Does tick size influence price discovery? Evidence from the Toronto Stock Exchange

We investigate the price discovery role of an exchange‐traded fund and the futures contract for the same market index. We find that the fund predicts the index in the subperiod after but not in the subperiod before a substantial decrease in the minimum tick size. The futures predict the index in both subperiods. The results are consistent with the view that the factors leading to successful price discovery do not depend on zero investment, as in futures markets, but do depend on a small tick size. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:49–66, 2003     

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     

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     

The effectiveness of coordinating price limits across futures and spot markets

We extend the work of Brennan ( 1986 ) to investigate whether the imposition of spot price limits can further reduce the default risk and lower the effective margin requirement for a futures contract that is already under price limits. Our results show that spot price limits do indeed further reduce the default risk and margin requirement effectively. In addition, the more precise the information is that comes from the spot market, the more the spot price limit rule constrains the information available to the losing party. The default probability, contract costs, and margin requirements are then lowered to a greater degree. Furthermore, for a given margin, both spot price limits and futures price limits can partially substitute for each other in ensuring contract performance. The common practice of imposing equal price limits on both the spot and futures markets, though not coinciding with the efficient contract design, has a lower contract cost and margin requirement than that without imposing spot price limits. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:577–602, 2003     

ISOLATING THE WILD CARD OPTION

Many embedded options are difficult to value the wild card option in the Treasury bond futures contract is one of these embedded options. We illustrate how narrow theoretical bounds on the value of this option, relative to the price of the contract, may be obtained in the presence of other embedded options. Simulations suggest that the value of the wild card option is close to zero. This implies that, in this economy, a simpler pricing model of the Treasury bond futures contract, which ignores the wild card option, will result in only a small loss of accuracy.     

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     

A simplified pricing model for volatility futures

We develop a general model to price VIX futures contracts. The model is adapted to test both the constant elasticity of variance (CEV) and the Cox–Ingersoll–Ross formulations, with and without jumps. Empirical tests on VIX futures prices provide out‐of‐sample estimates within 2% of the actual futures price for almost all futures maturities. We show that although jumps are present in the data, the models with jumps do not typically outperform the others; in particular, we demonstrate the important benefits of the CEV feature in pricing futures contracts. We conclude by examining errors in the model relative to the VIX characteristics. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:307–339, 2011     

A note on price futures versus revenue futures contracts

Here we consider the hedging roles of a price futures contract versus a revenue futures contract. In the absence of idiosyncratic output risk, the revenue contract almost always dominates the price contract. Idiosyncratic output risk provides conditions under which the price contract should dominate. When production risk is largely idiosyncratic, a producer with an anticipated long actuals position might combine a long revenue futures position with a short price futures position. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:503–512, 2004     

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     

Why do expiring futures and cash prices diverge for grain markets?

In recent years, cash and futures prices have failed to converge at expiration for selected corn, soybean, and wheat commodity contracts. This lack of convergence raises questions about the effectiveness of arbitrage activities, and increases concerns about the usefulness of these contracts for hedging. We describe the delivery process for these contracts, and show that it embeds a valuable real option on the long side—the option to exchange the deliverable for another futures contract. As the relative volatility of cash and futures prices increases, this option increases in value, which disconnects the cash market from the deliverable instrument in a futures contract. Our estimates of this option's value show that it may create significant price divergence. We parameterize an option pricing model using data on these three commodities from 2000 to 2008 and show that the option model fits closely to recent episodes of non‐convergence, which lends support to the importance of real option effects. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark

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Cointegration,unbiased expectations,and forecasting in the BIFFEX freight futures market

The relationship between freight cash and futures prices is investigated using cointegration econometrics. Results illustrate that the BIFFEX futures market is unbiased, and hence efficient for the current, one, two, and quarterly contract horizons. Since the futures contract is based on an index of various shipping routes, which has undergone several changes since its inception, stability in the relationship between the spot and futures rates is investigated using rolling cointegration techniques. Results indicate that the futures contract appears to have become more efficient over time in predicting the spot rate, and that the decrease in trading volume found in the BIFFEX market is not driven by a lack of efficiency in this market. Rather, the decrease in futures trading might be attributed to the growth rate of the freight forward market. This article incorporates the long‐run cointegrating relationships between cash and futures prices in a forecasting model and compares the forecasting performance of this model with several alternatives. It is found that while the futures price is the best predictor of future spot rates for the current‐month contract, time‐series models can outperform the futures contract at longer contract horizons. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:545–571, 2000.     

中国小麦期货市场效率的协整检验

本文采用扩展恩格尔-格朗杰检验对中国小麦期货市场效率进行研究,结果显示:未来现货价格与距最后交易日前第7、14、28天期货价格协整,并且距最后交易日越近,期货价格越接近对未来现货价格的无偏估计,期货市场接近有效率市场;未来现货价格与距最后交易日前第56天的期货价格不协整,因此可推断距最后交易日超过56天的期货市场没有效率。     

Reversing the lead,or a series of unfortunate events? NYMEX,ICE, and Amaranth

A number of studies compare the efficiency and transparency of floor trading with automated/electronic trading systems in the competition for order flow. Although most of these studies find that electronic systems lead price discovery, a few studies highlight the weaknesses of electronic trading in highly volatile market conditions. A series of unusual events in 2006, sparking extreme volatility in natural gas futures trading, provide an ideal setting to revisit the resilience of trading system price leadership in the face of high volatility. We estimate time‐varying Hasbrouck‐style information shares to investigate the intertemporal and cross‐sectional dynamics in price discovery. The results strongly suggest that the information share is time‐dependent and contract‐dependent. Floor trading dominates price discovery in the less liquid longer‐maturity contracts, whereas electronic trading dominates price discovery in the most liquid spot‐month contract. We find that the floor trading information share increases significantly with realized volatility. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:1130–1160, 2009     

Price limits,margin requirements,and default risk

This article investigates whether price limits can reduce the default risk and lower the effective margin requirement for a self‐enforcing futures contract by considering one more period beyond Brennan’s (1986) model to take into account the spillover of unrealized residual shocks due to price limits. The results show that, when traders receive no additional information, price limits can reduce the margin requirement and eliminate the default probability at the expense of a higher liquidity cost due to trading interruptions. Consequently, the total contract cost is higher than of that without price limits. When traders receive additional signals about the equilibrium price, we find that the optimal margin remains unchanged with or without the imposition of price limits, a result that is in conflict with Brennan’s assertion. Hence, we conclude that price limits may not be effective in improving the performance of a futures contract. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:573–602, 2000     

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     

The Valuation of Equity Futures on the Tokyo Stock Exchange: 1920–1923

The futures price of an asset should depend on the spot price of that asset, the interest rate, cash flows during the contract term, the convenience yield, and storage costs. Despite many tests of the spot–future relation for commodities in historical periods, there have been no tests of this historical relation for equities. We price single‐stock equity futures on the Tokyo Stock Exchange between 1920 and 1923 and find that mispricing is considerably worse than in contemporary U.S. markets, after adjusting for (unavoidable) asynchronous data issues. The main cause of the mispricing is short‐sales constraints, rather than investor naivety. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark     

Do designated market makers improve liquidity in open‐outcry futures markets?

On February 1, 2002, the Chicago Board of Trade appointed a designated market maker to enhance liquidity in its 10‐year interest rate swap futures contract. This market‐making program is the first of its kind in the open‐outcry futures industry. We find that introduction of the market maker has increased volume and reduced transaction costs. The market maker has also enhanced the speed and the efficiency of price discovery. Overall, the results suggest that the market‐making program is successful in improving liquidity. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:479–502, 2004     

Hedging long‐term commodity risk

This study focuses on the problem of hedging longer‐term commodity positions, which often arises when the maturity of actively traded futures contracts on this commodity is limited to a few months. In this case, using a rollover strategy results in a high residual risk, which is related to the uncertain futures basis. We use a one‐factor term structure model of futures convenience yields in order to construct a hedging strategy that minimizes both spot‐price risk and rollover risk by using futures of two different maturities. The model is tested using three commodity futures: crude oil, orange juice, and lumber. In the out‐of‐sample test, the residual variance of the 24‐month combined spot‐futures positions is reduced by, respectively, 77%, 47%, and 84% compared to the variance of a naïve hedging portfolio. Even after accounting for the higher trading volume necessary to maintain a two‐contract hedge portfolio, this risk reduction outweighs the extra trading costs for the investor with an average risk aversion. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:109–133, 2003     

ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Föllmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.     

The pricing of electricity futures: Evidence from the European energy exchange

This study investigates the pricing of electricity futures at the European Energy Exchange (EEX) over the period 2002 through 2004. To calculate theoretical contract values, the reduced‐form models of J. J. Lucia and E. S. Schwartz (2002) are used, and a thorough empirical analysis by means of an out‐of‐sample test is conducted for both one‐ and two‐factor models, incorporating a constant non‐zero price of risk. Although the models are proven to capture all basic spot market characteristics and provide an accurate in‐the‐sample fit to observed futures prices, the forecasting performance is subject to biases. For instance, it was found that the relative mispricing depends on both the spot price level and the remaining time‐to‐maturity of the futures contracts. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:387–410, 2007