THE RAPID DEREGULATION OF THE BULK POWER MARKET has exposed utilities and power generators to the harsh reality of spot price volatility. This new reality begs the question: How can merchant generators, independent power producers and investor-owned utilities analyze their risk exposure when energy prices vary daily or even hourly?
The answer lies with spark spread options (em the link between electric power and gas prices.
The spark spread, from a generator's perspective, refers to the difference between spot market prices for electricity and natural gas, expressed in equivalent terms through the nominal heat rate of the gas-fired unit under consideration. Reconciling the spark spread concept with actual spot prices creates the "spot market heat rate," which plays a critical role in the decision of the power plant operator to dispatch individual units.
The broader question, however, is how to integrate this spot market heat rate with information from the futures markets to calculate the present value of generating resources. What is a gas-fired plant worth today, based on the chain of traded futures contracts in power and gas? For that sort of determination, we introduce a discussion of the Black-Scholes option pricing model made famous by the work of Fisher Black, Robert Merton and Myron Scholes; the latter two won last year's Nobel Prize in Economics. As we will show, the Black-Scholes model can be applied to energy markets to infer the value of power plants, but only with certain caveats.
Heat Rates, Spot Markets and Profit
Consider an investor-owned utility that operates generating assets consisting of gas turbine units of varying heat rates. Associated with every natural gas-fueled power plant is a measure of energy conversion efficiency, or heat rate, which determines the amount of gas input, measured in British Thermal Units, required to produce one kilowatt-hour of electricity. A lower heat rate implies that the generation unit has a higher operating efficiency. A variety of economic factors exist that can help the operator decide whether to run his plants; among them are electricity and natural gas spot prices and unit heat rates. To the extent that the operator knows his fuel costs and the efficiency of his generation units, his decision criterion to fire up the plant is the following: Run the power plant only if it is profitable to do so. In general, this situation will occur when: Power spot price > operating heat rate 3 natural gas spot price.
OPERATING HEAT RATE. The heat rate can be interpreted as the quantity of natural gas, measured in millions of Btu, that the plant operator must purchase to produce one megawatt-hour of electricity. In effect, the operator is guaranteed an operating profit margin for each megawatt-hour of electricity that a plant generates. The decision criterion adopted by the operator must be viewed in the following light:
Profit per MWh 5 power spot price 2 operating heat rate 3 natural gas spot price.
Conversely, the operator should choose not to run the generation unit if energy pool prices are not favorable, when revenue is less than cost: %n1%n Power spot price , operating heat rate 3 natural gas spot price.
The operator's ability to decide whether to run his units shows that the power plant has the characteristics of a real option. To clarify the option concept, let Pe be the spot price of electricity in dollars per MWh; let Pg be the spot price of natural gas in dollars per MMBtu; and let HR be the plant operating heat rate, expressed in MMBtu per MWh, then:
Equation 1. Plant Profit (as a function of heat rate and spot prices for electricity and gas)
Profit per MWh 5 Pe 2 HR 3 Pg
As presented, the profit margin is the spread between the sale price of electricity and the fuel cost incurred by the plant operator to generate that electric energy. The operator will take advantage of the positive electric energy and natural gas price spread and "strike" the transaction by selling power at Pe and buying gas at Pg, earning a profit. %n2%n If the spread is not favorable to the operator, he stays put and does nothing. In effect, the owner-operator is holding a call option that allows him to bid the capacity of some unit within a specific period. Underlying the option is the energy prices Pe and Pg, as well as the conversion efficiency of the generation unit.
SPOT MARKET HEAT RATE. As in all commodity markets, whether agricultural, metal or energy, the definition of a spot market is essential for participants who are either speculating or hedging. For our applications we define the spot market as the prompt-month futures contract.
For the Southern California power pool region, the spot market for electricity can be the New York Mercantile Exchange prompt-month futures contract at Palo Verde, Ariz., at expiration. The spot market for natural gas is the California-Arizona border bid-week trading plus charges imposed for local distribution. %n3%n
Since the plant operator is familiar with the heat rates of his units, the spot market heat rate, or MHR, may prove a more informative indicator. The MHR ties together the market clearing prices of electric power and natural gas, and suggests the efficiency of units that are run at the margin during peak periods. The MHR is derived as follows:
Equation 2. Spot Market Heat Rate (plant efficiency in terms of current spot prices for electricity and gas)
MHR 5 Pe 4 Pg
The plant operator can now compare his operating heat rates with the spot market heat rate, which reflects the energy conversion efficiency of the market. His decision to generate power depends on whether the MHR is greater than his unit operating heat rate. If the MHR is greater, the operator makes a profit by purchasing natural gas and selling the electricity that he generates. In other words, the unit is "in the money." By substituting Equation 2 into Equation 1, and by rearranging the terms, the profit margin per MWh becomes the difference between the spot market heat rate and the plant operating heat rate:
Equation 3: Plant Profit Margin (the difference between market-reconciled and operating efficiencies)
Profit per MWh 5 Pg(MHR 2 HR)
AN EXAMPLE. This example illustrates the above concepts. Consider the Southern California energy market: MHRSoCal 5 (NYMEX Palo Verde prompt-month price) 4 (Calif.-Ariz. border bid week gas price 1 LDC)
Suppose a 500-MW gas-fired unit near the California-Arizona border has an operating heat rate of 9 MMBtu per MWh. In addition, assume that the prompt-month NYMEX Palo Verde energy contract is near expiration and is currently trading at $24 per MWh, while the gas price at the California-Arizona border, including LD charges, is trading at $2 per MMbtu. The spot market heat rate MHR is, therefore, 12 MMBtu per MWh or 12,000 Btu per kWh (see Equation 2). The plant operator can take advantage of the spread between electric power and gas prices and strike the call option by selling power at $24 per MWh and buying gas at $2 per MMBtu. As for total profit, the operator sells 250 NYMEX Palo Verde prompt-month contracts and purchases about 165.6 gas contracts in 10,000 MMBtu increments during bid week, thereby locking in a profit for the month in the amount of: %n4%n
Profit 5 (250 NYMEX Palo Verde contracts 3 736 MWh per contract 3 $24 per MWh)
2 (165.6 gas contracts 3 10,000 MMBtu per contract 3 $2 per MMBtu)
5 $1.1 million
Alternatively, we can determine profit per MWh by using the heat rate differential shown in Equation 3:
And the total profit for 250 NYMEX Palo Verde contracts is again:
Total profit 5 ($6 per MWh 3 736 MWh per contract 3 250 NYMEX Palo Verde contracts)
5 $1.1 million
Uncertain electricity and gas prices determine the payoff to the gas-fired power plant operator. Therefore, looking forward, he effectively holds a series of spark spread call options with different monthly expiration dates. This interpretation implies that the value of the gas-fired power plant is simply a derivative of electric power and gas prices. In other words, the present value of the power plant can be estimated by knowing the futures prices of electric power and gas: the underlying variables of the spark spread call option.
Applying the Black-Scholes Model
Last year's award of the Nobel Prize in Economics to Robert Merton and Myron Scholes has attracted wide interest to the application of the Black-Scholes option pricing formula. Can we use the Black-Scholes formulation to appraise the value of spark spread options, and subsequently the value of natural gas generation units in a competitive market?
Yes, but with strong caveats. The simplicity of the Black-Scholes formula explains its wide appeal. However, at the outset we must note that numerous assumptions are implied when we use the BS pricing formula, most of which are not met due to the current illiquid electricity market. One significant limitation for applying the BS formula to spark spread options stems from the fact that electricity cannot be stored cheaply. The BS method requires that one can replicate an option by buying and storing the underlying asset; this cannot be done with power. Another concern comes from the observation 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 < $2.87 million
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 a position in the market, the utility still holds the option of not generating and "unwinding" the futures contract by selling the gas it had purchased, and buying back the power to fulfill its generation obligation.
Suppose the August spot prices turn out quite different than projected in the futures market: at $20 per MWh (lower) and $2.50 per MMBtu (higher) for electricity and gas, respectively. These new prices imply a spot market heat rate of 8 MMBtu per MWh, which is less than the operating heat rate of the unit under negotiation. If the utility chooses to generate under this scenario it will receive the profit margin as specified by the futures transactions executed in February. However, the utility could earn an additional profit by shutting down the power plant in August. This profit is achieved by performing the following two transactions:
1. Buy electricity at the spot price to fulfill the NYMEX futures contract obligation. The cost of purchasing electricity on the spot market in August is about:
300 MW 3 368 on-peak hours per month 3 (2$20 per MWh) < 2$2.21 million
This transaction on electricity contracts produces a profit of $660,000 for August:
$2.87 million 2 $2.21 million 5 $660,000
2. Sell the gas purchased from the futures contract. The gas is worth on the August spot market:
The sale of gas on the spot market offsets the $2.21 million cost incurred in the purchase of gas futures, resulting in a $550,000 profit for August. Therefore, the total profit for shutting down the power plant and unwinding the original energy contracts is $1.21 million or $4,034 per MW. The choice of not generating when spot prices are considered "unfavorable" resulted in doubling the utility's anticipated profit per MW.
The key conclusion to draw from this example is that spot prices, rather than long-term contracts, dictate the dispatch of power plants. If the market heat rate is higher than the unit's operating heat rate then generate, and if it is lower, then shut the unit down.
In sum, the operating decision is independent from any financial contracts and/or physical obligations entered previously.
The example above shows that the utility is able to extract additional dollars from the generation unit greater than the $2,160 per MW quoted by the power marketer. Thus, it is reasonable to presume that the unit is "worth" more. But how much more? The BS option pricing method is a good starting point for determining that additional worth.
The value of a spark spread call option consists of its intrinsic value and its "option" value, which is driven by the uncertainties of the underlying energy prices. The power marketer's proposed $2,160 per MW or $5.87 per MWh is equivalent to the intrinsic value of the option, an amount that the utility can lock in today.
The BS pricing formula gives the total worth of the spark spread call option, including both the intrinsic and the "option" components. Therefore, using the parameters noted above, the spark spread call option maturing in 6 months is worth about $7.50 per MWh. %n6%n This translates to a price of $2,760 per MW (or $7.50 per MWh for 368 on-peak hours). The power marketer could realize as much as, if not more than, $600 per MW if the utility operator signs the proposed deal. The utility would have left about 20 percent of the money on the table. In sum, the BS pricing model has provided an indication of what the spark spread call option may be worth in the marketplace. However, actual transaction prices in an illiquid market still depend on the relative acumen of the negotiating parties.
Michael Hsu is senior analyst at Edison Enterprises. He is also a doctoral candidate in the Engineering Economic Systems and Operations Research at Stanford University. Nguyen T. Quan, Ph.D., teaches at UCLA Extension and is a principal at N. T. Quan and Associates, an economic consulting firm in Los Angeles. The authors thank Edward Kahn, Ph.D., and Robert Michaels, Ph.D., for their helpful comments. A more technical and detailed treatment of these concepts, written by the first author, "Spark Spread Options Are Hot" appears in the March 1998 issue of The Electricity Journal.
1 The plant operator also must consider various costs (e.g., start-up costs, no-load costs) and operating requirements (e.g., start-up time, minimum shut-down time and ramp rates) before bidding his units into the market place. When the operator runs multiple units, he should also consider portfolio impacts (e.g., one unit providing reserve requirement for another).
2 Using the nomenclature of options, the operating profit per MWh, or the payoff, is written as: Profit per MWh 5 max(Pe 2 HR 3 Pg, 0).
3 On the wholesale market, natural gas price is expressed in terms of dollars per MMBtu, while electricity contracts are valued in dollars per MWh. Note that when a futures contract is taken to physical delivery, the delivery period is over the entire month.
4 One NYMEX electricity contract calls for 2 MW to be delivered for 16 on-peak hours each day for 23 days, totaling 736 MWh over the entire month.
5 In other words, electricity and natural gas prices do not follow a log-normal distribution as assumed by the BS approach, rather they revert to a long-term mean value, possibly driven by production cost. Also, critical to the BS valuation formula are the volatility of prices and correlation between them, which should be forward looking rather than statistically determined from historical data.
6 Many financial software programs can evaluate BS option models. We use a program aptly called the Positron Energy Pricer.
Articles found on this page are available to Internet subscribers only. For more information about obtaining a username and password, please call our Customer Service Department at 1-800-368-5001.