Forward curves, scarcity and price volatility in oil and natural gas markets

The role of inventory in explaining the shape of the forward curve and spot price volatility in commodity markets is central in the theory of storage developed by Kaldor [Kaldor, N. (1939) "Speculation and Economic Stability", The Review of Economic Studies 7, 1–27] and Working [Working, H. (1949) “The theory of the price of storage”, American Economic Review, 39, 1254–1262] and has since been documented in a vast body of financial literature, including the reference paper by Fama and French [Fama, E.F. and K.R. French (1987) “Commodity futures prices: some evidence on forecast power, premiums and the theory of storage”, Journal of Business 60, 55–73] on metals. The goal of this paper is twofold: i) validate in the case of oil and natural gas the use of the slope of the forward curve as a proxy for inventory (the slope being defined in a way that filters out seasonality); ii) analyze directly for these two major commodities the relationship between inventory and price volatility. In agreement with the theory of storage, we find that: i) the negative correlation between price volatility and inventory is globally significant for crude oil; ii) this negative correlation prevails only during those periods of scarcity when the inventory is below the historical average and increases importantly during the winter periods for natural gas. Our results are illustrated by the analysis of a 15 year-database of US oil and natural gas prices and inventory

A Bayesian Reflection on Surfaces

The topic of this paper is a novel Bayesian continuous-basis field representation and inference framework. Within this paper several problems are solved: The maximally informative inference of continuous-basis fields, that is where the basis for the field is itself a continuous object and not representable in a finite manner; the tradeoff between accuracy of representation in terms of information learned, and memory or storage capacity in bits; the approximation of probability distributions so that a maximal amount of information about the object being inferred is preserved; an information theoretic justification for multigrid methodology. The maximally informative field inference framework is described in full generality and denoted the Generalized Kalman Filter. The Generalized Kalman Filter allows the update of field knowledge from previous knowledge at any scale, and new data, to new knowledge at any other scale. An application example instance, the inference of continuous surfaces from measurements (for example, camera image data), is presented.Comment: 34 pages, 1 figure, abbreviated versions presented: Bayesian Statistics, Valencia, Spain, 1998; Maximum Entropy and Bayesian Methods, Garching, Germany, 199

Understanding the fine structure of electricity prices

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a "jump-reversion" component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets

Seasonality in cocoa spot and forward markets: empirical evidence

This paper first describes the main features of supply and demand in cocoa spot markets. A state- variable model is proposed to describe the random evolution of cocoa forward curves over time, which essentially adapts to agricultural commodities, introduced by Borovkova and Geman (2006) for energy. In contrast to most of the literature on the subject, the first state variable is not the spot price, as it combines seasonal and stochastic features and may not be observable, instead, the average value of all liquid futures contracts is a quantity devoid of seasonality and conveys a robust representation of the forward curve level. The second state variable is a quantity analogous to the stochastic convenience yield, which accounts for the random changes in the shape of the forward curve. We conduct estimation procedures for the cocoa market over the period of 1980 to 2009 and exhibit an interesting result on cocoa seasonality as well as an extension of the Samuelson effect

Hierarchical testing designs for pattern recognition

We explore the theoretical foundations of a ``twenty questions'' approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (``background'') is statistically dominant, and it is imperative to restrict intensive computation to genuinely ambiguous regions. The focus here is then on pattern filtering: Given a large set Y of possible patterns or explanations, narrow down the true one Y to a small (random) subset \hat Y\subsetY of ``detected'' patterns to be subjected to further, more intense, processing. To this end, we consider a family of hypothesis tests for Y\in A versus the nonspecific alternatives Y\in A^c. Each test has null type I error and the candidate sets A\subsetY are arranged in a hierarchy of nested partitions. These tests are then characterized by scope (|A|), power (or type II error) and algorithmic cost. We consider sequential testing strategies in which decisions are made iteratively, based on past outcomes, about which test to perform next and when to stop testing. The set \hat Y is then taken to be the set of patterns that have not been ruled out by the tests performed. The total cost of a strategy is the sum of the ``testing cost'' and the ``postprocessing cost'' (proportional to |\hat Y|) and the corresponding optimization problem is analyzed.Comment: Published at http://dx.doi.org/10.1214/009053605000000174 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Shipping markets and freight rates: an analysis of the Baltic Dry Index

Shipping, although a crucial component of the transportation of commodities worldwide, is hardly present in the finance literature at this point. The first and foremost goal of this paper is to describe and explain from an economic perspective the key features of shipping markets; the second one is to analyze the behavior of freight rates, which define the final cost of an imported commodity. We focus on the major index, the BDI (Baltic Dry Index) and propose some diffusion models able to capture the unique features of its trajectories, namely large swings and continuity. Their performance is exhibited on a database covering the period 1988-2010. Such spot models should facilitate the growth of the market of freight rates options, a safe hedging instrument for farmers and cooperatives that ship their grains to distant destinations

Theory of storage, inventory and volatility in the LME base metals

The theory of storage, as related to commodities, makes two predictions involving the quantity of the commodity held in inventory. When inventory is low (i.e. a situation of scarcity), spot prices will exceed futures prices, and spot price volatility will exceed futures price volatility. Conversely, during periods of no scarcity, both spot prices and spot price volatility will remain relatively subdued. We test these predictions for the six base metals traded on the London Metal Exchange (aluminium, copper, lead, nickel, tin and zinc), and find strong validation for the theory. Including Chinese inventories reported by the Shanghai Futures Exchange strengthens the relationship further. We also introduce the concepts of excess volatility, inventory-implied spot price and inventory-implied spot volatility and illustrate some applications

Understanding the Fine Structure of Electricity Prices.

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean-reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a jump-reversion component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture - for the first time to our knowledge - both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major US power markets.Energy price risk; Simulation; Calibration; Statistical estimations; Jump diffusions; Electricity prices;

On pricing risky loans and collateralized fund obligations

Loan spreads are analyzed for two types of loans. The first type takes losses at maturity only; the second follows the formulation of collateralized fund obligations, with losses registered over the lifetime of the contract. In both cases, the implementation requires the choice of a process for the underlying asset value and the identification of the parameters. The parameters of the process are inferred from the option volatility surface by treating equity options as compound options with equity itself being viewed as an option on the asset value with a strike set at the debt level following Merton. Using data on the stock of General Motors during 2002-3, we show that the use of spectrally negative Lévy processes is capable of delivering realistic spreads without inflating debt levels, deflating debt maturities or deviating from the estimated probability laws