlying option is a put option.

Current Gasoline Price = $ 2.7 per gallon, Standard deviation = 59% and Option Tenure = 3 months and Risk-Free Rate = 5%

Strike Price of Gasoline Put Option = $ 2.8 per gallon

u = e^[Standard Deviation x (Time)^(0.5)] = e^[0.59 x (0.25)^(1/2)] = 1.34313 and = 1/u = 1/1.34313 = 0.74453

Risk-Neutral Probability of upward price move = [(Rf - d) / (u-d)] = [(1.05-0.74453) / (1.34313 - 0.74453)] = 0.51031

t=0	t=3	Strike price	Payoff
	(2.7 x 1.34313) = $ 3.626	$ 2.8	$ 0
2.7
	(3.9 x 0.74453) = $ 2.0102	$ 2.8	(2.8-2.0102) = $ 0.7898

Option Value = Total Present Value of Expected Payoffs = [0 x 0.51031+ (1-0.51031) x 0.7898] / e^(0.05 x 0.25) = $ 0.381953 ~ $ 0.382 per gallon

Total Option Value = Offered Sales Quanity x Premium per gallon = 3.4 x 0.382 = $ 1.2988 million or $ 1298800