Futures and futures options with basis risk: theoretical and empirical perspectives

Under a no-arbitrage assumption, the futures price converges to the spot price at the maturity of the futures contract, where the basis equals zero. Assuming that the basis process follows a modified Brownian bridge process with a zero basis at maturity, we derive the closed-form solutions of futures and futures options with the basis risk under the stochastic interest rate. We make a comparison of the Black model under a stochastic interest rate and our model in an empirical test using the daily data of S&P 500 futures call options. The overall mean errors in terms of index points and percentage are ?4.771 and ?27.83%, respectively, for the Black model and 0.757 and 1.30%, respectively, for our model. This evidence supports the occurrence of basis risk in S&P 500 futures call options.     

A Pricing Model for Quantity Contracts

An economic model is proposed for a combined price futures and yield futures market. The innovation of the article is a technique of transforming from quantity and price to a model of two genuine pricing processes. This is required in order to apply modern financial theory. It is demonstrated that the resulting model can be estimated solely from data for a yield futures market and a price futures market. We develop a set of pricing formulas, some of which are partially tested, using price data for area yield options from the Chicago Board of Trade. Compared to a simple application of the standard Black and Scholes model, our approach seems promising.     

Spot and derivative pricing in the EEX power market

Using spot and futures price data from the German EEX Power market, we test the adequacy of various one-factor and two-factor models for electricity spot prices. The models are compared along two different dimensions: (1) We assess their ability to explain the major data characteristics and (2) the forecasting accuracy for expected future spot prices is analyzed. We find that the regime-switching models clearly outperform its competitors in almost all respects. The best results are obtained using a two-regime model with a Gaussian distribution in the spike regime. Furthermore, for short and medium-term periods our results underpin the frequently stated hypothesis that electricity futures quotes are consistently greater than the expected future spot, a situation which is denoted as contango.     

Does Index Speculation Impact Commodity Prices? An Intraday Analysis

Using intraday data, we find unidirectional causality from commodity index‐linked futures to nonindex‐linked commodity futures for up to one hour which disappears when using daily data. Also, the economic significance of index‐linked to nonindex commodity transmission declines to zero within about an hour. Finally, we find that the magnitude of index‐linked to nonindex return transmission is positively related to the amount of speculation, both long and short, in S&P GSCI commodity index futures. We conclude that speculative pressures exerted by commodity index futures can impact nonindex commodities, mainly through the activity of uninformed, positive feedback traders.     

The volatility dynamics of spot and futures gold prices: Evidence from Russia

We examine the long memory property and structural break in the spot and futures gold volatility in Russia from 2008 through 2013. We find strong evidence of long memory in the volatility of both spot and futures gold series. The break dates are associated with the recent global financial crisis. Moreover, we investigate the volatility spillover effect between the Russian spot and futures gold markets using the corrected Dynamic Conditional Correlation model (cDCC). The findings show relatively high level of conditional correlation between spot and futures gold returns. This outcome decreases the portfolio diversification benefits for gold investors.     

Price discovery in spot and futures markets: a reconsideration

We reconsider the issue of price discovery in spot and futures markets. We use a threshold error correction model to allow for arbitrage opportunities to have an impact on the return dynamics. We estimate the model using quote midpoints, and we modify the model to account for time-varying transaction costs. We find that (a) the futures market leads in the process of price discovery and (b) the presence of arbitrage opportunities has a strong impact on the dynamics of the price discovery process.     

Futures volatility forecasting based on big data analytics with incorporating an order imbalance effect

Future markets play vital roles in supporting economic activities in modern society. For example, crude oil and electricity futures markets have heavy effects on a nation’s energy operation management. Thus, volatility forecasting of the futures market is an emerging but increasingly influential field of financial research. In this paper, we adopt big data analytics, called Extreme Gradient Boosting (XGBoost) from computer science, in an attempt to improve the forecasting accuracy of futures volatility and to demonstrate the application of big data analytics in the financial spectrum in terms of volatility forecasting. We further unveil that order imbalance estimation might incorporate abundant information to reflect price jumps and other trading information in the futures market. Including order imbalance information helps our model capture underpinned market rules such as supply and demand, which lightens the information loss during the model formation. Our empirical results suggest that the volatility forecasting accuracy of the XGBoost method considerably beats the GARCH-jump and HAR-jump models in both crude oil futures market and electricity futures market. Our results could also produce plentiful research implications for both policy makers and energy futures market participants.     

Optimal portfolios in commodity futures markets

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.     

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.     

Changing the Size of a Futures Contract: Liquidity and Microstructure Effects

We analyze the relation between contract size and liquidity using data from the respecification of Sydney Future Exchange's (SFE) Share Price Index (SPI) and 90-day Bank Accepted Bill (BAB) futures contracts. Respecification of SPI and BAB contracts presents a unique opportunity to investigate the effects of a change in futures contract size. SFE decreased the size of SPI futures by a factor of four while increasing its minimum tick. The BAB contract was doubled in size with the minimum tick size left unchanged. We find, after controlling for market factors, that the respecification of the SPI futures resulted in higher trading volume, while that of BAB futures decreased trading volume. The results regarding spreads are ambiguous. Based on two cases investigated, we conclude that decreasing the futures contract size was effective in terms of enhancing liquidity while increasing the size resulted in a reduction in liquidity.     

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.     

Price discovery and volatility spillovers in the European Union emissions trading scheme: A high-frequency analysis

This paper models the relationship of European Union Allowance spot- and futures-prices within the second commitment period of the European Union emissions trading scheme. Based on high-frequency data, we analyze the transmission of information in first and second conditional moments. To reveal long-run price discovery, we compute common factor weights of Schwarz and Szakmary (1994) and information shares of Hasbrouck (1995) based on estimated coefficients of a VECM. To analyze the short-run dynamics, we perform Granger-causality tests. We identify the futures market to be the leader of the long-run price discovery process, whereas the informational role of the futures market increases over time. In addition, we employ a version of the UECCC-GARCH model as introduced by Conrad and Karanasos (2010) to analyze the volatility transmission structure. The volatility analysis indicates a close relationship between the volatility dynamics of both markets, whereas in particular we observe spillovers from the futures to the spot market. As a whole the investigation reveals that the futures market incorporates information first and then transfers the information to the spot market.     

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.     

Jump-Dependent Model for Optimal Index Futures Hedging in Five Major Asian Stock Markets

This article develops a jump-dependent model to capture the dependences between spot and futures returns and their jumps simultaneously, named JD model. We examine hedging performance of the presenting JD model for the futures contracts of Hong Kong, Japan, Korea, Singapore, and Taiwan. The results have shown that the JD model has better out-of-sample performance than the OLS for Korea, Singapore, and Taiwan. Since these three markets have higher jump dependence between spot and futures, we consider that jump dependence plays an important role in hedging performance. The higher jump dependence means spot and futures markets move more closely when unusual news reveals itself and thus futures could hedge the spot more effectively when extreme unusual news arrives.     

What role do futures markets play in Bitcoin pricing? Causality,cointegration and price discovery from a time-varying perspective?

Recent papers that have explored spot and futures markets for Bitcoin have concluded that price discovery takes place either in the spot, or the futures market. Here, we consider the robustness of previous price discovery conclusions by investigating causal relationships, cointegration and price discovery between spot and futures markets for Bitcoin, using appropriate daily data and time-varying mechanisms. We apply the time-varying Granger causality test of Shi, Phillips, and Hurn [2018]; time-varying cointegration tests of Park and Hahn [1999], and time-varying information share methodologies, concluding that futures prices Granger cause spot prices and that futures prices dominate the price discovery process.     

沪深300股指期货VaR-GARCH模型风险管理研究——基于恒指期货的比较视角

股指期货是以股票指数作为标的的金融衍生产品,其在金融风险管理中具有重要作用,同时自身也面临较大的风险。VaR—GARCH模型能够较好地模拟金融市场时间序列数据,并作出相应的估计值,是当前主流的风险管理方法。本文基于香港恒指期货的比较视角,对我国去年推出的沪深300股指期货交易进行VaR—GARCH模型实证分析,得出VaR—GARCH模型能够较好地管理沪深300股指期货的风险的结论,并建议加强VaR技术的运用和加强跨市监管,更好地管理股指期货的风险。     

Mean-variance hedging with oil futures

We analyze mean-variance-optimal dynamic hedging strategies in oil futures for oil producers and consumers. In a model for the oil spot and futures market with Gaussian convenience yield curves and a stochastic market price of risk, we find analytical solutions for the optimal trading strategies. An implementation of our strategies in an out-of-sample test on market data shows that the hedging strategies improve long-term return-risk profiles of both the producer and the consumer.     

A two-factor cointegrated commodity price model with an application to spread option pricing

In this paper, we propose an easy-to-use yet comprehensive model for a system of cointegrated commodity prices. While retaining the exponential affine structure of previous approaches, our model allows for an arbitrary number of cointegration relationships. We show that the cointegration component allows capturing well-known features of commodity prices, i.e., upward sloping (contango) and downward sloping (backwardation) term-structures, smaller volatilities for longer maturities and an upward sloping correlation term structure. The model is calibrated to futures price data of ten commodities. The results provide compelling evidence of cointegration in the data. Implications for the prices of futures and options written on common commodity spreads (e.g., spark spread and crack spread) are thoroughly investigated.     

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.     

Commodity financialization and sector ETFs: Evidence from crude oil futures

We investigate the diversification benefits of energy assets in the setting of commodity financialization using data on crude oil futures and Sector ETFs (SPDRs). Correlations between commodities and financial assets increased during the post-Commodity Futures Modernization Act (CFMA)/commodity bull cycle period, resulting in lower benefits of diversification. However, we find that conditional correlations between crude oil futures and sector ETFs meaningfully increased only since the 2008–09 financial crisis. The results therefore suggest that the financial crisis, rather than CFMA regulation, explains changes in the diversification benefits of commodities. Moreover, we find that oil futures returns are less correlated with SPDRs than with the S&P index. Thus, energy futures, and crude oil in particular, offer the potential for diversification benefits in sector-style investing.