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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