Exotic electricity options and the valuation of electricity generation and transmission assets
Introduction
With deregulation sweeping through the US electric power industry and a fully competitive marketplace for electricity taking shape, electric utilities and their customers accustomed to a cost-recovery pricing structure for electricity must adapt to market-based pricing. Risk management needs this transition has generated have made electricity derivatives one of the fastest growing derivatives markets, as financial institutions, utilities and other energy market participants work to provide the tools necessary to manage the price and investment risks associated with competitive markets. While many of the risk-management tools and methods now well established in other markets [1], [2], [5], [8] can be readily transferred to the electricity markets, the unique characteristics of electricity and electricity markets also present new challenges to the risk-management discipline. The most important of these are the challenges that the non-storable nature of electricity presents to the traditional methods of modeling price processes and valuing derivatives [11]. Specifically, due to the non-storable nature of electricity, the traditional storage-based, no-arbitrage methods of valuing commodity derivatives are unavailable. In addition, electricity prices can (and do) demonstrate properties such as strong mean reversion over short time horizons that would be inconsistent with an efficient market for a storable good. A second risk-management challenge that electricity markets present is the need to value a range of cross-commodity transactions, such as spark and locational spreads [3].
In this paper, we present tools to address these unique properties of electricity and electricity derivatives. First, we develop a method to value electricity derivatives by replicating them with futures contracts rather than by attempting to store or borrow electricity in the spot market. This allows us to apply traditional no-arbitrage-based methods of derivatives valuation and to proceed without requiring the assumption that electricity is storable. We then present closed-form expressions for the value of a range of cross-commodity derivatives, including spark and locational spread options, both for the case in which the underlying price processes follow geometric Brownian motion, and for the more plausible case in which prices are mean reverting. These results are closely related to those of Shimko's [9] analysis of futures spread options and Margrabe's [7] analysis of exchange options. (Margrabe's work is relevant since an exchange option can be thought of a spread option with a zero strike price.) Shimko's results, however, are for a futures price process derived from a model of the spot price and convenience yield of a storable good, while Margrabe's are exclusively for geometric Brownian motion processes. After deriving the valuation formulae, we demonstrate how these results can be used to value both generation and transmission assets (see [4], [10] for a review of real options and decision analytic approaches to capacity valuation), and present a preliminary comparison between the values these models generate and the actual prices at which these types of assets have recently been sold.
The remainder of the paper is organized as follows. In Section 2, we introduce the set of cross-commodity derivatives we will consider in the paper, and identify some of their basic characteristics. In Section 3, we describe how these derivatives can be replicated (and thus valued by arbitrage) using futures contracts, and present the principal valuation results of the paper. In Section 4, we use these results to develop a real-options-based methodology for valuing generation and transmission assets, and present the results of our preliminary empirical evaluation of the effectiveness of the methodology.
Section snippets
Cross-commodity electricity derivatives
There are two principal categories of cross-commodity electricity derivatives; spark spread, or heat-rate-linked derivatives, and locational spread derivatives. We consider each below.
Valuation of electricity derivatives
In this section, we present a futures-based method of replicating electricity derivatives, and illustrate the method by using it to derive explicit expressions for the value of the spark spread and locational spread options defined above. Valuation equations are provided for these instruments for both geometric Brownian motion price processes and mean-reverting price processes. In both cases we explicitly derive only the value of the call options. The value of put options can then be derived
Real options valuation of generation and transmission assets
The right to operate a generation asset with heat rate H that uses generating fuel G is clearly given by the value of a spark spread option with “strike” heat rate H written on generating fuel G. Similarly, the value of a transmission asset that connects location 1 to location 2 is equal to the sum of the value of the locational spread option to buy electricity at location 1 and sell it at location 2 and the value of the option to buy electricity at location 2 and sell it a location 1 (in both
Conclusions
This article has presented a methodology for valuing electricity derivatives by constructing replicating portfolios with futures contracts and the risk-free asset. Futures-based replication is made necessary by the non-storable nature of electricity, which rules out the traditional spot market, storage-based method of valuing commodity derivatives. Once developed, the methodology was used to derive valuation formulae for both spark and locational spread options when the prices of the underlying
Dr. Shi-Jie Deng is an Assistant Professor of Industrial and Systems Engineering at Georgia Institute of Technology. His research interests include financial asset pricing and real options valuation, financial engineering applications in energy commodity markets, transmission pricing in electric power systems, stochastic modeling and simulation. Dr. Deng has served as a consultant to several private and public organizations on issues of risk management and asset valuation in the deregulated
References (11)
The pricing of commodity contracts
Journal of Financial Economics
(1976)- et al.
The pricing of options and corporate liabilities
Journal of Political Economy
(1973) - S. Deng, Financial methods in competitive electricity markets, PhD Dissertation (forthcoming), University of California...
- et al.
Investment Under Uncertainty
(1994) Dynamic Asset Pricing Theory
(1996)
Cited by (0)
Dr. Shi-Jie Deng is an Assistant Professor of Industrial and Systems Engineering at Georgia Institute of Technology. His research interests include financial asset pricing and real options valuation, financial engineering applications in energy commodity markets, transmission pricing in electric power systems, stochastic modeling and simulation. Dr. Deng has served as a consultant to several private and public organizations on issues of risk management and asset valuation in the deregulated electricity industry.
Dr. Deng holds a BS degree in Applied Mathematics from Beijing University in China, an MS degree in Mathematics from the University of Minnesota at Twin Cities, as well as MS and PhD degrees in Industrial Engineering and Operations Research from the University of California at Berkeley.
Dr. Blake Johnson is an Assistant Professor of Engineering Economic Systems and Operations Research at Stanford University. His research interests include. The application of multiperiod asset pricing methods to the valuation of real assets (e.g., businesses, technologies, large projects, real estate) as opposed to financial assets (e.g., stocks, bonds, derivatives).
Dr. Johnson has a PhD in Engineering Economic Systems from Stanford University.
Dr. Aram Sogomonian was recently named Chief Risk Officer of PacifiCorp. He is currently implementing his organization which will have primary responsibility for understanding the firms risk exposures and how to manage them. Prior to his current position, Dr. Sogomonian was vice president at PacifiCorp Power Marketing with primary responsibility for heading up the middle once and analytical functions. Prior to PacifiCorp, Dr. Sogomonian was vice president of Risk Management at Edison Source. Before coming to Edison Source, Dr. Sogomonian was director of the risk analytics and asset pricing group at Houston-based Enron Capital and Trade resources, which does project evaluation for Enron.
Dr. Sogomonian holds a PhD in Management Science from the Anderson Graduate School of Management at UCLA, an MS degree in Operations Research and BA degrees in Applied Mathematics and Economics from the University of California at Berkeley.