Price dynamics in refined petroleum spot and futures markets

This article characterizes the spot and futures price dynamics of two important physical commodities, gasoline and heating oil. Using a non-linear error correction model with time-varying volatility, we demonstrate many new results. Specifically, the convergence of spot and futures prices is asymmetric, non-linear, and volatility inducing. Moreover, spreads between spot and futures prices explain virtually all spot return volatility innovations for these two commodities, and spot returns are more volatile when spot prices exceed futures prices than when the reverse is true. Furthermore, there are volatility spillovers from futures to spot markets (but not the reverse), futures volatility shocks are more persistent than spot volatility shocks, and the convergence of spot and futures prices is asymmetric and non-linear. These results have important implications. In particular, since the theory of storage implies that spreasd vary with fundamental supply and demand factors, the strong relation between spreads and volatility suggests that these fundamentals — rather than trading induced noise — are the primary determinants of spot price volatility. The volatility spillovers, differences in volatility persistence, and lead-lag relations are consistent with the view that the futures market is the primary locus of informed trading in refined petroleum product markets. Finally, our finding that error correction processes may be non-linear, asymmetric, and volatility inducing suggests that traditional approaches to the study of time series dynamics of variables that follow a common stochastic trend that ignore these complexities may be mis-specified.     

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.     

Initial margin policy and stochastic volatility in the crude oil futures market

This article examines the relationship between the volatilityof the crude oil futures market and changes in initial marginrequirements. To closely match changes in futures market volatilitywith the corresponding changes in margin requirements, we inferthe volatility of the futures market from the prices of crudeoil futures options contracts. Using a mean-reverting diffusionprocess for volatility, we show that changes in margin policydo not affect subsequent market volatility.     

Determinants of the crude oil futures curve: Inventory,consumption and volatility

Since 2008, the WTI oil futures curve has been positively sloped for extended periods. We test whether changes in inventory alone can explain this atypically long contango. To do this, we estimate monthly VARs of the CME WTI oil futures spread and OECD and U.S. inventory in line with standard theory, and add petroleum consumption and implied volatility to the vector of endogenous variables. When we model the futures spread as one continuous series, results confirm two-way causation between inventory and the futures curve, as predicted by the theory of storage. However when we separate negative and positive futures spreads we find that: two-way causation between the futures spread and U.S. inventory breaks down; shocks to OECD petroleum consumption cause more negative spreads and shocks to U.S. consumption cause more positive spreads in addition to inventory-driven changes; and increases in volatility directly raise positive spreads. These new causal channels have become significant since 2008 and can be related to higher inventory, inelastic supply of oil and uncertainty about global economic conditions.     

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.     

基本有色金属期货市场价格波动实证分析

依据铜、铝和锌三种典型性基本有色金属在金融危机前后的期货价格波动数据,运用分解-合成框架和时变TVP-VAR分析模型,考量影响基本有色金属期货价格波动重大事件和长期趋势价格波动的因素及价格时变特征。结果发现：铜、铝和锌三种基本有色金属期货的价格走势基本一致,且与中国宏观经济密切相关,其价格的最低点都出现在金融危机期间,而价格的最高点基本都出现在经济繁荣期;基本有色金属价格存在同涨同跌关系,而且涨跌幅基本趋势相一致。鉴此,可以对具有周期变化特征的基本有色金属价格走势进行预测,并规避价格波动的风险。     

Oil Price Uncertainty

The theories of investment under uncertainty and real options predict that uncertainty about, for example, oil prices will tend to depress current investment. We reinvestigate the relationship between the price of oil and investment, focusing on the role of uncertainty about oil prices. We find that volatility in oil prices has had a negative and statistically significant effect on several measures of investment, durables consumption, and aggregate output. We also find that accounting for the effects of oil price volatility tends to exacerbate the negative dynamic response of economic activity to a negative oil price shock, while dampening the response to a positive oil price shock.     

Equilibrium Forward Curves for Commodities

We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option's value changes over time due to both endogenous inventory and exogenous transitory shocks to supply and demand. Our model makes predictions about volatilities of forward prices at different horizons and shows how conditional violations of the 'Samuelson effect' occur. We extend the model to incorporate a permanent second factor and calibrate the model to crude oil futures data.     

Dynamic volatility spillovers across oil and natural gas futures markets based on a time-varying spillover method

This paper analyzes dynamic volatility spillovers between four major energy commodities (i.e., crude oil, gasoline, heating oil and natural gas) in the oil-natural gas future markets. We construct a time-varying spillover method by combining the TVP-VAR-SV model and the spillover method of Diebold and Yilmaz (2009, 2012, 2014). We use the spillover method to obtain time-varying total, directional and pairwise volatility spillover indices. Our results summarize as follows: (1) The volatility spillover indices present peaks and troughs during some periods, such as shale gas revolution, financial crisis, and oil price crash; (2) After the U.S. shale gas revolution, the size of volatility spillover from natural gas future market has reduced sharply, but volatility doesn't decouple from the other three oil future markets; (3) The directional spillover is asymmetric. The crude oil and heating oil futures market are main net transmitter of volatility risk information, while the gasoline and natural gas futures markets are the net receiver; (4) For natural gas future market, the pairwise volatility spillover from crude oil future market has the most significant influence.     

What is going on in the oil market?

Conclusion In this article, we propose a consistent view on the recent oil-price history based on fundamental data and economic theory. We sum up: After the turn of the century three major stylized shocks have hit market. First, the demand curve has shifted fight outwards, mainly driven, as extensively reported in the media, by sustained growth in China and other Asian Countries. Second, supply disruptions in countries with low extraction costs (Iraq and Venezuela) have shifted the supply curve to the left. Third, we show that speculators adjust their inventories in order to take advantage of predictable price fluctuations and play themselves a major role in the price formation. Optimal storage theory implies that aggregate inventories are negatively related to the oil price and positively to the volatility of supply and demand shocks. We provide evidence that the political events in the last years have increased volatility and induced the inventory curve to shift right outwards. We analyze in a graphical framework the interaction of all these shocks and conclude that speculators have caused the oil price to overshoot in the short run its long-run fundamental value. However, this is not at all attributable to market failure or the harmfulness of speculators. In fact, the opposite is true. Speculators have in general a dampening effect on the oil price. The record oil price in the very recent history is partly a consequence of speculators maintaining or building-up inventories to cope with the supply and demand shocks to come. Hence, high prices represent a short-term toll for future price stability. It follows from our analysis that the oil price is expected to fall towards its long-term mean, provided that no further shocks hit the economy and, critically, the oil supply. As we saw, this prediction is consistent with the observed prices in the futures markets. Also in terms of future price volatility, the outlook is rather upbeat. The increased inventory levels held by speculators will cushion the spot market against fluctuations in natural supply and demand and limit the degree to which the currently high underlying volatility will translate into higher price volatility. We would like to thank Manuel Ammann, Bernd Brommundt, Stephan Kessler, Ralf Seiz, Michael Verhofen, Hemrich von Wyss, and two anonymous referees for helpful comments We are particularly indebted to Sergej Peisotchenko at United Energy System (UES) of Russia and Jan Gjerde at Shell for clearing us up on technical aspects of oil production     

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.     

Volatility spillovers and hedging effectiveness between the oil market and Eurozone sectors: A tale of two crises

This paper aims to analyze the mean and volatility spillovers between oil prices and the Eurozone supersector returns. It uses daily data of the Brent prices and 19 Eurozone supersector indices for the period from August 2004 to August 2015. This area experienced two important instabilities in that period, the global financial crisis (GFC) and the Euro debt crisis (EDC). Because financial turbulences are suspected to induce changes in the volatility dynamics, the full sample is divided into three sub-samples. Empirically, this study employs a bivariate VAR-BEKK-GARCH model that allows for transmission in volatility. The obtained volatilities and covariances are used to compute the optimal weights and hedge ratios for oil–stock portfolio holdings. The findings show that both mean and volatility spillovers between the oil market and the different Eurozone sectors are time-varying and heterogeneous. In the GFC sub-period, there is evidence of contagion effects because there is an intensification of volatility spillovers. The EDC does not seem to have induced any particular change in the spillover effects. The optimal weights, hedge ratios, and correlation analysis results allow an accurate understanding of the time series relationship between the two markets and are useful for financial market participants and policymakers.     

On the seasonality in the implied volatility of electricity options

Seasonality is an important topic in electricity markets, as both supply and demand are dependent on the time of the year. Clearly, the level of prices shows a seasonal behaviour, but not only this. Also, the price fluctuations are typically seasonal. In this paper, we study empirically the implied volatility of options on electricity futures, investigate whether seasonality is present and we aim at quantifying its structure. Although typically futures prices can be well described through multi-factor models including exponentially decreasing components, we do not find evidence of exponential behaviour in our data set. Generally, a simple linear shape reflects the squared volatilities very well as a curve depending on the time to maturity. Moreover, we find that the level of volatility exhibits clear seasonal patterns that depend on the delivery month of the futures. Furthermore, in an out-of-sample analysis we compare the performance of several implementations of seasonality in the one-factor framework.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

基于波动效应与价格发现的期指仿真交易研究

沪深300股指期货仿真交易的推出,对我国现货市场的影响如何以及这种影响是否有利于现货效率的改进。首次采用修正的GARCH模型和向量误差修正模型（VEC）将股指期货推出后现货市场波动性的变化和股指期货与现货市场的价格发现功能结合起来进行对比研究。结果表明,期指仿真交易的推出对于现货市场效率的改进确实存在正面的影响。其引入在短期内加大了现货市场的波动,但这一波动正是市场信息流动加速的反映,因而提高了市场信息的传递效率。同时期货价格领先于现货价格,存在由期货市场到现货市场长期的单向因果关系,说明期货价格具有引导现货价格向均衡方向调整的功能,从而在经验上支持了股指期货市场的开放政策。     

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.     

Higher-order moment risk connectedness and optimal investment strategies between international oil and commodity futures markets: Insights from the COVID-19 pandemic and Russia-Ukraine conflict

This paper investigates the higher-order moment risk connectedness between West Texas Intermediate (WTI) oil futures, Brent oil futures, Chinese oil futures and commodity futures (agricultural, industrial metals, and precious metals) before and during the COVID-19 pandemic and following the outbreak of the Russia-Ukraine conflict, by combining ex-post moment measures and the novel time-varying parameter (TVP)-vector auto-regression (VAR)-based connectedness approach. Further, this paper depicts the dynamic overall and pairwise correlations between oil and commodity futures and constructs the hedging and optimal-weighted portfolio strategies using the DCC-GARCH t-Copula model. This paper also constructs the multivariate oil-commodity portfolio based on the newly proposed minimum connectedness portfolio approach and takes into account the higher-order moment risk connectedness. The empirical results demonstrate that the dynamic linkages between international oil and commodity futures are positive, time-varying, and have been greatly intensified by the outbreak of the 2018 China-US trade war, the 2020 COVID-19 pandemic, and the 2022 Russia-Ukraine conflict. The risk connectedness results are moment-dependent. The averaged total skewness and kurtosis spillovers are lower than the return and volatility connectedness. Brent (WTI) oil is the largest net transmitter of the return and volatility (skewness and kurtosis) risk spillovers. The dynamic total, net, and net-pairwise spillovers are all time-varying and highly reactive to major crises, especially the COVID-19 pandemic and the Russia-Ukraine conflict. Furthermore, the optimal-weighted portfolio shows a higher risk reduction than the hedging strategy. Finally, the minimum skewness connectedness portfolio shows relatively higher hedging effectiveness, while the minimum kurtosis connectedness portfolio offers the highest cumulative returns.     

INTRADAY MARKET BEHAVIOR AND THE EXTENT OF FEEDBACK BETWEEN S&P 500 FUTURES PRICES AND THE S&P 500 INDEX

In this study we empirically examine the intraday lead/lag relation between S&P 500 futures prices and the S&P 500 index, and whether daily market characteristics are associated with changes in the relation. We estimate daily Geweke measures of feedback and regress time series of these measures on daily price volatility and volume characteristics. Results indicate that the contemporaneous price relation is substantive and that measures of contemporaneous feedback are positively associated with the daily range of the futures price. The primary implication is that the relation between cash and futures prices becomes stronger as futures price volatility increases. As volatility increases, information is being impounded at a faster rate so that futures and equity markets operate more closely as one market. Large futures price moves, by themselves, are not responsible for breakdowns in the stock-futures price relation.     

Backwardation in Oil Futures Markets: Theory and Empirical Evidence

Oil futures prices are often below spot prices. This phenomenon, known as strong backwardation, is inconsistent with Hotelling's theory under certainty that the net price of an exhaustible resource rises over time at the rate of interest. We introduce uncertainty and characterize oil wells as call options. We show that (1) production occurs only if discounted futures are below spot prices, (2) production is non-increasing in the riskiness of future prices, and (3) strong backwardation emerges if the riskiness of future prices is sufficiently high. The empirical analysis indicates that U.S. oil production is inversely related and backwardation is directly related to implied volatility.     

基于Copula函数的国际原油价格与股票市场收益的相关性研究

针对国际原油价格与金砖五国股票市场收益之间的相关性问题,使用 AR(p)-GARCH(1,1)-Copula 模型进行检验。运用广义误差分布(GED)获取收益残差序列,对 WTI 原油价格和金砖五国股市收益之间的相关性进行实证分析。研究结果表明,国际原油价格与中国股市收益呈现微弱的相关关系,而与其他四国股市收益的相关关系较为明显。用时变 SJC Copula 模型刻画国际原油价格与金砖五国股票市场收益的相关性最为合适。