Term Structure Of Futures Research Articles

Food-fuel nexus beyond mean-variance: New evidence from a quantile approach

This paper investigates the dynamic relationship between crude oil, ethanol, and corn markets across various quantiles of return distributions, as well as at higher statistical moments. Using a quantile vector autoregression model and data from 2007 to 2022, we find that the cross-market linkages are quantile dependent, with the strongest connections observed in the tails of the distribution. A shock to the oil market significantly impacts ethanol and corn returns under extreme bearish and bullish conditions. Positive shocks to the corn market reduce ethanol returns when the ethanol market is highly bullish, but this effect becomes positive in the left tail of the distribution. We also identify significant co-movement in higher statistical moments between these markets. Extreme excess kurtosis in the food-fuel nexus is more likely to occur with high financial market uncertainty, a bullish stock market, contracting industrial production, and a strong US dollar. In addition to these variables, credit spreads, futures market liquidity, futures term structure, and hedging pressure also influence kurtosis in individual markets within the nexus.

Demand Risks and Term Structure of Volatility Index Futures

In this paper, we develop an equilibrium framework to explain the characteristics of volatility index (VIX) futures prices and returns across maturities. In the framework, the investors prefer VIX futures with specific maturities, and the arbitrageurs optimize portfolios based on mean-variance preferences. The model-implied futures prices are affected by the variance and demand risk factors. Theoretical and empirical analyses show that incorporating jump risks helps to explain the higher-order moments of futures and that including the demand factor improves futures pricing performance.

Functional Oil Price Expectations Shocks and Inflation

ABSTRACTThis paper investigates the inflation effects of oil price expectations shocks constructed as functional shocks, that is, as shifts in the entire oil futures term structure (both standard and risk‐adjusted). The latter are then included in a vector autoregressive model with exogenous variables (VARX) to examine the US case. Counterfactual analysis is also carried out to investigate second‐round effects on inflation through the inflation expectations channel. These are found to be significant, in contrast to earlier studies based on standard oil price shocks. Additional nonlinear local projections including a shock decomposition exercise show that inflation and inflation expectations are primarily driven by changes in the curvature (level and slope) factor when the latter are anchored (unanchored). These findings provide useful information to policymakers concerning the impact of oil price expectations on inflation and inflation expectations.

Relations among Bitcoin Futures, Bitcoin Spot, Investor Attention, and Sentiment

This research investigates the function of price discovery between the Bitcoin futures and the spot markets while also analyzing the impact of investor sentiment and attention on these markets. This study utilizes various statistical models to examine the short-term and long-term relations between these variables, including the bivariate Granger causality model, the ARDL and NARDL models, and the Johansen cointegration procedure with a vector error correction mechanism. The results suggest that there is no statistical evidence of price discovery between the Bitcoin spot price and futures, and the term structure of the Bitcoin futures neither enriches nor impairs this lead lag relation. However, the study finds robust evidence of a long-run cointegrating relation between the two markets and the presence of asymmetry in them. Moreover, this research indicates that investor sentiment exhibits a lead lag relation with both the Bitcoin futures and the spot markets, while investor attention only leads to the Bitcoin spot market, without showing any lead lag relation with the Bitcoin futures. These findings highlight the crucial role of investor behavior in affecting both Bitcoin futures and spot prices.

A general framework for a joint calibration of VIX and VXX options

We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in commodity smile modelling, we present a multi-factor stochastic-local volatility model that is able to jointly calibrate plain-vanilla options both on VIX futures and VXX notes, thus going beyond the failure of purely stochastic or simply local-volatility models. We discuss numerical results on real market data by highlighting the impact of model parameters on implied volatilities.

Breaks in term structures: Evidence from the oil futures markets

AbstractWe propose a new functional change point detection procedure, motivated by recent models for commodity futures term structure. We investigate our procedure's properties under the null hypothesis of no change and the alternative. Monte Carlo simulations reveal a reasonable power property in finite sample sizes although size distortion persists. An empirical analysis of oil futures markets identifies two change points near the 2008 financial crisis and 2020 crude oil negative territory. Regression models show that the price behaviour, in general, is exposed to the spot market index and exchange rate from 2007 to 2009. The main drivers of the price term structure are attributed to the trading activities of speculators and financial index innovations between 2017 and 2022.

The relative pricing of WTI and Brent crude oil futures: Expectations or risk premia?

This paper studies the spread of Brent-WTI futures prices using a no-arbitrage term structure model with one common and two latent idiosyncratic risk factors. We document more negative risk premia for WTI than for Brent, and the differences are more pronounced at longer maturities. The expectation of future spot price dominates the risk premium in determining the term structure of Brent-WTI futures spread, especially at short maturities. The common risk premia in both markets are negative and similar, while their corresponding idiosyncratic risk premia have opposite signs. The common risk prices of WTI and Brent are generally related to the US crude commercial stock, inflation, economic uncertainty, and hedging pressure; however, idiosyncratic risk prices are more related to their corresponding local production, short rate, and the term structure factors. The variance decomposition indicates that the idiosyncratic factors account for a considerable part at longer forecast horizons in both markets.

On the Term Structure of VIX Futures’ Implied Convexity

Before the global equity crash in October 1987, volatility could be reasonably approximated as a constant, consistent with Black-Scholes (1973) dynamics. Thereafter, a stylized feature of equity options markets is that both single-name and index options have exhibited consistent, regular deviations of volatility in both strike and maturity. The resulting volatility surface has been studied extensively (Rubinstein 1994, Jackwerth and Rubinstein 1996, Derman 1999, Cont and da Fonseca 2002, Gatheral 2006). Moreover, reduced-form representations of major equity indices’ volatility surfaces corresponding to “average” volatility (over strikes) accumulated through fixed maturities, for example, Cboe’s (formerly Chicago Board Options Exchange) Volatility Index (VIX), have been popularized as gauges of investor sentiment and risk-aversion. Likewise, there has been considerable interest in quantifying and interpreting the term structure of futures whose payoffs are tied to these indices (Zhu and Zhang 2007; Lu and Zhu 2009; Egloff et al. 2010). In the context of the risk-neutral distribution characterizing asset prices at contract maturity, these studies focus on futures’ expectations—their first moments; higher-order moments are less well-studied. Daigler et al. (2016) introduce <i>implied convexity</i> as a measure of variance, that is, the second moment. However, although many authors have studied the term structure of VIX futures’ expectations, to our knowledge, none has examined the term structure of their variances.This work extends the research of Daigler et al. in two important ways. First, it provides an alternative to their intermediate adjustments of the VIX near-term (VIN) and VIX far-term (VIF) component indices that is consistent with the assumptions underlying the calculation of all Cboe volatility indices. It is likewise consistent with volatility indices in foreign markets, for example, the Euro STOXX 50 Volatility (VSTOXX) index (Deutsche Börse Group 2022). Second, it characterizes the entire term structure of VIX futures’ second moments, rather than that of a single contract with a maturity of approximately one month. Additionally, we quantify the differences arising from various interpolation choices. We find that extrapolation based only on two maturities near thirty calendar days produces estimates of variance that differ considerably from interpolations based on all available expiries. Furthermore, the accuracy of extrapolation degrades as the absolute differences between a contract’s maturity and the maturities of the interpolants increase.

Consistent time‐homogeneous modeling of SPX and VIX derivatives

AbstractThis paper shows how to recover a stochastic volatility model (SVM) from a market model of the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore are better suited for pricing VIX futures and VIX derivatives. But the VIX itself is a derivative of the S&amp;P500 (SPX) and it is common practice to price SPX derivatives using an SVM. Therefore, consistent modeling for both SPX and VIX should involve an SVM that can be obtained by inverting the market model. This paper's main result is a method for the recovery of a stochastic volatility function by solving an inverse problem where the input is the VIX function given by a market model. Analysis will show conditions necessary for there to be a unique solution to this inverse problem. The models are consistent if the recovered volatility function is non‐negative. Examples are presented to illustrate the theory, to highlight the issue of negativity in solutions, and to show the potential for inconsistency in non‐Markov settings.

The information in global interest rate futures contracts

AbstractWe investigate information contained in the term structure of interest rate futures contracts in the United States, Eurozone, UK, and Switzerland. We find that current forward‐spot differentials often predict return premiums and, especially, future spot rates. This predictability follows time‐series patterns common to all four markets, except around crises. Macroeconomic indicators are important determinants of predictability within and between markets. One common factor captures a significant portion of variation in predictability. No single market has a dominant share of macroeconomic indicators linked with the common predictability factor. Inflation and exchange rates arise as the most important determinants of the common factor.

Correction to: Risk premia in the term structure of crude oil futures: long‑run and short‑run volatility components

Correction to: Risk premia in the term structure of crude oil futures: long‑run and short‑run volatility components

Risk premia in the term structure of crude oil futures: long-run and short-run volatility components

Risk premia in the term structure of crude oil futures: long-run and short-run volatility components

Dynamics in the VIX complex

AbstractThis paper provides a characterization of the dynamic interactions in the Volatility Index (VIX) complex, composed of the VIX itself, the term structure of VIX futures, and VIX exchange‐traded products (ETPs). I investigate a model that summarizes the VIX futures term structure using latent factors (level, slope, and curvature) and expand it with the VIX and VIX futures demand stemming from VIX ETPs. I find evidence of VIX ETPs impacting the VIX futures term structure, but no evidence of any impacts on the VIX.

The Term Structure of Currency Futures' Risk Premia

AbstractThe use of futures instead of forwards exchange contracts completes the maturity spectrum of the correlation between spot yields and the premium. We find that the forward premium puzzle appears to be a precrisis phenomenon and is only observed for maturities longer than about 1 month. Differences in the exposure to risk help to explain cross‐sectional spreads in currency excess returns. However, this only applies for medium and longer maturities. Considering that most studies that test the validity of a risk‐based approach to currency excess returns focus on short maturity securities, this explains why this approach is so often rejected.

Forecasting WTI crude oil futures returns: Does the term structure help?

Nelson-Siegel (NS) factors extracted from the term structure of WTI oil futures are shown to predict subsequent WTI holding period returns in-sample. This in-sample predictability is not diminished by augmenting with macroeconomic indicators or oil market specific predictors. Allowing the decay factor in the Nelson-Siegel model to vary over time improves in-sample predictions at medium horizon return forecasts. We conduct out-of-sample forecasting exercises on models that use NS factors, such as a simple two factor model that uses a composite leading indicator along with the NS decay factor, and a LASSO model that combines NS factors with macroeconomic indicators and oil market specific predictors. These models significantly reduce forecast errors relative to a no change benchmark across a range of return horizons and futures contract maturities. We also find consistent evidence that models that use the NS factors result in trading strategies with higher Sharpe ratios and better skewness properties than buy and hold strategies and historical mean strategies.

Trading Signals in VIX Futures

ABSTRACT We propose a new approach for trading VIX futures. We assume that the term structure of VIX futures follows a Markov model. Our trading strategy selects a position in VIX futures by maximizing the expected utility for a day-ahead horizon given the current shape and level of the term structure. Computationally, we model the functional dependence between the VIX futures curve, the VIX futures positions, and the expected utility as a deep neural network with five hidden layers. Out-of-sample backtests of the VIX futures trading strategy suggest that this approach gives rise to reasonable portfolio performance, and to positions in which the investor will be either long or short VIX futures contracts depending on the market environment.

Price volatilities of bitcoin futures

In this study, we first investigate the volatility term structure of the Bitcoin futures prices and observe that the price volatilities of Bitcoin futures contracts decrease as the delivery date nears, which is opposite to the Samuelson effect frequently observed in the commodity market. Then, we modify the stochastic multifactor model in Schwartz and Smith (2000) and fit it to the Bitcoin futures prices data. The results show that the standard stochastic multifactor model performs well in explaining the fluctuations of Bitcoin futures prices and generates an upward volatility term structure of the Bitcoin futures contracts prices. Nevertheless, some of the parameter's estimations exhibit non-negligible differences compared with those based on other commodity futures prices data in the existing literature, which indicates that the Bitcoin futures market might be different from the standard commodity futures market.

Dynamics in the VIX Complex

This paper provides a characterization of the dynamic interactions in the VIX complex, composed of the VIX itself, the term structure of VIX futures, and VIX ETPs. I investigate a model that summarizes the VIX futures term structure using latent factors (level, slope, and curvature) and expand it with the VIX and VIX futures demand stemming from VIX ETPs. I find evidence of VIX ETPs impacting the VIX futures term structure, but no evidence of any impacts on the VIX.

Interpolating commodity futures prices with Kriging

The shape of the futures term structure is essential to commodity hedgers and speculators as futures prices serve as a forecast of future spot prices. Commodity markets quotes futures prices on a selection of maturities and delivery periods. In this note we investigate a Bayesian technique known as Kriging to build a term structure of futures prices by embedding trends and seasonalities and by ensuring no-arbitrage conditions between different delivery periods.

Quadratic Hedging of Futures Term Structure Risk in Merchant Energy Trading Operations

Quadratic Hedging of Futures Term Structure Risk in Merchant Energy Trading Operations