Convenience Yield Research Articles

Further evidence on the relationship between spot and futures prices

Based on a theoretical model, Tiltonet al. (2011) concluded that spot and futures prices should be highly correlated during periods of strong contango and much less correlated during periods of weak contango and backwardation. More recently, Gulley and Tilton (2014) found empirical support of this hypothesis for copper data during the period of 1994–2011.In this note, we show that Gulley and Tilton's findings can be rationalized by the theory of storage, as periods of contango and backwardation can be singled out by the sign of the interest-adjusted basis (i. e., storage cost rate minus convenience yield). Our estimation results for the six base metals of the London Metal Exchange show that a stronger association between futures and spot returns during periods of high stocks (i.e., positive interest-adjusted basis) holds only contemporaneously. Indeed, Granger causality, especially from futures to spot returns, may take place regardless of stock levels.

Relative scarcity and convenience yield: evidence from non-ferrous metals

ABSTRACTWe study the relationship between convenience yield and relative scarcity in the non-ferrous metal market for the period January 2000–March 2015. We identify various sets of economic relationships for six major base metals, namely, aluminium, copper, lead, nickel, tin and zinc. Our bivariate and multivariate VARs and associated Granger-causality test results generally support the existence of a positive relationship between convenience yields of base metals and our relative scarcity measure. Furthermore, the time-varying characteristics observed in the results, especially during contango and backwardation periods, provide useful information to market players in developing inventory strategies.

Commodities as Collateral

We propose and test a theory of using commodities as collateral for financing. Under capital control and collateral constraint, investors import commodities and pledge them as collateral to earn higher expected returns. Higher collateral demands increase commodity prices and make the inventory–convenience yield relation less negative. Our model illustrates these equilibrium effects and suggests that the violation of covered interest-rate parity is a proxy for collateral demands. Evidence from eight commodities in China and developed markets supports the theoretical predictions. Our findings complement the theory of storage and provide new insights into the financialization of commodity markets.

Convenience Yields and Risk Premiums in the EU‐ETS—Evidence from the Kyoto Commitment Period

AbstractWe examine convenience yields and risk premiums in the EU‐wide emissions trading scheme (EU‐ETS) during the first Kyoto commitment period (2008–2012). We find that the market has changed from initial backwardation to contango with significantly negative convenience yields in futures contracts. We further examine the impact of interest rate levels in the Eurozone, the increasing level of surplus allowances and banking, as well as returns, variance, or skewness in the EU‐ETS spot market. Our findings suggest that the drop in risk‐free rates during and after the financial crisis has impacted on the deviation from the cost‐of‐carry relationship for emission allowances (EUA) futures contracts. Our results also illustrate a negative relationship between convenience yields and the increasing level of inventory during the first Kyoto commitment period, providing an explanation for the high negative convenience yields. Finally, we find that market participants are willing to pay an additional risk premium in the futures market for a hedge against increased volatility in EUA prices. Overall, our results contribute to the literature on the determinants and empirical properties of convenience yields and risk premiums for this relatively new class of assets. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 36:587–611, 2016

Bond Convenience Yields and Exchange Rate Dynamics

This paper proposes a new explanation for the failure of Uncovered Interest Parity (UIP) that rationalizes both the classic UIP puzzle and the evidence that the puzzle reverses direction at longer horizons. In the model, excess currency returns arise as compensation for endogenous fluctuations in bond convenience yield differentials. Due to the interaction of monetary and fiscal policy, the impulse response of the equilibrium convenience yield is nonmonotonic, which generates the reversal of the puzzle. The calibrated model fits exchange rate dynamics very well. I also find direct evidence linking convenience yields to excess currency returns. (JEL E43, E52, F31, F41, H63)

Futures markets and fundamentals of base metals

According to the theory of storage, the interest-adjusted basis equals the warehousing cost minus the convenience yield (i.e., benefit of holding a physical commodity) per time unit. By assuming that warehousing costs relatively constant at alternative stock levels, the interest-adjusted basis will be inversely associated with the convenience yield.In this article, we explore whether the sign of the interest-adjusted basis determines the degree of association between spot and futures returns on the six London Metal Exchange base metals—aluminum, copper, lead, nickel, tin, and zinc. In addition, we study to what extent the sign of the interest-adjusted basis correlates with the business cycle of industrial production of various countries (e.g., US, G7, OECD, Russia, and China), and with the business cycle of consumption/production of the aforementioned six base metals.We conclude that a negative interest-adjusted basis is generally associated with booming industrial production, a negative or small metal surplus (i. e., production minus consumption), and low metal stocks. To our knowledge, this is the first study to link metal market fundamentals to futures markets dynamics.

Not Risk Free: The Relative Pricing of Euro Area Inflation-Indexed and Nominal Bonds

Selective default is an event in which a sovereign issuer chooses not to meet obligations on a class of bonds, while servicing her other debt. This paper presents unique empirical evidence of selective default risk premium in inflation-linked sovereign bond (ILB) yields of Germany, France and Italy. I identify this effect from the difference of breakeven rates from country pairs. Differencing controls for common components, such as the effect of inflation expectations, monetary policy or interest rate risk. I find that the remaining part in breakeven rates is explained by two systematic risk factors, liquidity and sovereign credit risks - both within and across countries. I link these findings to the ILB-nominal puzzle, which shows that ILBs are underpriced relative to nominal bonds of the same issuer. I show that this underpricing is in part due to relative risk premia differences between nominal and inflation-linked debt: ILBs are less liquid, moreover investors perceive them to have higher credit risk during the financial and euro crises. This implies an implicit seniority and a subsequent convenience yield in nominal bonds.

The End of the Month Option and Other Embedded Options in Futures Contracts

Futures contracts often contain several different kinds of embedded options related to the delivery of the underlying. The end of the month option allows the holder of the short end of a futures contract to deliver the underlying at any time during the last week of the contract period at a fixed price determined at the start of the last week. We derive a formula for this price in a general incomplete financial market, in which the process underlying the futures contract is a general adapted cadlag process and the risk free interest rate process is a general adapted process, both satisfying certain integrability conditions. In a similar setting we also derive a formula for the futures price process of a futures contract which first has no option active, then it has an active timing option (which lets the holder of the short end deliver at any time during the last month of the contract period) and lastly it has an active end of the month option. This combination of delivery options is present in the real-world financial markets. We show that this futures price process is dominated by a standard futures price process with maturity at the time of the activation of the end of the month option. We also show that if the underlying is an asset with a non-positive convenience yield and the interest rate is non-negative then it is optimal to deliver when the end of the month option becomes active. The main contribution of this paper is to properly define the end of the month option and to derive a formula for the futures price process of a futures contract with the combination of options described above.

The convenience yield implied in the European natural gas markets: the impact of storage and weather

This paper determines the convenience yield implied in the European natural gas markets and investigates driving factors and according dynamics. For this, we approximate the convenience yield via an option-based approach, in which the convenience yield is determined as the difference between two average floating-strike Asian options written on the spot and futures contracts. In a second step, we fit an exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model to explain the convenience yield via storage and weather as well as other key driving factors. The empirical analysis reveals distinct results for the impact of storage, which indicates that the release of natural gas storage levels generates considerable volatility. Further, we illustrate that the mixed evidence and the absence of a clear pattern to explain the convenience yield's characteristics underline the transitory state of European natural gas markets.

Pricing Commodity Futures Options in the Schwartz Multi Factor Model with Stochastic Volatility: An Asymptotic Method

In this paper we investigate the applicability of the asymptotic approach developed in Fouque et al. (2000) for pricing commodity futures options in a Schwartz (1997) multi factor model, featuring both stochastic convenience yield and stochastic volatility. We show that the zero order term in the expansion coincides with the Schwartz (1997) two factor term, with expected long-term volatility replacing the constant volatility term, and provide an explicit expression for the first order correction term. Using empirical data from the natural gas futures market, we demonstrate that a significantly better calibration can be achieved by involving the correction term as compared to the standard Schwartz (1997) two factor expression. This improvement comes at virtually no extra effort.

Decomposing Euro Area Sovereign Spreads: Credit, Liquidity and Convenience

We conduct an empirical analysis of sovereign bond spreads for a selected number of euro area countries. We analyze several methodologies to measure and to assess the relative importance of three components of sovereign spreads: credit premia, liquidity premia and convenience yields. We find that, except for Germany, credit premia explain the bulk of the level and variability in sovereign spreads, while liquidity premia and convenience yields seem to play a limited role, although they are in several cases statistically significant and they can become economically relevant during short episodes of illiquidity.

Dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield

The main objective of this paper is to address, in an a continuous-time framework, the issue of using storable commodity futures as vehicles for hedging purposes when, in particular, the convenience yield as well as the market prices of risk evolve randomly over time. Following the martingale route and by operating a suitable constant relative risk aversion utility function (CRRA) specific change of numéraire, we solve the investor's dynamic optimization program to obtain quasi analytical solutions for optimal demands, which can be expressed in terms of two discount bonds (traded and synthetic). Contrary to the existing literature, we explicitly derive the individual optimal proportions invested in the spot commodity, in a discount bond and in the futures contracts, which can be computed in a simple recursive way. We suggest various decompositions allowing an investor to assess the sensitivity of the optimal demands to the state variables and to specify the role played by each risky asset. Empirical evidence shows that the convenience yield has a strong impact on the speculation and hedging positions and the interaction among time-varying risk premia determines the magnitude and the sign of these positions.

The role of incompleteness in commodity futures markets

This paper proposes a convenience yield-based pricing for commodity futures, which embeds incompleteness of commodity futures markets in convenience yields. By using the pricing method, we conduct empirical analyses of the prices of WTI crude oil, heating oil, and natural gas futures traded on the NYMEX in order to assess the incompleteness of energy futures markets. We show that the fluctuation from the incompleteness is partly driven by the fluctuation from convenience yields. In addition, it is shown that the incompleteness of natural gas futures market is more highlighted than the incompleteness of WTI crude oil and heating oil futures markets. We apply the implied market price of risk from the NYMEX data to pricing an Asian call option written on WTI crude oil futures. Finally, we try to apply the market incompleteness analysis to the post-crisis periods after 2009.

Spot and Futures Markets Linkages: Does Contango Differ from Backwardation?

Recent research has concluded that spot and futures copper returns are more closely correlated during periods of contango than of backwardation. It is argued speculation and investor demand in futures markets should affect spot prices to a much lesser extent during backwardation, due to an infeasible inter‐temporal arbitrage. This article expands this line of research by analyzing daily spot and 3‐, 15‐, and 27‐month futures contract prices for industrial metals traded on the London Metal Exchange over a period of more than two decades. Estimates of convenience yields are provided, along with tests for Granger causality between futures and spot returns after accounting for cointegration, and tests for statistical differences between correlations of contemporaneous spot and futures returns during periods of contango and backwardation. After various robustness checks, the evidence supporting a stronger linkage between spot and futures markets in contango is weak. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:375–396, 2016

The Return-Volatility Relation in Commodity Futures Markets

By employing a continuous time stochastic volatility model, the dynamic relation between price returns and volatility changes in the commodity futures markets is analysed. An extensive daily database of gold and crude oil futures and futures options is used to estimate the model that is well suited to assess the return-volatility relation for the entire term structure of futures prices. The empirical results indicate a positive relation in the gold futures market and a negative relation in the crude oil futures market, especially over periods of high volatility principally driven by market-wide shocks. However, the opposite reaction occurs over quiet volatility periods when typically commodity-specific effects dominate. As leverage effect, volatility feedback effect and inventory effect do not adequately explain this reaction especially for the crude oil futures, the convenience yield effect is proposed. Accordingly, commodity futures markets in backwardation entail a positive relation, while futures markets in contango entail a negative relation.

Pricing derivatives with modeling CO2 emission allowance using a regime-switching jump diffusion model: with regime-switching risk premium

Carbon markets trade the spot European Union Allowance (EUA), with one EUA providing the right to emit one tone of carbon dioxide (CO2). We examine the spot EUA returns in BlueNext that exhibit jumps and a volatility clustering feature. We propose a regime-switching jump diffusion model (RSJM) with a hidden Markov chain to capture not only a volatility clustering feature, but also the dynamics of the spot EUA returns that are influenced by change in the CO2 emission economic conditions. In addition, the switching jump intensities of the RSJM are shown to be affected by change in the carbon-market macroeconomic environment. We further derive the theoretical futures-option prices with a constant convenience yield under the RSJM via the generalized Esscher transform where regime-switching risk is priced with a risk premium. The empirical study shows that the derived futures-option pricing model under the RSJM with regime-switching risk is a more complete model than a jump diffusion model for pricing CO2 options.

Empirical analysis of corn and soybean basis in Canada

The article examines the factors affecting the basis for corn and soybeans using several time-series techniques to account for potential structural breaks, seasonality, residual serial correlation and structural breaks, as well as potential endogeneity and nonstationarity. The spatio-temporal empirical framework is based on storage and trade theories which assume the relationship between nondelivery location’s spot price and futures price of a storable commodity depends on opportunity cost of capital, warehousing costs, a convenience yield and shipping costs. The interest rate effect is strong for both crops with shipping costs also affecting soybean basis and own inventory levels positively correlated with corn basis. The effect of the wedge between the price of carrying physical grain and the maximum storage rate on basis is positive for both crops. The empirical results, which are robust to multiple estimators, provide stronger evidence of a structural break for the soybean basis than for the corn basis.

Valuation of commodity derivatives with an unobservable convenience yield

This paper extends the existing literature on commodity derivatives to account for an unobservable stochastic convenience yield. Investors operate in an economy with incomplete information. In contrast to other incomplete information models, analytical formulas for forward and futures prices, as well as for European options on forward and futures contracts are obtained. These formulas reveal the important role played by the initial values of the estimator of the convenience yield and of the estimation error respectively when valuing commodity derivatives. We estimate Schwartz׳s [11] model and the incomplete information model based on the discrete-time Kalman filtering method. For futures prices, the latter seems to perform better than the former. Moreover, Schwartz׳s model provides higher option prices than the incomplete information model. The most important differences are obtained for higher futures prices and for longer options maturities.

Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields.

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results.

Convenience Yield Revisited: Using Profit Maximization Discrete-Time Model

This study analyzes the relationships of commodity spot and futures prices with convenience yield. Convenience yield is received by the owner of a spot commodity but not by the owner of the right to the commodity (e.g., futures). This is the first study to explicitly model commodity spot and futures prices using firms and speculators (i.e., supply and demand of a commodity). We found that spot and futures prices are related to convenience yield. Based on this we were able identify the structure of convenience yield, which can be decomposed into two components: yield and cost. Furthermore, these relations offer a basis for at least three ways of interpreting convenience yield. We obtained similar results using models that consider cash settlement and hedging with output commodity futures. We found that, when speculators are introduced, the differences in valuation of the futures price between risk-neutral and risk-averse entities consisted of future marginal storage costs plus convenience yield on futures. Thus, convenience yield arises from heterogeneous agents. Our model can be generalized to include multiple firms that take multiple input and output commodities and multiple speculators. We also derived the optimal production and trading strategy for spot commodities and futures, and we define and prove the existence of the equilibrium for this economy using additional assumptions.