Question

Gasworks, Inc., has been approached to sell up to 4.4 million gallons of gasoline in three months at a price of $3.55 per gallon. Gasoline is currently selling on the wholesale market at $3.20 per gallon and has a standard deviation of 60 percent.

  

If the risk-free rate is 4 percent per year, what is the value of this option? Use the two-state model to value the real option. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Value of contract

$

Answer 1

The exercise price or strike price of this real option is the price at which Gasworks Inc. has been given the option of selling its gas three months from now which is K = $ 3.55 per gallon. Also, the real option under consideration is a put option under which the underlying asset (natural gas in this case) can be sold at a fixed price.

The current wholesale price is $ 3.2 per gallon with a standard deviation (price volatility) of 60 %. This implies that the price after three months can be either above current levels by 60% or below current levels by the same % amount.

Let the risk neutral probability of the price going up be p and consequently, the probability of a fall in price will be (1-p).

Therefore, p = (e^(0.04 x 0.25) - 0.4) / (1.6 - 0.4) = 0.5084 approximately.

If the price goes up by 60%, then future price F(u) = 3.2 x 1.6 = $ 5.12 per gallon and put option payoff = $ 0

If the price goes downby 60% then future price F(d) = 3.2 x 0.4 = $ 1.28 per gallon and put option payoff = $ 2.27 per gallon

Therefore, option price = [(0 x 0.5084) + (2.27 x 0.4916)] / e^(0.04 x 0.25) = $ 1.1048 or $ 1.1 approximately per gallon

If the contract is for the entire amount to be sold then the value gets multiplied by 4.4 million which is $ 4.84 million per contract approximately.