Contemporaneous intraday volume, option, and futures volatility transmissions across parallel markets

The primary objective of this article is to investigate volatility transmission across three parallel markets operating on the Sydney Futures Exchange (SFE), both within and out of sample. Half-hourly observations are sampled from transaction data for the share price index (SPI) futures, SPI futures options, and 90-day bank accepted bill (BAB) futures markets, and the analysis is carried out using the simultaneous volatility (SVL) system of equations as well as competing volatility models. The results confirm the poor ability of GARCH models to fit intraday data. This study also applies an artificial nesting procedure to evaluate the out-of-sample volatility forecasts. Implied volatility has very limited (if any) predictive power when evaluated in isolation, whereas the SVL model with implied volatility embedded provides incremental information relative to competing model forecasts.     

Is idiosyncratic volatility priced in commodity futures markets?

This article investigates the relationship between expected returns and past idiosyncratic volatility in commodity futures markets. Measuring the idiosyncratic volatility of 27 commodity futures contracts with traditional pricing models that fail to account for backwardation and contango leads to the puzzling finding that idiosyncratic volatility is significantly negatively priced cross-sectionally. However, idiosyncratic volatility is not priced when the phases of backwardation and contango are suitably factored in the pricing model. A time-series portfolio analysis similarly suggests that failing to recognize the fundamental risk associated with the inexorable phases of backwardation and contango leads to overstated profitability of the idiosyncratic volatility mimicking portfolios.     

Forecasting Commodity Market Returns Volatility: A Hybrid Ensemble Learning GARCH-LSTM based Approach

This study investigates the advantage of combining the forecasting abilities of multiple generalized autoregressive conditional heteroscedasticity (GARCH)-type models, such as the standard GARCH (GARCH), exponential GARCH (eGARCH), and threshold GARCH (tGARCH) models with advanced deep learning methods to predict the volatility of five important metals (nickel, copper, tin, lead, and gold) in the Indian commodity market. This paper proposes integrating the forecasts of one to three GARCH-type models into an ensemble learning-based hybrid long short-term memory (LSTM) model to forecast commodity price volatility. We further evaluate the forecasting performance of these models for standalone LSTM and GARCH-type models using the root mean squared error, mean absolute error, and mean fundamental percentage error. The results highlight that combining the information from the forecasts of multiple GARCH types into a hybrid LSTM model leads to superior volatility forecasting capability. The SET-LSTM, which represents the model that combines forecasts of the GARCH, eGARCH, and tGARCH into the LSTM hybrid, has shown the best overall results for all metals, barring a few exceptions. Moreover, the equivalence of forecasting accuracy is tested using the Diebold–Mariano and Wilcoxon signed-rank tests.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Time-variations in commodity price jumps

In this paper, we study jumps in commodity prices. Unlike assumed in existing models of commodity price dynamics, a simple analysis of the data reveals that the probability of tail events is not constant but depends on the time of the year, i.e. exhibits seasonality. We propose a stochastic volatility jump–diffusion model to capture this seasonal variation. Applying the Markov Chain Monte Carlo (MCMC) methodology, we estimate our model using 20 years of futures data from four different commodity markets. We find strong statistical evidence to suggest that our model with seasonal jump intensity outperforms models featuring a constant jump intensity. To demonstrate the practical relevance of our findings, we show that our model typically improves Value-at-Risk (VaR) forecasts.     

Predicting Volatility in the Foreign Exchange Market

Measures of volatility implied in option prices are widely believed to be the best available volatility forecasts. In this article, we examine the information content and predictive power of implied standard deviations (ISDs) derived from Chicago Mercantile Exchange options on foreign currency futures. The article finds that statistical time-series models, even when given the advantage of “ex post” parameter estimates, are outperformed by ISDs. ISDs, however, also appear to be biased volatility forecasts. Using simulations to investigate the robustness of these results, the article finds that measurement errors and statistical problems can substantially distort inferences. Even accounting for these, however, ISDs appear to be too variable relative to future volatility.     

Valuation of commodity derivatives in a new multi-factor model

This paper extends existing commodity valuation models to allow for stochastic volatility and simultaneous jumps in the spot price and spot volatility. Closed-form valuation formulas for forwards, futures, futures options, geometric Asian options and commodity-linked bonds are obtained using the Heston (1993) and Bakshi and Madan (2000) methodology. Stochastic volatility and jumps do not affect the futures price at a given point in time. However, numerical examples indicate that they play important roles in pricing options on futures. This revised version was published online in June 2006 with corrections to the Cover Date.     

Neural network volatility forecasts

We analyse whether the use of neural networks can improve ‘traditional’ volatility forecasts from time-series models, as well as implied volatilities obtained from options on futures on the Spanish stock market index, the IBEX-35. One of our main contributions is to explore the predictive ability of neural networks that incorporate both implied volatility information and historical time-series information. Our results show that the general regression neural network forecasts improve the information content of implied volatilities and enhance the predictive ability of the models. Our analysis is also consistent with the results from prior research studies showing that implied volatility is an unbiased forecast of future volatility and that time-series models have lower explanatory power than implied volatility. Copyright © 2008 John Wiley & Sons, Ltd.     

The hedging effect of green bonds on carbon market risk

This paper explores effective hedging instruments for carbon market risk. Examining the relationship between the carbon futures returns and the returns of four major market indices, i.e., the VIX index, the commodity index, the energy index and the green bond index, we find that the connectedness between the carbon futures returns and the green bond index returns is the highest and this connectedness is extremely pronounced during the market's volatile period. Further, we develop and evaluate hedging strategies based on three dynamic hedge ratio models (DCC-APGARCH, DCC-T-GARCH, and DCC-GJR-GARCH models) and the constant hedge ratio model (OLS model). Empirical results show that among the four market indices the green bond index is the best hedge for carbon futures and performs well even in the crisis period. The paper also provides evidence that the dynamic hedge ratio models are superior to the OLS model in the volatile period as more sophisticated models can capture the dynamic correlation and volatility spillover between the carbon futures and market index returns.     

Power ARCH modelling of commodity futures data on the London Metal Exchange

A recent addition to the ARCH family of econometric models was introduced by Ding and co-workers wherein the power term by which the data is transformed was estimated within the model rather than being imposed by the researcher. This paper considers the ability of the Power GARCH class of models to capture the stylized features of volatility in a range of commodity futures prices traded on the London Metals Exchange (LME). The results of this procedure suggest that asymmetric effects are not generally present in the LME futures data. Further, unlike stock market data which is well described by the model, futures data is not as well described by the APGARCH model. Nested within the APGARCH model are several other models from the ARCH family. This paper uses the standard log likelihood procedure to conduct pairwise comparisons of the relative merits of each and the results suggest that it is the Taylor GARCH model which performs best.     

Markov models for commodity futures: theory and practice

The objective of this paper is to develop a generic, yet practical, framework for the construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results concerning the low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switching models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their ‘smile’, and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed form and of the same complexity as the Black–Scholes formula.     

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.     

Forecasting Stock Index Futures Price Volatility: Linear vs. Nonlinear Models

The study examines the relative ability of various models to forecast daily stock index futures volatility. The forecasting models that are employed range from naïve models to the relatively complex ARCH-class models. It is found that among linear models of stock index futures volatility, the autoregressive model ranks first using the RMSE and MAPE criteria. We also examine three nonlinear models. These models are GARCH-M, EGARCH, and ESTAR. We find that nonlinear GARCH models dominate linear models utilizing the RMSE and the MAPE error statistics and EGARCH appears to be the best model for forecasting stock index futures price volatility.     

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.     

The predictability of aggregate returns on commodity futures

This paper provides evidence that aggregate returns on commodity futures (without the returns on collateral) are predictable, both in-sample and out-of-sample, by various lagged variables from the stock market, bond market, macroeconomics, and the commodity market. Out of the 32 candidate predictors we consider, we find that investor sentiment is the best in-sample predictor of short-horizon returns, whereas the level and slope of the yield curve have much in-sample predictive power for long-horizon returns. We find that it is possible to forecast aggregate returns on commodity futures out-of-sample through several combination forecasts (the out-of-sample return forecasting R² is up to 1.65% at the monthly frequency).     

Empirical performance of multifactor term structure models for pricing and hedging Eurodollar futures options

This article compares two one-factor, two two-factor, two three-factor models in the HJM class and Black's [Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3, 167-179.] implied volatility function in terms of their pricing and hedging performance for Eurodollar futures options across strikes and maturities from 1 Jan 2000 to 31 Dec 2002. We find that three-factor models perform the best for 1-day and 1-week prediction, as well as for 5-day and 20-day hedging. The moneyness bias and the maturity bias appear for all models, but the three-factor models produce lower bias. Three-factor models also outperform other models in hedging, in particular for away-from-the-money and long-dated options. Making Black's volatility a square root or exponential function performs similar to one-factor HJM models in pricing, but not in hedging. Correctly specified and calibrated multifactor models are thus important and cannot be replaced by one-factor models in pricing or hedging interest rate contingent claims.     

Samuelson Hypothesis & Indian Commodity Derivatives Market

Samuelson (1965) devised that futures price volatility increases as the futures contract approaches its expiration. The relation amid the volatility and time to maturity has significant inference for hedging strategies. Interestingly, so far the empirical evidence in favor of the Samuelson Hypothesis (maturity effect) is mixed in various markets. Considering no significant work to examine the relationship is so far carried out in commodity derivative markets of India, this paper ordeal the Samuelson Hypothesis on 8 commodities traded on Multi-Commodity Exchange (MCX), India. We have examined the issue by applying different regression techniques to test the hypothesis for 8 commodities (Aluminium, Nickel, Copper, Gold, Silver, Natural Gas, Crude Oil and Wheat) using inter-day data on MCX India. In order to test the Samuelson’s hypothesis, tests have been conducted using a series of GARCH, EGARCH and TGARCH models by including trading volume, open interest and time-to-maturity in the conditional variance equation. From our results, it is concluded that Samuelson’s hypothesis does not hold true for majority of commodity contracts considered. Our results also find that volatility series depend on the trading volume, compared to the time-to-maturity or open interest. As Samuelson hypothesis does not hold true for majority of commodity contracts, traders in Indian commodity derivative markets should not bias their decisions solely based on the time-to-maturity, but should also consider trading volume and open interest as they are an important determinant of price volatility. They should also consider the possibility of leverage effect while predicting future price volatilities, and the associated margin requirements.     

A four-factor stochastic volatility model of commodity prices

The number of factors driving the uncertain dynamics of commodity prices has been a central consideration in financial literature. While the majority of empirical studies relies on the assumption that up to three factors are sufficient to explain all relevant uncertainty inherent in commodity spot, futures, and option prices, evidence from Trolle and Schwartz (Rev Financ Stud 22(11):4423–4461, 2009b) and Hughen (J Futures Mark 30(2):101–133, 2010) indicates a need for additional risk factors. In this article, we propose a four-factor maximal affine stochastic volatility model that allows for three independent sources of risk in the futures term structure and an additional, potentially unspanned stochastic volatility process. The model principally integrates the insights from Hughen (2010) and Tang (Quant Finance 12(5):781–790, 2012) and nests many well-known models in the literature. It can account for several stylized facts associated with commodity dynamics such as mean reversion to a stochastic level, stochastic volatility in the convenience yield, a time-varying correlation structure, and time-varying risk-premia. In-sample and out-of-sample tests indicate a superior model fit to futures and options data as well as lower hedging errors compared to three-factor benchmark models. The results also indicate that three factors are not sufficient to model the joint dynamics of futures and option prices accurately.     

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.     

Does the stock market drive herd behavior in commodity futures markets?

This paper contributes to the debate on commodity financialization by extending tests of herd behavior to commodity futures markets. Utilizing a regime-switching model, we test the presence of herd behavior in a number of commodity sectors including energy, metals, grains and livestock during the low and high market volatility states. We find significant evidence of herd behavior in grains only during the high volatility state. We also find that large price movements in the energy and metal sectors significantly contribute to herd behavior in the market for grains. Finally, we find no significant effect of the stock market on herd behavior in the commodity futures market. Our findings in general do not support the much debated commodity financialization hypothesis.