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Spark Spread Options: Linking Spot and Futures Markets for Gas and Electricity
that electric power and natural gas prices do not behave according to the random motion specified by the BS model, which was developed to value bond and stock options. For energy commodities, such as gas and power, prices will spike (up or down) due to supply and demand imbalances. %n5%n
In spite of these limitations, the BS model can give the plant operator an indication of value when it is used judiciously, as the following example illustrates.
Suppose a major power marketer proposes a tolling arrangement to a utility operator on the West Coast, keyed to the utility's idle 300-MW gas-fired power plant. The arrangement calls for a fee of $2,160 per MW paid today (February), by the marketer to the utility, for the right (awarded to the marketer) to dispatch the unit in August. The power marketer assures the utility that the proposed up-front fee is based on the current futures prices of electricity and gas, and thus represents a true measure of the present value of the dispatch rights conveyed by the utility to the marketer.
This proposal looks very attractive for the inefficient power plant. The utility receives a guaranteed payment today so it can maintain sufficient funds to meet debt obligations. At the same time, it eliminates exposure to price risk. Nevertheless, as we will show below using an option model based in part on the BS formulation, the plant in all events should be worth today no less than $2,160 per MW, but may in fact be worth a lot more (em a fact that could allow the judicious utility operator to extract more value from the deal than the simple settlement offered initially by the marketer.
Sample input parameter values for the Black-Scholes spark spread option pricing formula:
Price of electricity futures contract, Palo Verde on-peak, August $ 26 per MWh
Price of Topock natural gas futures contract, plus LDC, August $ 22 per MMBtu
Operating heat rate of power plant under negotiation 10 MMBtu per MWh
Volatility of the electricity price 55 percent
Volatility of the natural gas price 45 percent
Correlation between electricity and natural gas prices 1 0.25
Risk-free discount rate 3.75 percent
Time to maturity 0.5 year
Dividend rate of futures contracts 3.75 percent
The power marketer remains veracious in his claim. If the utility sells power futures contract and purchases gas futures contract, it will lock in a present value margin of about $2,160 per MW. This calculation is shown below.
Sell electricity futures: 300 MW 3 368 on-peak hours per month 3 $26 per MWh Buy gas futures:
So, according to the marketer, the deal will be worth $660,000 in August. When that amount is discounted at 3.75 percent, its present value comes in at $648,000 per month or $2,160 per MW.
However, this figure represents only the intrinsic value of the spark spread call option. If the utility buys and sells these futures contracts today, when August arrives it can do no worse than the margin that it has already locked-in. Why is that? Because, even after having taken