A continuous time equilibrium model of forward prices and futures prices in a multigood economy

This paper is a theoretical investigation of equilibrium forward and futures prices. We construct a rational expectations model in continuous time of a multigood, identical consumer economy with constant stochastic returns to scale production. Using this model we find three main results. First, we find formulas for equilibrium forward, futures, discount bond, commodity bond and commodity option prices. Second, we show that a futures price is actually a forward price for the delivery of a random number of units of a good; the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract. Third, we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices; these conditions reflect the usefulness of forward and futures contracts as consumption hedges.     

A comparison of futures and forward prices

This paper uses the pricing models of Cox, Ingersoll and Ross (1981), Richard and Sundaresan (1981), and French (1982) to examine the relation between futures and forward prices for copper and silver. There are significant differences between these prices. The average differences are generally consistent with the predictions of the futures and forward price models. However, these models are not helpful in describing intra-sample variations in the futures-forward price differences. This failure is apparently caused by measurement errors in both the price differences and in the explanatory variables.     

Futures and forward price differential and the effect of marking‐to‐market: Australian evidence

The objective of this paper is to examine the effects of marking‐to‐market of futures contracts on the price differential between futures and forward contracts based on the predictions of the Cox, Ingersoll and Ross (1981) (CIR) model. Cox et al ., (1981) derive a series of propositions with respect to the relationship between futures and forward prices and a set of testable implications. These are tested empirically in this paper using Australian data from November 1991 to June 1997. The results provide evidence of the presence of significant futures and forward price differences, where the futures price is consistently below the forward price. Only partial support is found for the Cox et al ., (1981) propositions, implying that the effect of marking‐to‐market is not able to fully account for the price differential. Therefore, it is not possible to rule out the influence of other institutional factors on the futures‐forward price difference.     

Futures and forward price differential and the effect of marking‐to‐market: Australian evidence

The objective of this paper is to examine the effects of marking‐to‐market of futures contracts on the price differential between futures and forward contracts based on the predictions of the Cox, Ingersoll and Ross (1981) (CIR) model. Cox et al ., (1981) derive a series of propositions with respect to the relationship between futures and forward prices and a set of testable implications. These are tested empirically in this paper using Australian data from November 1991 to June 1997. The results provide evidence of the presence of significant futures and forward price differences, where the futures price is consistently below the forward price. Only partial support is found for the Cox et al ., (1981) propositions, implying that the effect of marking‐to‐market is not able to fully account for the price differential. Therefore, it is not possible to rule out the influence of other institutional factors on the futures‐forward price difference.     

The relationship between reciprocal currency futures prices

Consider a futures contract on Country 2’s currency denominated in Country 1’s currency, and its reciprocal, a futures contract on Country 1’s currency denominated in Country 2’s currency. Because both are marked to market in different currencies, the relationship between the associated futures prices is not simple. We investigate the functional relationship between these two futures prices.     

Forward contracts and futures contracts

This paper provides a detailed discussion of the similarities and differences between forward contracts and futures contracts. Under frictionless markets and continuous trading, simple arbitrage arguments are invoked to value forward contracts, to relate forward prices and spot prices, and to relate forward prices and futures prices. We also argue that forward prices need not equal futures prices unless default free interest rates are deterministic.     

The role of speculation in international futures markets on commodity prices

The role of futures contracts on spot prices has been one of the key focus areas of research since the recent surge in commodity prices and increase in the volatility of commodity returns. However, no consensus arises from this literature, and hence it is difficult to link the use of futures contracts in agricultural commodities by non-hedgers and the growing food insecurity within developing countries. The purpose of this paper is to highlight causal relationships from futures contracts to spot prices of underlying assets, namely agricultural commodities. As research that focus on exchange-traded funds do not provide any clear conclusions, we focus on the imbalance between short- and long-open positions, this imbalance being caused by the exchange traded funds’ participation in futures markets. In this paper, we estimate relationships between financial variables including indicators for speculation in futures markets and the returns of cocoa, corn, soybean, wheat, coffee, rice, and sugar on a weekly basis from 1998 to 2013. Significant results lead to Granger-causality tests that in turn validate the hypothesis of a positive impact of speculation in futures markets to returns on the underlying commodities.     

Futures and realized cash or settle prices for gold,silver, and copper

This article examines the relation between 15-, 30-, 45-, and 60-day gold, silver, and copper futures, and their realized cash or delivery settle prices, for deliveries on the first, middle, and last business day (FD, MD, and LD, respectively) of the delivery month. Samples of futures prices for gold, silver, and copper, and the realized cash or delivery settle prices, based on fixed maturities for a cross-section of contracts are used, because time-series over fixed maturities are unfeasible owing to the restrictive maturity periods in these contracts. This study contrasts with similar studies for forwards, which are not hampered by this problem (e.g., Baillie and Bollerslev in 1989), studies that use contemporaneous time-series of futures and cash prices to obtain optimal hedge ratios (e.g., Ghosh and Clayton in 1996), and studies that examine for parity between different futures prices (e.g., Franses and Kofman in 1991). Near-term gold, closest to delivery silver and all copper futures (the latter only with settle prices at delivery) are good predictors of the future cash price, except for silver and copper deliveries on the last day of delivery months. These results are consistent with previous studies on short-term cash (Ma in 1985) and futures (Ma and Soenen in 1988) parity between gold and silver, and with Gross's (1988) results for copper. The longer-term gold (45- and 60-day) and silver (30-, 45-, and 60-day) futures reject an unbiased expectations hypothesis. This result is consistent with Leistikow (1990) because cash prices respond less than futures prices in these instances.     

Do economic statistics contain information to predict stock indexes futures prices and returns? Evidence from Asian equity futures markets

This research examines the impact of local and international market factors on the pricing of stock indexes futures in East Asian countries. The purpose of this paper is to present a study of the significant factors that determine the major stock indexes futures’ prices of Hong Kong, Malaysia, Singapore, South Korea and Taiwan. This study first investigates the relationships between Hang Seng Index Futures, KLCI Futures, SiMSCI Futures, KOSPI Futures, Taiwan Exchange Index Futures and local interest rates, dividend yields, local exchange rates, overnight S&P500 index and a newly constructed index, Asian Tigers Malaysia Index (ATMI). 11 years historical data of stock indexes futures and the economic statistics are studied; 10 years in-sample data are used for testing and developing the pricing models, and 1 year out-of-sample data is used for the purpose of verifying the predicted values of the stock indexes futures. Using simple linear regressions, local interest rates, dividend yields, exchange rates, overnight S&P500 and ATMI are found to have significant impact on these futures contracts. In this research, the next period close is predicted using simple linear regression and non-linear artificial neural network (ANN). An examination of the prediction results using nonlinear autoregressive ANN with exogenous inputs (NARX) shows significant abnormal returns above the passive threshold buy and hold market returns and also above the profits of simple linear regression (SLR). The empirical evidence of this research suggests that economic statistics contain information which can be extracted using a hybrid SLR and NARX trading model to predict futures prices with some degree of confidence for a year forward. This justifies further research and development of pricing models using fundamentally significant economic determinants to predict futures prices.

     

Determination of stock closing prices and hedging performance with stock indices futures

This paper examines the impact of the determination of stock closing prices on futures price efficiency and hedging effectiveness with stock indices futures. The empirical results indicate that the increase in the length of the batching period of the stock closing call improves price efficiency in the futures closing prices and then enhances hedging performance in terms of the hedging risks. Additionally, from a utility‐maximization point of view, hedging performance does not improve after the introduction of the 5 min stock closing call, which can be explained by an improvement in price efficiency at the futures market close.     

Futures prices and inflation information

This study examines the timing and speed with which inflation futures prices absorb inflation information. Results of the study show that inflation futures prices already reflect the expected inflation. Moreover, 71% of unexpected inflation has been reflected in futures prices about 25 business days prior to the Consumer Price Index (CPI) announcement, which usually coincides with the end of the CPI measurement period. Reaction to the remaining 29% occurs on and shortly after the CPI announcement date, especially on day 0 and day 2. The inflation risk premium that investors are willing to pay to avoid uncertain inflation is estimated to be 1.41% per annum.     

Long memory in energy futures prices

This paper extends the work in Serletis [Serletis, A. (1992). Unit root behavior in energy futures prices. The Energy Journal 13, 119-128] by re-examining the empirical evidence for random walk type behavior in energy futures prices. It tests for fractional integrating dynamics in energy futures markets utilizing more recent data (from January 3, 1994 to June 30, 2005) and a new semi-parametric wavelet-based estimator, which is superior to the more prevalent GPH estimator (on the basis of Monte-Carlo evidence). We find new evidence that energy prices display long memory and that the particular form of long memory is anti-persistence, characterized by the variance of each series being dominated by high frequency (low wavelet scale) components.     

Pricing a class of exotic commodity options in a multi-factor jump-diffusion model

In a recent paper, Crosby introduced a multi-factor jump-diffusion model which would allow futures (or forward) commodity prices to be modelled in a way which captured empirically observed features of the commodity and commodity options markets. However, the model focused on modelling a single individual underlying commodity. In this paper, we investigate an extension of this model which would allow the prices of multiple commodities to be modelled simultaneously in a simple but realistic fashion. We then price a class of simple exotic options whose payoff depends on the difference (or ratio) between the prices of two different commodities (for example, spread options), or between the prices of two different (i.e. with different tenors) futures contracts on the same underlying commodity, or between the prices of a single futures contract as observed at two different calendar times (for example, forward start or cliquet options). We show that it is possible, using a Fourier transform-based algorithm, to derive a single unifying form for the prices of all these aforementioned exotic options and some of their generalizations. Although we focus on pricing options within the model of Crosby, most of our results would be applicable to other models where the relevant ‘extended’ characteristic function is available in analytical form.     

Futures trading volume as a determinant of prices in different momentum phases

Recent studies contend that trading volume has predictive power for ex ante stock prices, particularly small stocks that do not react quickly to macroeconomic information. This study postulates that a significant amount of macro-information that flows on to stock markets is derived from derivative markets. We examine the impact of short-term futures trading volume and prices on cash stock prices using a case study of 15-min data from the Australian stock index futures market which reports actual trading volume. After applying vector error correction modelling (VECM), variance decomposition and impulse functions, we conclude that futures prices provide a short-term information lead to stock prices that dominates trading volume effects. We also observe asymmetric changes in the impact of trading volume between bull and bear price momentum phases and after large trading volume shocks. These results suggest that, in future, studies on trading volume should control for the cross-correlation impact from derivative prices and the differential impact of trading phases.     

Commodity prices and GDP growth

This paper explores the extent to which commodity prices can predict GDP growth rates of various countries using indices of 27 commonly traded commodity futures. Commodity returns can strongly predict the next quarter's GDP growth, while the basis shows a reasonable level of predictive power. Overall, commodity prices can be considered a leading indicator of economic growth; increasing commodity prices and basis values indicate a stronger future economy.     

The role of gold futures in mitigating the impact of economic uncertainty on spot prices: Evidence from China

This paper studies the co-integration relationship and volatility spillover effect between China's gold futures and spot prices through the VECM-BEKK-GARCH model. Then, MSGARCH and DCCE-GARCH are applied to study the relationship among China's gold futures market, spot market price volatility and the stabilization effect in uncertain economic environments. This paper enriches the current research, providing gold market participants with hints to address economic uncertainty. The empirical results show that China's gold futures market has a weak stabilization effect on spot price volatility. In scenarios with uncertain economic information and uncertain macroeconomic changes, the correlation between gold futures and spot price volatility is reduced in China, and the role of gold futures in stabilizing the spot price weakens. Furthermore, with economic uncertainty, the fluctuation range of the gold futures price is greater than that of the spot price, with a tendency of more frequent fluctuations. This also means that the effectiveness of the futures market in regulating the spot price will be reduced, and gold market regulators need to stabilize the market through alternative methods to futures.     

Index-futures arbitrage and the behavior of stock index futures prices

This article examines intraday transaction data for S&P500 stock index futures prices and the intraday quotes for theunderlying index. The data indicate that the futures price changesare uncorrelated and that the variability of these price changesexceeds the variability of price changes in the S&P 500index. This excess variability of the futures over the indexremains even after controlling for the nonsynchronous pricesin the index quotes, which induces auto-correlation in the indexchanges. We advance and examine empirically two hypotheses regardingthe difference between the futures price and its theoreticalvalue: that this 'mispricing' increases on average with maturity,and that it is path-dependent. Evidence supporting these hypothesesis presented.     

New No-arbitrage Conditions and the Term Structure of Interest Rate Futures

Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts. Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (J Finance 52(1); 409–430, 1997), the starting point of this paper is a model of futures prices. Using, as the input to the model, the prices of futures on interest related assets new no-arbitrage restrictions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.     

Calibrating a market model with stochastic volatility to commodity and interest rate risk

Based on the multi-currency LIBOR Market Model, this paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function allowing the model to simultaneously fit the implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given correlation structure between forward interest rates and commodity prices (cross-correlation). When calibrating to options on forwards (rather than futures), the fitting of cross-correlation preserves the (separate) calibration in the two markets (interest rate and commodity options), while in the case of futures a (rapidly converging) iterative fitting procedure is presented. The fitting of cross-correlation is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the ‘orthonormal Procrustes’ problem in linear algebra. The calibration approach is demonstrated in an application to market data for oil futures.     

Currency risk hedging: Futures vs. forward

The objective of this paper is to address the issue of choosing between currency forward and currency futures contracts when hedging against currency risk within a stochastic interest rates environment. We compare between the hedging effectiveness of the two derivative assets both within a narrow sense (i.e., volatility minimization) and within a wide sense (i.e., risk-return trade-off). When judging hedging effectiveness in the narrow sense, forward and futures contracts give identical results even if they do not have identical prices. When judging hedging effectiveness in the wide sense, the choice between the two contracts is determined by the correlation between the domestic and the foreign term structures dynamics.