Modeling VXX under jump diffusion with stochastic long-term mean

We develop a model for the VXX, the most actively traded VIX futures exchange-traded note, using Duffie, Pan, and Singleton's affine jump diffusion framework, where the volatility process has jumps and a stochastic long-term mean. We calibrate the model parameters using the VIX term structure data and show that our model provides the theoretical link between the VIX, VIX futures, and the VXX. Our model can be used for pricing VIX futures, the VXX and other short-term VIX futures exchange-traded products (ETPs). Our model could be extended to price options on the VXX and other short-term VIX futures ETPs.     

VIX term structure and VIX futures pricing with realized volatility

Using an extended LHARG model proposed by Majewski et al. (2015, J Econ, 187, 521–531), we derive the closed-form pricing formulas for both the Chicago Board Options Exchange VIX term structure and VIX futures with different maturities. Our empirical results suggest that the quarterly and yearly components of lagged realized volatility should be added into the model to capture the long-term volatility dynamics. By using the realized volatility based on high-frequency data, the proposed model provides superior pricing performance compared with the classic Heston–Nandi GARCH model under a variance-dependent pricing kernel, both in-sample and out-of-sample. The improvement is more pronounced during high volatility periods.     

Assessing the asymmetric volatility linkages of energy and agricultural commodity futures during low and high volatility regimes

This study investigated the volatility linkages between energy and agricultural futures, including possible causes for these comovements, such as external macroeconomic and financial shocks during low and high volatility regimes. A combination of Markov-switching regressions and quadrivariate VAR–DCC–GARCH and VAR–BEKK–GARCH modeling revealed that external shocks have an asymmetric effect on the relationship of these assets with higher cross-correlations reported during high volatility regimes. This comovement effect outweighs the substitution effect between energy and agricultural products. Furthermore, the quadrivariate VAR–BEKK–GARCH model provides strong evidence of a bidirectional price volatility spillover between the agricultural and energy markets during periods of high volatility. Overall, the results suggest that energy futures can be effectively used for hedging in a portfolio comprising agricultural futures (and vice versa), while a combination of macroeconomic and financial index futures can serve as an effective hedging tool in investment portfolios comprising both energy and agricultural commodities.     

Maturity effects in the Mexican interest rate futures market

This study investigates the relationship between volatility and contract expiration for the case of Mexican interest rate futures. Specifically, it examines the hypothesis that the volatility of futures prices should increase as contracts approach expiration (the “maturity effect”). Using panel data techniques, the study assesses the differences in volatility patterns between contracts. The results show that although the maturity effect was sometimes present, the inverse effect prevails; volatility decreases as expiration approaches. On the basis of the premises of the negative covariance hypothesis, the study provides additional criteria that explain this behavior in terms of the term structure dynamics. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:371–393, 2011     

Time series volatility of commodity futures prices

This article examines the pattern of volatility over time of a series of commodity futures prices, and focuses in particular on the futures price variability as the maturity date of the futures contract approaches. In a rational expectations model of asymmetric information, the article provides conditions under which the Samuelson hypothesis—that the variability of futures prices increases as maturity approaches—will be true. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 127–144, 2000     

A test of the Samuelson Hypothesis using realized range

This study examines the Samuelson Hypothesis, which postulates that futures price volatility increases as the futures contract approaches its expiration. Investigating intraday data and drawing on the recently developed concept of realized range, this study provides empirical evidence regarding the Samuelson Hypothesis for 14 agricultural, metal, energy, and financial futures markets in six futures exchanges. While utilizing a nonparametric test, a simple linear regression model and a system of seemingly unrelated regressions, the study finds strong support for the Samuelson Hypothesis in agricultural futures. In contrast, no support for the Samuelson Hypothesis is observed in any of the metal and financial futures. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:680–696, 2008     

Volatility and maturity effects in the Nikkei index futures

Many financial data series are found to exhibit stochastic volatility. Some of these time series are constructed from contracts with time-varying maturities. In this paper, we focus on index futures, an important subclass of such time series. We propose a bivariate GARCH model with the maturity effect to describe the joint dynamics of the spot index and the futures-spot basis. The setup makes it possible to examine the Samuelson effect as well as to compare the hedge ratios under scenarios with and without the maturity effect. The Nikkei-225 index and its futures are used in our empirical analysis. Contrary to the Samuelson effect, we find that the volatility of the futures price decreases when the contract is closer to its maturity. We also apply our model to futures hedging, and find that both the optimal hedge ratio and the hedging effectiveness critically depend on both the maturity and GARCH effects. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 895–909, 1999     

Economic uncertainty,trading activity,and commodity futures volatility

This paper investigates the dynamics of commodity futures volatility. I derive the variance decomposition for the futures basis and show unexpected excess returns result from new information about expected future interest rates, convenience yields, and risk premia. Measures of uncertainty in economic conditions have significant predictive power for realized volatility of commodity futures returns, after controlling for lagged volatility, returns, commodity index trading, hedging pressure, and other trading activity, even during the so-called “index financialization” period. During this period, hedge fund performance predicts volatility in grain commodities, which are affected by the US ethanol mandate.     

A dimension-invariant cascade model for VIX futures

We propose a new stochastic volatility model by allowing for a cascading structure of volatility components. The model, under a minor assumption, allows us to add as many components as desired with no additional parameters, effectively defeating the curse of dimensionality often encountered in traditional models. We derive a semi-closed-form solution to the VIX futures price, and find that our six-factor model with only six parameters can closely fit spot VIX and VIX futures prices from 2004 to 2015 and produce out-of-sample pricing errors of magnitudes similar to those of in-sample errors.     

The new market for volatility trading

This study analyses the new market for trading volatility; VIX futures. We first use market data to establish the relationship between VIX futures prices and the index itself. We observe that VIX futures and VIX are highly correlated; the term structure of average VIX futures prices is upward sloping, whereas the term structure of VIX futures volatility is downward sloping. To establish a theoretical relationship between VIX futures and VIX, we model the instantaneous variance using a simple square root mean‐reverting process with a stochastic long‐term mean level. Using daily calibrated long‐term mean and VIX, the model gives good predictions of VIX futures prices under normal market situation. These parameter estimates could be used to price VIX options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:809–833, 2010     

论中国利率市场化进程与利率期货的推出

中国利率市场化的进程正在有步骤地加速推进,利率的市场化必然带来利率波动幅度的加大,如果没有有效的利率风险管理工具作为配套机制,必然会影响利率市场化的顺利进展,也影响到整个金融市场应有作用的发挥.发达国家的经验表明,利率市场化要求利率期货作为利率风险管理的机制予以配合,因此,在推进中国利率市场化的进程中应研究推出利率期货交易的问题.利率期货的最主要承载体是国债期货.根据中国目前利率市场化进展的实际情况,从各类经济实体已经或可能面临的利率风险看,对国债期货的需求日渐强烈.本文的主旨是,在论述中国利率市场化进程中,分析各类经济实体所面临的各种利率风险,以及国债期货对于这一风险管理所起的应有作用,从而得出应当推出国债期货的结论.     

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.     

Derivatives pricing when supply and demand matter: Evidence from the term structure of VIX futures

We decompose the VIX futures term structure into systematic components driving the VIX and idiosyncratic components reflecting demand by various types of futures end-users. We model two distinct channels by which trading activity manifests itself into futures prices: a contemporaneous “level effect” across the term structure due to the aggregate size of nondealer net demand and a mean-reverting “roll effect” due to large trades in specific contracts. The observed futures term structure was, on average, higher and steeper than it would have been in the absence of the observed nondealer demand, but the impact varies in sign and magnitude over time.     

The time-to-maturity pattern of futures price sensitivity to news

This paper examines the effect time-to-maturity has on how sensitive futures prices are to news flows. Unscheduled daily news flows that relate to the underlying asset of a futures contract are related to the daily realized volatility of futures to calculate a price-news sensitivity ratio. The observed pattern follows an inverted U-shape relationship and has a bearing on whether the maturity effect will be noticeable in a futures contract. This paper also shows that by examining the peak-to-maturity of the price sensitivity to news pattern, it is possible to better identify which contracts are more likely to yield higher volatility.     

Estimating the connectedness of commodity futures using a network approach

Using a network approach of variance decompositions, we measure the connectedness of 18 commodity futures and characterize both static and dynamic connectedness. Our results show that metal futures are net transmitters of shocks to other futures, and agricultural futures are vulnerable to shocks from the others. Furthermore, almost two-thirds of the volatility uncertainty for commodity futures are due to the connectedness of shocks across the futures market. Dynamically, we find connectedness always increases in times of turmoil. An analysis of connectedness networks suggests that investors could be forewarned that the connectedness of various classes of futures could threaten their portfolios.     

Market quality and the connectedness of steel rebar and other industrial metal futures in China

We examine the market quality of China's steel rebar futures, along with three other important industrial metal futures. Steel rebar futures are the most active metal futures contracts in China. Our analyses show that while steel rebar and copper futures are comparable in terms of informational efficiency, they are more informationally efficient than iron ore and aluminum futures, with low bid–ask spread, volatility persistence, pricing error variance, and probability of informed trading. We find a bidirectional connection between iron ore and steel rebar futures. Furthermore, we show that these metal futures are weakly related to the Chinese stock market.     

Smiling less at LIFFE

This study investigates the structure of the implied volatility smile, using the prices of equity options traded on the LIFFE. First, the slope of the implied volatility curve is significantly negative for both individual stocks and index options, and the slope is less negative for longer‐term options. The implied volatility skew can be described by risk‐neutral skewness and kurtosis, with the former having the first‐order effect. Moreover, the implied volatility skew for individual stock options is less severe than for index options. Finally, the relationship between the real and risk‐neutral moments implied in option prices is significant. The results indicate that, for equity options traded on the LIFFE, the slope of the implied volatility skew is flatter than that on the Chicago Board of Exchange (CBOE). © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:57–81, 2008     

Return and volatility transmission between China's and international crude oil futures markets: A first look

We examine return and volatility transmission between the newly established crude oil futures in China and international major crude oil futures markets using intraday data. For the first time, we document evidence for cointegration relationships among these oil futures markets. Both China's and Oman's oil futures markets react to deviations from their long-run equilibrium with West Texas Intermediate and Brent oil futures. There is also new evidence for asymmetric volatilities and correlations across these oil futures markets. Furthermore, the Chinese oil futures have stronger linkages with the international major futures markets than Oman futures.     

The untold story of commodity futures in China

We investigate the behavior of commodity futures risk premia in China. In the presence of retail-dominance and barriers-to-entry, the term structure and momentum premia remain persistent, whereas hedging pressure, skewness, volatility, and liquidity premia are distorted by time-varying margins and strict position limits. Furthermore, open interest, currency, and inflation premia are sensitive to institutional settings. The observed premia cannot be attributed to common risks, sentiment, transactions costs, or data-snooping, but are related to liquidity, anchoring, and regulation-induced limits-to-arbitrage. We highlight the distinctive features of Chinese futures markets and assess the challenges posed to theories of commodity risk premia.     

Speculation and volatility—A time-varying approach applied on Chinese commodity futures markets

Experts have long discussed and empirically investigated whether speculative activity increases volatility on commodity futures markets. Little empirical research, however, analyzes the role of speculators on commodity futures markets in China. Using time-varying vector autoregression models with stochastic volatility, this paper investigates for four heavily traded metal and agricultural contracts, how the relationship between returns volatility and speculation evolves over time. Our findings indicate that speculative activity has little to no impact on volatility. On the contrary, for all commodities examined, returns volatility seems to amplify speculation.