Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates

We characterize a three‐factor model of commodity spot prices, convenience yields, and interest rates, which nests many existing specifications. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time‐varying risk premia. Both may induce mean reversion in spot prices, albeit with very different economic implications. Empirical results show strong evidence for spot‐price level dependence in convenience yields for crude oil and copper, which implies mean reversion in prices under the risk‐neutral measure. Silver, gold, and copper exhibit time variation in risk premia that implies mean reversion of prices under the physical measure.     

The Traditional Hedging Model Revisited with a Nonobservable Convenience Yield

This article examines the hedging of constrained commodity positions with futures contracts. We extend the study of Adler and Detemple (1988a, 1988b) to include a partial information framework where the convenience yield is not observable. As a consequence, futures prices depend on investor's beliefs regarding the value of the convenience yield, and every component of the hedge is impacted by these beliefs. We achieve a decomposition of the demand that clarifies the impact on the optimal hedge of the beliefs, the spot price and the risk‐free rate as well as the hedging horizon.     

Central bank announcements of asset purchases and the impact on global financial and commodity markets

We present evidence on the effects of large-scale asset purchases by the Federal Reserve and the Bank of England since 2008. We show that announcements about these purchases led to lower long-term interest rates and depreciations of the U.S. dollar and the British pound on announcement days, while commodity prices generally declined despite this more stimulative financial environment. We suggest that LSAP announcements likely involved signaling effects about future growth that led investors to downgrade their U.S. growth forecasts lowering long-term US yields, depreciating the value of the U.S. dollar, and triggering a decline in commodity prices. Moreover, our analysis illustrates the importance of controlling for market expectations when assessing these effects. We find that positive U.S. monetary surprises led to declines in commodity prices, even as long-term interest rates fell and the U.S. dollar depreciated. In contrast, on days of negative U.S. monetary surprises, i.e. when markets evidently believed that monetary policy was less stimulatory than expected, long-term yields, the value of the dollar, and commodity prices all tended to increase.     

Oil convenience yields estimated under demand/supply shock

This paper extends the call option model of Milonas and Thomadakis (1997) to estimate oil convenience yields with futures prices. We define the business cycle of a seasonal commodity with demand/supply shocks and find that the convenience yield for crude oil exhibits seasonal behavior. The convenience yield for West Texas Intermediate (WTI) crude oil is the highest in the summer, while that for Brent crude oil is the highest in the winter. This implies that WTI crude oil is more sensitive to high summer demand and that Brent crude oil is more sensitive to shortages in winter supply. Convenience yields are negatively related to the inventory level of the underlying crude oil and positively related to interest rates due to the business cycle. We also show that convenience yields may explain price spread between WTI crude oil and Brent crude oil. Our computed convenience yields are consistent with Fama and French (1988) in that oil prices are more volatile than futures prices at low inventory level, verifying the Samuelson (1965) hypothesis that future prices are less variables than spot prices at lower inventory levels.

The Stochastic Seasonal Behaviour of Natural Gas Prices

Previous studies have explored the seasonal behaviour of commodity prices as a deterministic factor. This paper goes further by proposing a general (n+2m)‐factor model for the stochastic behaviour of commodity prices, which nests the deterministic seasonal model by Sorensen (2002) . We consider seasonality as a stochastic factor, with n non‐seasonal and m seasonal factors. The non‐seasonal factors are as defined in Schwartz (1997) , Schwartz and Smith (2000) and Cortazar and Schwartz (2003) . The seasonal factors are trigonometric components generated by stochastic processes. The model has been applied to the Henry Hub natural gas futures contracts listed by NYMEX. We find that models allowing for stochastic seasonality outperform standard models with deterministic seasonality. We obtain similar results with other energy commodities. Moreover, we find that stochastic seasonality implies that the volatility of futures returns follows a seasonal pattern. This result has important implications in terms of option pricing.     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

Limits to arbitrage and hedging: Evidence from commodity markets

We build an equilibrium model of commodity markets in which speculators are capital constrained, and commodity producers have hedging demands for commodity futures. Increases in producers' hedging demand or speculators' capital constraints increase hedging costs via price-pressure on futures. These in turn affect producers' equilibrium hedging and supply decision inducing a link between a financial friction in the futures market and the commodity spot prices. Consistent with the model, measures of producers' propensity to hedge forecasts futures returns and spot prices in oil and gas market data from 1979 to 2010. The component of the commodity futures risk premium associated with producer hedging demand rises when speculative activity reduces. We conclude that limits to financial arbitrage generate limits to hedging by producers, and affect equilibrium commodity supply and prices.     

No-arbitrage conditions for storable commodities and the modeling of futures term structures

One distinguishable feature of storable commodities is that they relate to two markets: cash market and storage market. This paper proves that, if no arbitrage exists in the storage-cash dual markets, the commodity convenience yield has to be non-negative. However, classical reduced-form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield. To avoid negative convenience yield, this paper proposes a semi-affine arbitrage-free model, which prices futures analytically and fits futures term structures reasonably well. Importantly, our model prices commodity-related contingent claims (such as calendar spread options) quite differently with classical models.     

Estimating Early Exercise Premiums on Gold and Copper Options Using a Multifactor Model and Density Matched Lattices

We use the standard geometric Brownian motion augmented by jumps to describe the spot underlying and mean regressive models of interest rates and convenience yields as state variables for gold and copper prices. Estimates of parameters of the diffusion processes are obtained by the Kalman filter. Using these estimates, jump parameters are estimated in the second stage by least squares. Early exercise premia on puts and calls are computed using a lattice with probabilities assigned by the density matching technique. We find that while deep in the money options have greater absolute early exercise premiums, the early exercise premium is roughly constant as a percent of option price. Our findings also confirm that gold behaves like an investment asset and copper behaves like a commodity.     

MARKET TIMING IN REGRESSIONS AND REALITY

We compare price‐to‐earnings ratios and dividend yields, which are indirect measures of sentiment, with the bullish sentiment index, which is a direct measure. We find that the sentiment index does better as a market‐timing tool than do P/E ratios and dividend yields, but none is very reliable. We do not argue that market timing is impossible. Rather, we observe that stock prices reflect both sentiment and value, both of which are difficult to measure and neither of which is perfectly known in foresight. Successful market timing requires insights into future sentiment and value, insights beyond those that are reflected in widely available measures.     

The stochastic behavior of commodity prices with heteroskedasticity in the convenience yield

We document a new stylized fact regarding the dynamics of the commodity convenience yield: the volatility of the convenience yield is heteroskedastic for industrial commodities; specifically, the volatility (variance) of the convenience yield depends on the convenience yield level. To explore the economic and statistical significance of the improved specification of the convenience yield process, we propose an affine model with three state variables (log spot price, interest rate, and the convenience yield). Our model captures three important features of commodity futures—the heteroskedasticity of the convenience yield, the positive relationship between spot-price volatility and the convenience yield and the dependence of futures risk premium on the convenience yield. Moreover our model predicts an upward sloping implied volatility smile, commonly observed in commodity option market.     

The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions

We present hedge fund performance estimates that adjust for stale prices, Fama‐French risk factors and skewness. We contrast these new performance estimates with traditional performance measures. Using three‐factor models to adjust for staleness in prices and to incorporate Fama‐French factors along with the Harvey‐Siddique (2000) two‐factor model that incorporates skewness, we find that for the period 1990–2003, all hedge fund categories achieve above average performance when measured against an aggregate market index. More significantly, however, when we estimate performance at the individual hedge fund level, we discover that only 40 to 47% of the funds are shown to achieve an above average performance over that time period depending on the model used. These results have important implications for investors, endowments and pensions when they choose hedge fund managers.     

END‐OF‐DAY PRICING IN THE U.S. TREASURY MARKET: A COMPARISON OF GovPX AND THE FEDERAL RESERVE BANK OF NEW YORK

We compare end‐of‐day indicative U.S. Treasury prices from GovPX and the Federal Reserve Bank of New York (FRBNY). We find that the two sources rarely quote identical prices, and differences are not simply due to noise or rounding. The average bid price differential is 2 cents for notes and bonds, but it is only ¹/₁₀ of 1 cent for bills. Bid‐ask spreads in both sources appear to be largely artificial and contain limited information. Finally, we find that the end‐of‐day indicative FRBNY bid prices are closer to true intraday GovPX market quotes than end‐of‐day indicative quotes provided by GovPX itself.     

A Parimutuel Market Microstructure for Contingent Claims

Parimutuel principles are widely used as an alternative to fixed odds gambling in which a bookmaker acts as a dealer by quoting fixed rates of return on specified wagers. A parimutuel game is conducted as a call auction in which odds are allowed to fluctuate during the betting period until the betting period is closed or the auction ‘called’. The prices or odds of wagers are set based upon the relative amounts wagered on each risky outcome. In financial microstructure terms, trading under parimutuel principles is characterised by (1) call auction, non‐continuous trading; (2) riskless funding of claim payouts using the amounts paid for all of the claims during the auction; (3) special equilibrium pricing conditions requiring the relative prices of contingent claims equal the relative aggregate amounts wagered on such claims; (4) endogenous determination of unique state prices; and (5) higher efficiency. Recently, a number of large investment banks have adopted a parimutuel mechanism for offering contingent claims on various economic indices, such as the US Nonfarm payroll report and Eurozone Harmonised inflation. Our paper shows how the market microstructure incorporating parimutuel principles for contingent claims which allows for notional transactions, limit orders, and bundling of claims across states is constructed. We prove the existence of a unique price equilibrium for such a market and suggest an algorithm for computing the equilibrium. We also suggest that for a broad class of contingent claims, that the parimutuel microstructure recently deployed offers many advantages over the dominant dealer and exchange continuous time mechanisms.     

Commodity price modelling that matches current observables: a new approach

We develop a stochastic model of the spot commodity price and the spot convenience yield such that the model matches the current term structure of forward and futures prices, the current term structure of forward and futures volatilities, and the inter-temporal pattern of the volatility of the forward and futures prices. We let the underlying commodity price be a geometric Brownian motion and we let the spot convenience yield have a mean-reverting structure. The flexibility of the model, which makes it possible to simultaneously achieve all these goals, comes from allowing the volatility of the spot commodity price, the speed of mean-reversion parameter, the mean-reversion parameter, and the diffusion parameter of the spot convenience yield all to be time-varying deterministic functions.     

Optionality and Daily Dynamics of Convenience Yield Behavior: An Empirical Analysis

In this article I empirically examine the daily convenience yield behavior for six commodity markets (crude oil, heating oil, gasoline, wheat, corn, and copper). The results illustrate that convenience yield behavior can be statistically explained within an option pricing framework. However, because one of the assumptions of the standard call option formula is not fully satisfied by the observed convenience yield series, an alternative option—exchange option—may be more appropriate for modeling the daily convenience yield behavior. Furthermore, I empirically test two hypotheses on convenience yield behavior. The results confirm the assertion that the convenience yield is increasing in marginal production costs. In addition, the findings offer limited support for the hypothesis that the convenience yield is decreasing in the serial autocorrelation of spot prices. The observed switch in the sign of regression coefficients as the order of autocorrelation increases is attributed to the probable presence of mean reversion in these markets.     

Commodity prices and BRIC and G3 liquidity: A SFAVEC approach

This paper investigates the influence of liquidity in the major developed and major developing economies on commodity prices. Liquidity is taken to be M2. A novel finding is that unanticipated increases in the BRIC countries’ liquidity is associated with significant and persistent increases in commodity prices that are much larger than the effect of unanticipated increases in G3 liquidity, and the difference increases over time. Over 1999–2012 BRIC liquidity is strongly linked with global energy prices and global real activity whereas G3 liquidity is not. The impact of BRIC liquidity on mineral and metal prices is twice as large as that of G3 liquidity. Granger casualty goes from liquidity to commodity prices. BRIC and G3 liquidity and commodity prices are cointegrated. BRIC and G3 liquidity and global output and global prices are cointegrated. We construct a structural factor-augmented error correction (SFAVEC) model.     

Commodity derivatives valuation with autoregressive and moving average components in the price dynamics

In this paper, we develop a continuous time factor model of commodity prices that allows for higher-order autoregressive and moving average components. We document the need for these components by analyzing the convenience yield’s time series dynamics. The model we propose is analytically tractable and allows us to derive closed-form pricing formulas for futures and options. Empirically, we estimate a parsimonious version of the general model for the crude oil futures market and demonstrate the model’s superior performance in pricing nearby futures contracts in- and out-of-sample. Most notably, the model substantially improves the pricing of long-horizon contracts with information from the short end of the futures curve.     

Liquidity commonality in commodities

We examine liquidity commonality in commodity futures markets. Using data from 16 agricultural, energy, industrial metal, precious metal, and livestock commodities, we show there is a strong systematic liquidity factor in commodities. Liquidity commonality was present in 1997–2003 when commodity prices were relatively stable and during the recent boom. There is some support for both “supply-side” and “demand-side” explanations for this commonality. We find no evidence of a consistent link between stock and commodity liquidity in general. Energy commodities appear to provide a better hedge against equity market liquidity risk than the other commodity families.     

Hedging with Two Futures Contracts: Simplicity Pays

We propose to use two futures contracts in hedging an agricultural commodity commitment to solve either the standard delta hedge or the roll‐over issue. Most current literature on dual‐hedge strategies is based on a structured model to reduce roll‐over risk and is somehow difficult to apply for agricultural futures contracts. Instead, we propose to apply a regression based model and a naive rules of thumb for dual‐hedges which are applicable for agricultural commodities. The naive dual strategy stems from the fact that in a large sample of agricultural commodities, De Ville, Dhaene and Sercu (2008) find that GARCH‐based hedges do not perform as well as OLS‐based ones and that we can avoid estimation error with such a simple rule. Our semi‐naive hedge ratios are driven from two conditions: omitting exposure to spot price and minimising the variance of the unexpected basis effects on the portfolio values. We find that, generally, (i) rebalancing helps; (ii) the two‐contract hedging rules do better than the one‐contract counterparts, even for standard delta hedges without rolling‐over; (iii) simplicity pays: the naive rules are the best one–for corn and wheat within the two‐contract group, the semi‐naive rule systematically beats the others and GARCH performs worse than OLS for either one‐contract or two‐contract hedges and for soybeans the traditional naive rule performs nearly as well as OLS. These conclusions are based on the tests on unconditional variance ( Diebold and Mariano, 1995 ) and those on conditional risk ( Giacomini and White, 2006 ).