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     

Samuelson hypothesis,arbitrage activity,and futures term premiums

The Samuelson hypothesis asserts that futures volatility increases as maturity decreases. On the basis of 10 US commodity futures and by capturing the dynamics of the futures volatility terms structure with three factors, we show that in most markets the slope factor is strongly negative in certain periods and at best only weakly negative in other periods. High inventory levels are found to correspond to flatter volatility term structures in seven futures. This finding is consistent with the linkage between carry arbitrage and the Samuelson hypothesis. We also find that a flatter volatility term structure corresponds to lower absolute futures term premiums.     

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.     

Volume and Volatility Surrounding Quarterly Redesignation of the Lead S&P 500 Futures Contract

During the last weeks before each quarterly expiration of Standard & Poor's (S&P) 500 futures, the bulk of trading volume begins to shift away from the next‐to‐expire (nearby or lead) contract toward the second‐to‐expire (next out) contract. At some point, the exchange formally redesignates the next out as the new lead contract, and the next out replaces the nearby in the futures pit location designated for the lead contract. This event invariably results in a dramatic increase (decrease) in trading activity in the next out (nearby) contract. This shift in relative trading volumes is due to the microstructure of the futures exchange rather than new information or underlying volatility conditions. The event thus offers us an opportunity to examine how volatility responds to noninformation‐based exogenous changes in volume. This study examines the volatility behavior of nearby and next out S&P 500 futures contracts on the 10 days surrounding quarterly redesignation of the lead contract. Our model measures possible changes in (a) the level of volatility and/or (b) the association between volume and volatility after redesignation of the lead contract. Results indicate that when we account for the association between volume and volatility, the higher volume lead contract consistently experiences a lower level of volatility. This outcome supports the view that the larger population of liquidity providers who trade the more active lead contract fosters greater market depth and lower volatility. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1119–1149, 2001     

New evidence on expiration‐day effects using realized volatility: An intraday analysis for the Spanish stock exchange

Additional evidence is provided on expiration effects in the Ibex 35 stock index futures market using realized volatility as proposed by T. G. Andersen, T. Bollerslev, F. X. Diebold, and P. Labys (2003). Findings reveal not only a significant increase in spot trading activity, but also the existence of a significant jump in spot volatility at index futures expiration. Moreover, the importance of the data frequency considered is analyzed. Our research reveals that the use of GARCH methodology from daily data does not have the ability to statistically assess such expiration‐day effect. Additional empirical evidence is provided for the S&P 500 stock index futures market. Neither unconditional nor conditional realized volatility has a significant increase at expiration for the U.S. market, suggesting that this effect is specific for the Spanish market, at least for the period analyzed. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:923–938, 2006     

Approximation for convenience yield in commodity futures pricing

The pricing of commodity futures contracts is important both for professionals and academics. It is often argued that futures prices include a convenience yield, and this article uses a simple trading strategy to approximate the impact of convenience yields. The approximation requires only three variables—underlying asset price volatility, futures contract price volatility, and the futures contract time to maturity. The approximation is tested using spot and futures prices from the London Metals Exchange contracts for copper, lead, and zinc with quarterly observations drawn from a 25‐year period from 1975 to 2000. Matching Euro‐Market interest rates are used to estimate the risk‐free rate. The convenience yield approximation is both statistically and economically important in explaining variation between the futures price and the spot price after adjustment for interest rates. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1005–1017, 2002     

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     

Information and Noise in U.K. Futures Markets

This paper examines the extent to which futures price changes are driven by noise and information for three U.K. futures contracts by utilizing T. Andersen's (1996) specification of the mixture of distributions hypothesis. Use of the generalized method of moments approach demonstrates that the link between futures volume and volatility can be attributed to the flow of information. More importantly, it is shown that price movements are dominated by informed rather than noise trading for the FTSE‐100, the Long Gilt, and the Brent Oil futures contracts. The results suggest that further regulation based on the notion that noise traders dominate futures trading is unwarranted. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:711–731, 2004     

Cash trading and index futures price volatility

This study examines the effect of cash market liquidity on the volatility of stock index futures. Two facets of cash market liquidity are considered: (1) the level of liquidity trading proxied by the expected New York Stock Exchange (NYSE) trading volume and (2) the noise composition of trading proxied by the average NYSE trading commission cost. Under the framework of spline–GARCH with a liquidity component, both the quarterly average commission cost and the quarterly expected NYSE volume are negatively associated with the ex ante daily volatility of S&P 500 and NYSE composite index futures. Conversely, liquidity and noise trading in the cash market both dampen futures price volatility, ceteris paribus. This negative association between secular cash trading liquidity and daily futures price volatility is amplified during times of market crisis. These results retain statistical significance and materiality after controlling for bid–ask bounce of futures prices and volume of traded futures contracts. This study establishes empirical evidence to affirm the conventional prediction of a liquidity–volatility relationship: the liquidity effect is secular and persistent across markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:465–486, 2011     

Examining futures price changes and volatility on the trading day after a limit‐lock day

This paper examines the effect that price limits have on futures prices by testing what happens to price changes and volatility on the trading day following a limit‐lock day. The results show evidence that prices continue to rise on average the day after an up‐limit day. In addition, limits appear to influence price volatility for some but not all of the futures contracts. However, since the findings vary across the different commodity futures contracts, it is likely that limits do not directly impact price volatility. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:445–466, 2000     

Volatility and trading demands in stock index futures

In this study we examine how volatility and the futures risk premium affect trading demands for hedging and speculation in the S&P 500 Stock Index futures contracts. To ascertain if different volatility measures matter in affecting the result, we employ three volatility estimates. Our empirical results show a positive relation between volatility and open interest for both hedgers and speculators, suggesting that an increase in volatility motivates both hedgers and speculators to engage in more trading in futures markets. However, the influence of volatility on futures trading, especially for hedging, is statistically significant only when spot volatility is used. We also find that the demand to trade by speculators is more sensitive to changes in the futures risk premium than is the demand to trade by hedgers. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:399–414, 2003     

Do volatility determinants vary across futures contracts? Insights from a smoothed Bayesian estimator

We apply a new Bayesian approach to multiple‐contract futures data. It allows the volatility of futures prices to depend upon physical inventories and the contract's time to delivery—and it allows those parametric effects to vary over time. We investigate price movements for lumber contracts over a 13‐year period and find a time‐varying negative relationship between lumber inventories and lumber futures price volatility. The Bayesian approach leads to different conclusions regarding the size of the inventory effect than does the standard method of parametric restrictions across contracts. The inventory effect is smaller for the most recent contracts when the inventory levels are larger. In contrast, the Bayesian approach does not lead to substantively different conclusions about the time‐to‐delivery effect than do traditional classical methods. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:257–277, 2010     

Clustering in the futures market: Evidence from S&P 500 futures contracts

We document trade price clustering in the futures markets. We find clustering at prices of x.00 and x.50 for S&P 500 futures contracts. While trade price clustering is evident throughout time to maturity of these contracts, there is a dramatic change when the S&P 500 futures contract is designated a front‐month contract (decrease in clustering) and a back‐month contract (increase in clustering). We find that trade price clustering is a positive function of volatility and a negative function of volume or open interest. In addition, we find a high degree of clustering in the daily opening and closing prices, but a lower degree of clustering in the settlement prices. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:413–428, 2004     

Option‐Expiration Effects in Small Markets: The Spanish Stock Exchange

This study analyzes the effect of the expiration of the Ibex‐35 Index derivatives, as well as the first four stock options traded in the Spanish Equity Derivatives Exchange, on the return, conditional volatility, and trading volume of the underlying assets. The analysis covers the period from the introduction of the various derivatives to December 1995. This period has been divided into two subperiods in order to determine if there are changes in the conclusions. The expiration of the Ibex‐35 index derivatives is associated with an increase in the trading volume of the underlying asset, but it has no significant effect on either the underlying asset prices or on the level of volatility on the expiration day. However, the expiration of the stock options has significant impact on their underlying assets. We observed a downward pressure on prices and a reduction of volatility level in the week before the expiration date and a significant increase in trading volume on the expiration day. The absence of futures contracts on individual stocks, among other possible causes, may explain these differences. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:905–928, 2001     

Efficiency of the IBEX spot–futures basis: The impact of the mini‐futures

This paper considers whether the introduction of the mini‐futures contract for the Spanish Ibex index affects overall market efficiency. Using linear, non‐linear, and fractional integration modeling techniques for the basis term, results of this study suggest the following salient points. First, the equilibrium speed of adjustment is reduced after the introduction of the mini‐futures contract. This effect is particularly pronounced in the mini‐futures second year when its contracts are more heavily traded. Second, fractional integration tests support longer memory in the basis term after the contract introduction, again particularly in the second year. Third, the relationship between the full‐size and mini‐futures contracts appears highly efficient, with a quick speed of adjustment and short memory. Finally, an examination of the volatility dynamics suggests that in the second year of the mini‐futures contract shocks to spot return volatility exhibit longer memory. The results reported here suggest that the increased use of the mini‐futures contract after its introduction has had a detrimental impact on price discovery. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 398–415, 2008     

Mispricing of index futures contracts and short sales constraints

This article examines if changes in short sales constraints affect the extent to which index futures contracts are mispriced. In particular, the study analyzes the mispricing of the Hong Kong Hang Seng Index futures contracts. Tests are conducted over three distinct regulatory regimes relating to the short selling of stocks in Hong Kong. This permits a study of how changes in short selling regulations affect the mispricing of futures contracts. The study indicates that relaxing the constraints on short selling reduces the extent of futures mispricing. Multiple regression analysis is used to test the relationship between the magnitude of mispricing and various economic factors including cash market volatility, time-to-maturity of the contract, trading cost, and dividend payout rates. The study also finds that lifting of the short selling restrictions speeds up market adjustment, especially when a long-hedge (long futures, short stock) signal is detected. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 695–715, 1999     

The pricing of stock index futures spreads at contract expiration

This paper conducts an empirical analysis of the mispricing of calendar spreads for stock index futures. Using recent data drawn from the Sydney Futures Exchange, a sharp increase in the magnitude of spread mispricing immediately prior to maturity of the near contract is documented. This pattern in mispricing is related to a sharp decline in open interest in the near contract and an increase in open interest in the deferred contract. Further, the direction of mispricing of the near and deferred contracts are more likely to move in opposite directions as the near contract approaches maturity. These findings are consistent with the hypothesis that traders seeking to roll‐over their positions from near to deferred futures contracts close to maturity increase the magnitude of spread mispricing. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:451–469, 2002     

Implied volatility forecasts in the grains complex

This article finds that the implied volatilities of corn, soybean, and wheat futures options 4 weeks before option expiration have significant predictive power for the underlying futures contract return volatilities through option expiration from January 1988 through September 1999. These implied volatilities also encompass the information in out‐of‐sample seasonal Glosten, Jagannathan, and Runkle (GJR;1993) volatility forecasts. Evidence also demonstrates that when corn‐implied volatility rises relative to out‐of‐sample seasonal GJR volatility forecasts, implied volatility substantially overpredicts realized volatility. However, simulations of trading rules that involve selling corn option straddles when corn‐implied volatility is high relative to out‐of‐sample GJR volatility forecasts indicate that none of the trading rules would have been significantly profitable. This finding suggests that these options are not necessarily overpriced. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:959–981, 2002     

The economic value of volatility transmission between the stock and bond markets

This study has two main objectives. Firstly, volatility transmission between stocks and bonds in European markets is studied using the two most important financial assets in these fields: the DJ Euro Stoxx 50 index futures contract and the Euro Bund futures contract. Secondly, a trading rule for the major European futures contracts is designed. This rule can be applied to different markets and assets to analyze the economic significance of volatility spillovers observed between them. The results indicate that volatility spillovers take place in both directions and that the stock‐bond trading rule offers very profitable returns after transaction costs. These results have important implications for portfolio management and asset allocation. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1066–1094, 2008     

In search of the convexity adjustment: Evidence from the sterling futures and IMM FRA markets

This study examines daily and intraday data on sterling interest rate futures and IMM forward rate agreement (FRA) contracts for evidence of the convexity adjustment in FRA quotes. The futures/FRA differential is marginally negative, contrary to the predictions of convexity models. Standard statistical tests confirm that the futures/FRA differential does not differ between contract maturities. Regression analysis also fails to find any support for the predicted positive relationships between the differential and the term to settlement and volatility of interest rates. These results suggest that dealers in the sterling FRA market do not price convexity into quotes on FRA contracts. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:617–633, 2008