مدل سازی و اندازه گیری کشف قیمت در بازارهای کالا

In this paper we present an equilibrium model of commodity spot (View the MathML sourcest) and futures (View the MathML sourceft) prices, with finite elasticity of arbitrage services and convenience yields. By explicitly incorporating and modelling endogenously the convenience yield, our theoretical model is able to capture the existence of backwardation or contango in the long-run spot-futures equilibrium relationship, View the MathML sourcest=β2ft+β3. When the slope of the cointegrating vector β2>1(β2<1)β2>1(β2<1) the market is under long run backwardation (contango). It is the first time in this literature in which the theoretical possibility of finding a cointegrating vector different from the standard β2=1β2=1 is formally considered. Independent of the value of β2β2, this paper shows that the equilibrium model admits an economically meaningful Error Correction Representation, where the linear combination of (View the MathML sourcest) and (View the MathML sourceft) characterizing the price discovery process in the framework of Garbade and Silber (1983), coincides exactly with the permanent component of the Gonzalo and Granger (1995) Permanent–Transitory decomposition. This linear combination depends on the elasticity of arbitrage services and is determined by the relative liquidity traded in the spot and futures markets. Such outcome not only provides a theoretical justification for this Permanent–Transitory decomposition; but it offers a simple way of detecting which of the two prices is dominant in the price discovery process. All the results are testable, as can be seen in the application to spot and futures non-ferrous metals prices (Al, Cu, Ni, Pb, Zn) traded in the London Metal Exchange (LME). Most markets are in backwardation and futures prices are “information dominant” in highly liquid futures markets (Al, Cu, Ni, Zn).

Futures markets contribute in two important ways to the organization of economic activity: (i) they facilitate price discovery; and (ii) they offer a means of transferring risk or hedging. In this paper we focus on the first contribution. Price discovery refers to the use of futures prices for pricing cash market transactions (Working, 1948, Wiese, 1978 and Lake, 1978). In general, price discovery is the process of uncovering an asset’s full information or permanent value. The unobservable permanent price reflects the fundamental value of the stock or commodity. It is distinct from the observable price, which can be decomposed into its fundamental value and transitory effects. The latter consists of price movements due to factors such as bid-ask bounce, temporary order imbalances or inventory adjustments. Whether the spot or the futures market is the center of price discovery in commodity markets has for a long time been discussed in the literature. Stein (1961) showed that futures and spot prices for a given commodity are determined simultaneously. Garbade and Silber (1983) (GS thereafter) develop a model of simultaneous price dynamics in which they establish that price discovery takes place in the market with the highest number of participants. Their empirical application concludes that “about 75% of new information is incorporated first in the futures prices.” More recently, the price discovery research has focused on microstructure models and on methods to measure it. This line of literature applies two methodologies (see Lehman, 2002; special issue in the Journal of Financial Markets), the Information Shares of Hasbrouck (1995) (IS thereafter) and the Gonzalo and Granger (1995) Permanent–Transitory decomposition (PT thereafter). Our paper suggests a practical econometric approach to characterize and measure the phenomenon of price discovery by demonstrating the existence of a perfect link between an extended GS theoretical model and the PT decomposition. Building on GS, we develop an equilibrium model of commodity spot and futures prices where the elasticity of arbitrage services, contrary to the standard assumption of being infinite, is considered to be finite, and the existence of convenience yields is endogenously modeled as a linear combination of stst and ftft satisfying the standard no-arbitrage condition. The assumption of finite elasticity is more realistic since it reflects the existence of factors such as basis risks, storage costs, convenience yields, etc. Convenience yields are natural for goods, like art or land, that offer exogenous rental or service flows over time. It is observed in commodities, such as agricultural products, industrial metals and energy, which are consumed at a single point in time. Convenience yields and subsequent price backwardations have attracted considerable attention in the literature (see Routledge et al., 2000). Backwardation (contango) exists when prices decline (increase) with time-to-delivery, so that spot prices are greater (lower) than futures prices. By explicitly incorporating and modelling convenience yields, we are able to detect the existence of backwardation and contango in the long-run equilibrium relationship between spot and futures prices. In our model, this is reflected on a cointegrating vector, (1,−β2)(1,−β2), different from the standard β2=1β2=1. When View the MathML sourceβ2>1(<1) the market is under long run backwardation (contango). As a by-product of this modeling we find a theoretical justification for a cointegrating vector between log-variables different from the standard (1,−11,−1). To the best of our knowledge, this is the first time this has been formally considered in this literature.1 Independent of the value of β2β2, this paper shows that the proposed equilibrium model not only implies cointegration; but it leads into an economically meaningful Error Correction Representation (see Engle and Granger, 1987). The weights defining the linear combination of stst and ftft that constitute the common permanent component in the PT decomposition, coincide exactly with the price discovery parameters proposed by GS. These weights depend on the elasticity of arbitrage services and are determined by the liquidity traded in the spot and in the futures market. This result not only offers a theoretical justification for the PT decomposition; but it provides a simple way of detecting which of the two prices is long run dominant in the price discovery process. Information on price discovery is important because spot and futures markets are widely used by firms engaged in the production, marketing and processing of commodities. Consumption and production decisions depend on the price signals from these markets. All the results produced in the paper can easily be tested, as may be seen directly from our application to London Metal Exchange (LME) data. We are interested in these metal markets because they have highly developed futures contracts. Applying our model to LME spot and futures data we find: (i) All markets with the exception of copper are backwarded in equilibrium. This is reflected in a cointegrated slope greater than one, and (ii) The futures price is information dominant for all metals with a liquid futures markets: Aluminium (Al), Copper (Cu), Nickel (Ni) and Zinc (Zn). The spot price is information dominant for Lead (Pb), the least liquid LME contract. The paper is organized as follows. Section 2 describes the equilibrium model with finite elasticity of supply of arbitrage services incorporating endogenously convenience yields. It demonstrates that the model admits an economically meaningful Error Correction Representation, and derives the contribution of the spot and futures prices to the price discovery process. In addition, it shows that the weights of the linear combination defining price discovery in the PT metric correspond to the price discovery parameters proposed by GS. Section 3 discusses the theoretical econometric background of the two techniques available to measure price discovery, the Hasbrouck’s IS and the PT of Gonzalo–Granger. Section 4 presents empirical estimates of the model developed in Section 2 for five LME traded metals, it tests for cointegration and the presence of long run backwardation (β2>1β2>1), and estimates the contribution of the spot and futures prices to price discovery, testing the hypothesis of the futures price being the sole contributor to price discovery. A by-product of this empirical section is the computation of the unobserved convenience yields for all commodities. Section 5 concludes. Graphs are collected in the Appendix.

The process of price discovery is crucial for all participants in commodity markets. The present paper models and measures this process by extending the work of GS to consider the existence of convenience yields in spot-future price equilibrium relationships. The proposed model of convenience yields with I.1/ prices captures the presence of long-run backwardation or contango structures, which are reflected in the cointegrating vector .1;