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     

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     

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     

Realized volatility and correlation in energy futures markets

Using high‐frequency returns, realized volatility and correlation of the NYMEX light, sweet crude oil, and Henry‐Hub natural gas futures contracts are examined. The unconditional distributions of daily returns and daily realized variances are non‐Gaussian, whereas the distributions of the standardized returns (normalized by the realized standard deviation) and the (logarithms of) realized standard deviations appear approximately Gaussian. The (logarithms of) standard deviations exhibit long‐memory, but the realized correlation between the two futures does not, implying rather weak inter‐market linkage in the long run. There is evidence of asymmetric volatility for natural gas but not for crude oil futures. Finally, realized crude oil futures volatility responds with an increase in the weeks immediately before the OPEC events recommending price increases. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:993–1011, 2008     

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     

An analysis of the failed municipal bond and note futures contracts

This study analyzes the failure of the municipal bond and municipal note futures contracts. The municipal bond contract is shown to have been the most effective hedge in the municipal market over its tenure. Changes in volume in the municipal bond contract were closely related to changes in the volume in the U.S. Treasury bond futures contract, the spot–municipal‐over‐bonds (MOB) ratio, and visible supply. The failure of the municipal bond contract is mainly attributed to a decrease in trading volume in the U.S. Treasury futures market. This was impacted by the onset of electronic trading, which the municipal futures market was reluctant to embrace. The municipal note contract was a less effective hedge than U.S. Treasury note futures and ten‐year London Interbank Offered Rate swaps. The failure of the municipal note futures contract is attributed to the existence of well‐established alternative hedges, and segmentation in the municipal market. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:656–679, 2008     

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     

Long memory in commodity futures volatility: A wavelet perspective

The authors reexamine the volatility of agricultural commodity futures for evidence of fractional integration, providing new empirical results and extending the extant literature in important dimensions. First, they utilize two relatively new estimators based on wavelets, which are generally superior to, for example, the popular estimator by J. Geweke and S. Porter‐Hudak (GPH; 1983) and exact maximum likelihood estimators (MLEs) on the basis of mean squared error (MSE). Second, they provide simulations to contrast their point estimates with those obtained by a fractionally integrated GARCH (generalized autoregressive conditional heteroscedasticity) model. Third, they conduct a wavelet coef.cient decomposition of futures volatility. They .nd that futures volatilities display the self‐similarity property consistent with long memory and that futures volatilities exhibit persistent long memory with .nite unconditional variance. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:411–437, 2007     

Intraday volatility in the bond,foreign exchange,and stock index futures markets

Intraday volatility for the Eurodollar, the Euro/dollar foreign exchange rate, and the E‐mini S&P 500 futures contracts traded on a continuous 23‐hour schedule on the Chicago Mercantile Exchange Globex electronic platform is studied. Volatility transmission in a single market across different regions is mainly explained by intraregion volatility (heat waves); interregion volatility (meteor showers) plays a secondary role. The joint impact of liquidity variables such as volume and open interest on volatility is also analyzed. Volume tends to increase volatility, but open interest does not affect it. The results are explained by the type of trading venue. Unlike floor‐based trading systems, in electronic markets open interest does not seem to provide additional information on market liquidity and its relation to volatility beyond any information contributed by volume. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:313– 334, 2008     

Is it time to reduce the minimum tick sizes of the E‐mini futures?

On the Chicago Mercantile Exchange (CME), so‐called “E‐mini” index futures contracts trade on the electronic GLOBEX trading system alongside the corresponding full‐size contracts that trade on the open outcry floor. This paper finds that the current minimum tick sizes of the E‐mini S&P 500 and E‐mini Nasdaq‐100 futures contracts act as binding constraints on the bid‐ask spreads by not allowing the spreads to decline to competitive levels. We also find that, while exchange locals trade very actively on GLOBEX, they do not tend to act as liquidity suppliers. Taken together, our empirical results suggest that it is time for the CME to consider decreasing the minimum tick sizes of the S&P 500 and Nasdaq‐100 E‐mini futures contracts. A tick size reduction is likely to result in lower trading costs in the E‐mini futures markets. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:79–104, 2005     

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     

The realized volatility of FTSE‐100 futures prices

Five‐minute returns from FTSE‐100 index futures contracts are used to obtain accurate estimates of daily index volatility from January 1986 to December 1998. These realized volatility measures are used to obtain inferences about the distributional and autocorrelation properties of FTSE‐100 volatility. The distribution of volatility measured daily is similar to lognormal while the volatility time series has persistent positive autocorrelation that displays long‐memory effects. The distribution of daily returns standardized using the measures of realized volatility is shown to be close to normal, unlike the unconditional distribution. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:627–648, 2002     

Liquidity supply and volatility: futures market evidence

This article examines the provision of liquidity in futures markets as price volatility changes. We find that customer trading costs do not increase with volatility. However, for three of the four contracts studied, the nature of liquidity supply changes with volatility. Specifically, for relatively inactive contracts, customers as a group trade more with each other and less with market makers, on higher volatility days. By contrast, for the most active contract, trading between customers and market makers increases with volatility. We also find that market makers' income per contract decreases with volatility for one of the least active contracts in our sample, but is not significantly affected by volatility for the other contracts. These results are consistent with the idea that, for high‐cost, inactive contracts, market makers react to temporary increases in volatility by raising their bid‐ask spreads significantly, and customers provide increased liquidity through standing limit orders. An implication of our results is that electronic systems, where market maker participation is not required, are able to supply adequate liquidity during volatile periods. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1–17, 2001     

New insights into the impact of the introduction of futures trading on stock price volatility

We examine whether, and to what extent, the introduction of trading in share futures contracts on individual stocks (i.e., individual share futures, or ISFs) has impacted on the systematic risk and volatility of the underlying shares. The use of ISFs allows a unique experimental design that complements existing work on index futures. Our major findings are as follows. First, we found a general reduction in systematic risk on individual stocks after the listing of futures. Second, we found evidence of a decline in unconditional volatility. Third, we found mixed evidence concerning the impact on conditional volatility. Fourth, the introduction of futures was found to impact on the market dynamics, as reflected by a change in the asymmetric volatility response, although the direction of that change is stock‐specific. In general, the results point to a number of features that are case‐specific and provide new insights into the mixed results that are typical of existing studies. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:237–255, 2001     

Volatility dynamics of NYMEX natural gas futures prices

We examine the volatility dynamics of NYMEX natural gas futures prices via the partially overlapping time‐series model of Smith (2005. Journal of Applied Econometrics, 20, 405–422). We show that volatility exhibits two important features: (1) volatility is greater in the winter than in the summer, and (2) the persistence of price shocks and, hence, the correlations among concurrently traded contracts, displays substantial seasonal and cross‐sectional variation in a way consistent with the theory of storage. We demonstrate that, by ignoring the seasonality in the volatility dynamics of natural gas futures prices, previous studies have suggested sub‐optimal hedging strategies. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:438–463, 2008     

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     

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     

What moves German Bund futures contracts on the Eurex?

The German 10‐year Bund futures contract traded on the Eurex futures and options exchange in Frankfurt became the world's most actively traded derivative product by the end of 1999. In this article, we provide a detailed exploration of the interday and intraday return volatility in the Bund futures contract using a sample of five‐min returns from 1997 to 1998. The evolution of interday volatility is described best by a MA(1)‐fractionally integrated process that allows for the long‐memory features. At the intraday level, we find that macroeconomic announcements from both Germany and the U.S. are an important source of volatility. Among the various German announcements, we identify the IFO industry survey of business climate, industrial production (preliminary), and Bundesbank policy meeting as being by far the most important. The three most significant U.S. announcements include the employment report, the National Association of Purchasing Managers (NAPM) survey, and employment costs. Overall, U.S. macroeconomic announcements have a far greater impact on the Bund futures market than their German counterparts. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:679–696, 2002     

VIX futures

VIX futures are exchange‐traded contracts on a future volatility index (VIX) level derived from a basket of S&P 500 (SPX) stock index options. The authors posit a stochastic variance model of VIX time evolution, and develop an expression for VIX futures. Free parameters are estimated from market data over the past few years. It is found that the model with parameters estimated from the whole period from 1990 to 2005 overprices the futures contracts by 16–44%. But the discrepancy is dramatically reduced to 2–12% if the parameters are estimated from the most recent one‐year period. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:521–531, 2006     

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.