A Survey of Commodity Markets and Structural Models for Electricity Prices

Abstract

Abstract. The goal of this survey is to review the major idiosyncrasies of the commodity markets and the methods which have been proposed to handle them in spot and forward price models. We devote special attention to the most idiosyncratic of all: electricity markets. Following a discussion of traded instruments, market features, historical perspectives, recent developments and various modeling approaches, we focus on the important role of other energy prices and fundamental factors in setting the power price. In doing so, we present a detailed analysis of the structural approach for electricity, arguing for its merits over traditional reduced-form models. Building on several recent articles, we advocate a broad and flexible structural framework for spot prices, incorporating demand, capacity and fuel prices in several ways, while calculating closed-form forward prices throughout.

A Model for Hedging Load and Price Risk in the Texas Electricity Market

“…This is a special case of a formula in [7,6] which conveniently rewrites the integral of the product of an exponential, a univariate Gaussian density and Gaussian cdf as a simple bivariate Gaussian cdf (which collapses again to a univariate cdf when integrating over (−∞, ∞) as above). In this case, we obtain the following closed-form expression:…”

“…While such approaches may be successful for capturing price spikes and overall price distributions, they rarely capture the complicated dependence structure between price, load and other factors, which is equally vital for hedging purposes in practice. Hence, we instead favor the category often known as 'structural' models, as reviewed for example in the recent survey paper of [6]. In such a model, power price is written as a function of several underlying supply and demand factors, and its dynamics are therefore not specified directly through an SDE (stochastic differential equation), but produced indirectly as a result of the dynamics chosen for the factors.…”

Models with Short-Term Variations and Long-Term Dynamics in Risk Management of Commodity Derivatives

“…In recent times, stochastic models of commodity futures prices have played a central role in evaluating commodity-related securities among academics and practitioners, such as Schwartz (1997), Schwartz and Smith (2000), Sorensen (2002), Cortazar and Schwartz (2003), Cortazar and Naranjo (2006), Mirantes, Poblacion and Serna (2012), Carmona and Coulon (2014), and et al. A detailed survey of these types of models is written by Pirrong (2011).…”

Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options

“…Long-side options in futures markets depend totally on the idiosyncrasies of each commodity's exchange traded structure. The survey paper by Carmona and Coulon (2013) demonstrates the appropriate model for a commodity varies highly depending on storability, instantaneous utility, and alternatives. At expiration, a CBOT agricultural futures contract does not deliver the physical grains but an artificial instrument called the shipping certificate that entitles its holder to demand loading of the grains from a warehouse at any time.…”