How options provided by storage affect electricity prices.

• Author: Evans, Lewis

1. Introduction

   Electricity markets have high-price episodes, and it is at such times that the attribution of prices between market power and resource scarcity becomes particularly controversial. (1) The most famous such episode occurred in California in 2000-2001, where the average price in December 2000 was more than 10 times the average price 1 year earlier. This experience spurred a series of academic studies that attempted to determine how much of the high prices was due to "market fundamental" factors such as high fuel costs, high demand, drought, and other factors beyond firms' control, and how much was due to firms exercising market power to raise prices (Borenstein, Bushnell, and Wolak 2002; Joskow and Kahn 2002; Bushnell, Mansur, and Saravia 2004; Bushnell 2005). These studies typically find that observed prices significantly exceeded estimated operational marginal costs and conclude that firms were withholding supply in order to raise prices.

   However, the empirical analysis of market power in electricity markets has mostly been performed in a static setting, with little consideration of the intertemporal linkages present in electricity generation. (2) Specifically, generating electricity from water and natural gas typically involves storing the fuel when it is plentiful (water) or cheap (gas) and electricity prices are low, and releasing the fuel from storage to generate electricity when electricity demand and prices are high. Thus, firms will consider the option value of retaining fuel in storage, as well as the marginal cost of turning it into electricity when they make their generation decisions. This has been noted in the existing analyses, but these studies have not directly addressed the issues that arise. (3) Therefore, in this paper we develop a real options model of electricity generation by firms with fuel storage and use it to analyze the optimal generation policies of firms that have no market power. Our model includes volatility in the future spot prices of electricity and gas and allows for the fact that generators' decisions to release fuel from storage cannot be immediately reversed. In the case of hydroelectric generators, this irreversibility can arise because of uncertainty about future inflows into storage lakes; in the case of generators burning natural gas, it reflects the restrictions on the speed with which storage facilities can be emptied and refilled.

   We find that an electricity generator with no market power (by which we mean it has no ability to influence the distribution of current or future electricity or gas prices) will not generally offer to generate electricity whenever the electricity price exceeds the operational marginal cost. (We define operational marginal cost to be the direct financial cost incurred in running a plant to produce one extra unit of electricity.) Instead, such a firm will be willing to generate electricity only if the spot price of electricity is sufficiently high that the firm can recover its operational marginal cost and the value of the real options destroyed by generating electricity. We find that the value of these real options can be substantially greater than this marginal cost. In fact, the electricity price threshold above which a price-taking firm will generate is typically much more sensitive to the long-run level of the electricity price than it is to the firm's marginal cost.

   If option premia (and not firms unilaterally exercising market power) are to explain high-price episodes, it must be the case that option premia are especially high during these periods. We show that this is the case, for example, when electricity prices are more volatile than usual. A price volatility increase will typically be the case during high-demand periods because the convexity of electricity supply curves means that at high levels of demand even a small demand shock can lead to a large shock to the market-clearing electricity price. (4) We show that a sufficient condition for the option premium to be relatively high is that uncertainty surrounding future fuel supplies is relatively high. Scarce or uncertain future fuel supplies make generation decisions largely irreversible, and our comparative statics analysis indicates that this makes the option premium relatively high. Although this does not rule out the possibility that firms are exercising market power, it does imply that simply looking at the difference between offer prices and estimated marginal costs that exclude the option premium is insufficient to establish that firms are manipulating prices.

   Our approach thus differs from the existing literature assessing market power in electricity markets in that we explicitly allow for the intertemporal linkages that are present in electricity generation even in the short run. In contrast, the two most popular approaches (strategic offering and direct analysis) compare actual price and supply outcomes with those arising in a static full information electricity market under perfect, and Cournot, competition. Strategic offering analysis compares the actual offers of individual generators with estimates of the operational marginal cost of turning fuel into electricity. For example, Wolfram (1998) applies this approach to the U.K. electricity market and finds that firms that have a greater ability or greater incentive to manipulate market prices choose higher markups over operational marginal cost. Joskow and Kahn (2002) apply a similar approach to the California electricity market in the summer of 2000 and find evidence that all but one firm, which used forward markets to contract 90% of its potential output, were withholding supply. Wolak (2001, 2003) uses revealed bid information to estimate Lerner indices for individual generators and attributes the increase in these indices between 2000 and two previous years entirely to unilateral market power. In contrast to strategic offering analysis, direct analysis uses the entire market. It estimates the marginal cost functions of all generators in the market for each period and stacks them from least expensive to most expensive to obtain a hypothetical supply curve. Given the actual level of demand, the operational marginal cost of the most expensive dispatched generator is then taken as the competitive price benchmark against which actual market prices are compared. When actual market prices exceed the simulated competitive prices, the exercise of unilateral market power is regarded as being more likely. Borenstein, Bushnell, and Wolak (2002) and Joskow and Kahn (2002) use this approach to examine the California electricity market and find a large gap between actual market prices and their estimated competitive prices in the summer of 2000. (5) A recent review of market power monitoring of electricity markets acknowledges opportunity cost issues in estimating marginal cost (Twomey et al. 2005, p. 23) but provides no solution or recommendation about its treatment in market power evaluations. (6) All of these studies estimate the operational marginal cost of generating electricity, which treats suppliers as myopically responding along their operationally defined supply curves. However, this approach does not model supply in the specific circumstances of electricity markets. (7) Deregulated electricity markets are characterized by volatile input and output prices and restrictions on resource availability. These market characteristics imply that generation decisions will, and should, reflect intertemporal trade-offs in the use of fuel.

   Our paper also fits into the literature on commodity price behavior, especially the theory of storage and the theoretical underpinnings of the convenience yield. Much of the literature on commodity storage derives from the empirical observation that firms store commodities even when the commodity's spot price is high relative to its futures price. The usual explanation for this behavior is that there is a "convenience yield" associated with holding commodities in inventory (Kaldor 1939; Working 1948, 1949; Brennan 1958; Telser 1958). This convenience yield reflects the flexibility created by holding inventory. For example, inventories allow firms to smooth production and thereby lower adjustment costs and to vary production in response to changed market conditions. However, the early literature does not explicitly model the convenience yield. The dominant approach in the recent literature on the theory of storage models the convenience yield as a consequence of the nonnegativity of inventory (Deaton and Laroque 1992, 1996; Chambers and Bailey 1996; Routledge, Seppi, and Spatt 2000). (8) Except in states where firms wish to hold negative inventory, the current spot price will be related to the future expected spot price by the usual intertemporal arbitrage condition. However, when the nonnegativity constraint on inventory is binding, firms would like to sell current stocks and drive inventory negative. They cannot do so, and so the current spot price remains above that implied by the intertemporal arbitrage condition. Storing the commodity allows firms to benefit from such temporary "stock-outs," selling the commodity when the spot price is high and buying it again in the future when the intertemporal condition has been restored. Thus, holding inventory gives the firm the option to exploit any temporary high-price episodes that might arise in the future. More recently, some authors have analyzed the convenience yield by explicitly valuing the real options embedded in stored commodities (Heinkel, Howe, and Hughes 1990; Litzenberger and Rabinowitz 1995). (9) As long as releasing a commodity from storage is at least partially irreversible, reducing storage destroys (at least temporarily) the real option to wait and release the commodity in the future. The firm must be compensated for the loss of this option, so that release will occur only when the spot price exceeds the...