This book weaves strands of research that date back more than 20 years, to approximately 1990–1991. Although I worked at a futures commission merchant (that is, a brokerage firm) while in graduate school, that work involved financial futures exclusively. Deciding to leave that business in mid-October 1987 (thereby causing the 1987 crash), first for a stint in litigation support consulting and then on to academia at the Michigan Business School, I worked on research completely unrelated to futures markets. But in spring and summer 1989, the Italian conglomerate Ferruzzi cornered the soybean market in Chicago. The corner, and the Chicago Board of Trade's response to it, resulted in sharp criticism of the exchange. To address this criticism, the CBOT decided to commission an academic study of the grain market delivery mechanism.

My senior colleague at Michigan who was primarily responsible for bringing me there, the late Roger Kormendi, succeeded in wrangling a grant from the CBOT to carry out the study. He walked into my office and said: “I know nothing about commodity markets. You worked in them. Would you be part of the team on this study?” I responded: “Well, I know nothing about commodity futures, but I'm game to learn.”

This nudge completely changed the trajectory of my research, and virtually everything I have worked on since relates to commodities and derivatives in one way or another. My formal training is as an industrial organization economist, and so my research initially focused on trying to understand the causes and effects of market power in commodity markets and commodity derivatives.

Introduction

The previous chapters have explored various structural models of continuously produced commodities. This chapter examines a different, important category of commodities: seasonally produced ones, such as corn or soybeans.

These commodities are important in their own right. But, as the results of this chapter demonstrate, an examination of seasonal commodities, and the ability of structural models to explain the high-frequency behavior of their spot and forward prices, points out some serious deficiencies in the storage model.

Specifically, I analyze a two-factor model of a commodity that is produced seasonally. One of the risk factors is the by-now-familiar highly persistent demand shock. The other is an output shock. The commodity is produced once a year, and the size of the harvest is random because of factors such as weather and insect infestations. Moreover, information about the size of the next harvest accumulates throughout the year. I solve the model using the techniques employed throughout the book and then examine particular implications of the model. These implications include the sensitivities of spot prices and futures prices with different expiration dates to demand and harvest shocks, and the correlations between spot and futures prices. I then compare these predictions to the empirical behavior of the spot and futures prices for several important seasonally produced commodities.

Introduction

Many important commodities are storable. These include grains, many energy products such as oil and natural gas, and industrial and precious metals. Because of the ability to store, agents have the ability to influence the allocation of consumption of these products over time. Moreover, they typically do so under conditions of uncertainty. Because finance is at root the study of the allocation of resources over time in risky circumstances, the commodity storage problem is fundamentally a problem in finance. Indeed, it is the Ur problem (or pre-Ur problem) of finance: humans have had to make decisions about how to allocate consumption of commodities over time since the dawn of agriculture.

Even a brief consideration of the economics of storage demonstrates that although the problem is a very old one, it is a very challenging one analytically. The problem is inherently a dynamic one with complicated intertemporal dependencies. Storage involves an opportunity cost. If I own a bushel of wheat, I can consume it today or store it for consumption tomorrow – or later. The opportunity cost of consumption today is the value of the commodity tomorrow. I must also pay a physical storage cost and forego any interest I could earn on the money I spend to buy the economy. But under conditions of uncertainty (about future supply or demand, say), the value of the commodity tomorrow is uncertain.

Introduction

The previous chapter showed how continuously produced commodities' prices, volatilities, and correlations behave in a competitive market with two homoscedastic net demand shocks of differing persistences. The model studied there implies that these prices can exhibit rich dynamics, with time-varying correlations and volatilities that depend on the shape of the forward curve and, hence, with underlying fundamental supply-and-demand conditions.

Empirically observed commodity prices also exhibit rich dynamics, including time-varying – and often extreme – volatilities. Commodity forward curves exhibit a variety of shapes, including backwardation, contango, and “humps,” and correlations between forward prices of different maturities are time varying (Ng and Pirrong 1994). Hence the question: How well do the dynamics generated by the model match with the dynamics observed for actual commodity prices?

Empirical work on the theory has lagged its theoretical development. In some respects, this is not surprising, given the complexity of the problem and the associated computational costs.

Heretofore, confrontations between the theory and the data have involved modest calibration exercises based on relatively simple one-factor versions of the model of Routledge et al. (2000) (RSS), or more ambitious estimations involving low-frequency (annual) data (Deaton and Laroque 1992, 1995, or 1996). These empirical investigations have not been particularly kind to the theory. RSS find that the theory has difficulty explaining the dynamics of longer-term forward prices. Deaton-Laroque claim that storage apparently has little role in explaining commodity price dynamics; instead, autocorrelation in the underlying net demand process, rather than speculative storage, seems to be the main source of autocorrelation in commodity prices.

Introduction

I now turn attention from storable commodities to non-storable ones. There are many important non-storable commodities, including electricity, weather, and shipping, that are actively traded on spot, forward, and derivatives markets.

By their very nature, non-storable commodities present fewer modeling challenges than storable ones. The very fact that they are not storable breaks the intertemporal linkages that necessitate the use of computationally intensive recursive techniques such as those utilized in the previous chapters. Storability means that every decision today must be made with an eye on tomorrow, and the tomorrow after that, and ad infinitum. In contrast, non-storable commodities can be modeled myopically, instant by instant, because in the absence of storage, current decisions do not affect tomorrow's economic opportunities. This lack of the need to look forward and consider the implications of current decisions on decision makers' future opportunity sets dramatically reduces the complexity of the modeler's task.

Structural models are eminently feasible for some commodities and, indeed, not only can these models be used to derive testable implications about the behavior of the prices of such commodities, they can also be used to price derivatives. In particular, two commodities with very transparent fundamentals – electricity and weather – are very well suited to structural models. Other non-storable commodities, notably shipping, can be modeled structurally, but the inputs necessary to calibrate these models and to use them for real-world derivatives pricing are not readily observable, as is the case for weather and power.

Introduction

Many important commodities are produced and consumed continuously and exhibit little seasonality in demand. These include the industrial metals (such as copper and lead) and some important energy products (such as crude oil). These products are important (representing a large fraction of total traded commodity production, value, and trading volume). Moreover, it is easiest to analyze the high-frequency price behavior of these commodities in the structural storage model framework because the continuous nature of product and non-seasonality of demand makes it reasonable to impose time homogeneity, which makes numerical solution simpler; it is not reasonable to impose such homogeneity for seasonally produced commodities, such as corn. Therefore, considerations of importance and tractability make it desirable to focus initially on continuously produced commodities. These will be the subject of the next three chapters.

Most received storage models posit a single source of uncertainty. Sometimes this single source is portrayed as a “net demand shock.” Whatever its interpretation, it is readily evident that a one-shock model is inadequate to describe the rich behavior of actual commodity prices.

This is most evident when one looks at correlations between commodity futures prices with different times to expiration, or correlations between spot and futures prices. In a single factor model, all prices on the same commodity, regardless of expiration date, are instantaneously perfectly correlated. If there is only one source of uncertainty, futures prices with different times to expiration may exhibit different variances because they have different sensitivities to shocks to these uncertainties.

Introduction

Not to put too fine a point on it, but the study of commodity prices has long been something of an academic stepchild. Most work on the subject is in the domain of specific fields, notably agricultural economics. Only a smattering of articles on the subject has appeared in broader publications, such as the Journal of Political Economy or the Journal of Finance.

Especially in finance, this relative obscurity arguably reflects the niche role of commodities in the broader financial markets, as compared to equity and fixed-income markets. But commodities are in the process of becoming mainstream. In the 1990s, and especially the 2000s, many major banks and investment banks have entered into commodities trading. Indeed, commodity trading – especially in energy – has become an important source of profits for major financial institutions such as Goldman Sachs, Morgan Stanley, and Citibank. Simultaneously, and relatedly, many investors have entered into the commodities market. In particular, pension funds and other portfolio managers have increasingly viewed commodities as a separate asset class that, when combined with traditional stock and bond portfolios, can improve risk-return performance. Furthermore, financial innovation has eased the access of previously atypical participants into the commodity markets. Notably, commodity index products (such as the GSCI, now the S&P Commodity Index) and exchange traded funds (ETFs) have reduced the transaction costs that portfolio managers and individual investors incur to participate in the commodities markets.

Introduction

The previous chapter showed that the traditional commodity storage model cannot capture some features of the behavior of continuously produced commodity prices, in particular the behavior of price volatility. Although the standard model can generate time variation in spot and forward volatility that matches some features documented in empirical data, it cannot generate volatility levels that reach those observed in actual prices. Moreover, it cannot generate in forward price-implied volatilities similar to those observed in the data.

In the model studied in the earlier chapters, variations in price volatilities resulted from variations in the degree of supply-demand tightness in the market. Volatility peaks in these models when stocks are low and/or demand is high. That is, volatility is a consequence of supply-and-demand fundamentals in this model. These results suggest that to generate richer volatility behavior, it is necessary to introduce another factor related to volatility that is not driven completely by the y and z shocks.

An obvious way to do this is to make the variability of the fundamental net demand shocks stochastic – that is, to introduce stochastic fundamental volatility.

The introduction of this factor is not ad hoc because there is considerable independent basis to believe that the supply and demand for commodities exhibit stochastic volatility. For instance, for industrial commodities such as copper, demand is affected by macroeconomic factors. Moreover, (a) stock prices also reflect macroeconomic fundamentals, and (b) stock prices exhibit stochastic volatility.

Introduction

Carbon permits issued as part of cap-and-trade systems around the world, and derivatives thereon, are likely to become one of the world's largest commodity markets in the coming years. Virtually every economic activity involving the production or consumption of energy will be affected by cap and trade, and this system for controlling greenhouse gases will therefore entail the purchase and sale of large quantities of carbon permits and derivatives.

This raises the question: How will carbon prices behave? The answer to that question depends on the design of the carbon market, which points to one of the distinctive things about this commodity: its market will be one of our own design. Throughout this book, I have noted that storage decisions and, hence, commodity prices depend on characteristics of the commodity, such as the nature of production (is it seasonally produced or not?) and spatial factors (how easy is it to trade across space?). With most of the commodities we are familiar with, say wheat or copper, some of these factors are outside of human control. Fundamental natural factors make wheat a periodically produced commodity, and nothing humans can do will change that.

Things are quite different with carbon. It is possible to choose – to design – virtually all of the salient features of this commodity. For instance, the frequency of production can be determined by legislative fiat. The author of the laws establishing cap and trade can specify that the permits will be issued yearly, or monthly, or weekly, or whatever.