Hedging in Futures and Options Markets with Basis Risk

This paper analyzes the hedging decisions for firms facing price and basis risk. Two conditions assumed in most models on optimal hedging are relaxed. Hence, (i) the spot price is not necessarily linear in both the settlement price and the basis risk and (ii) futures contracts and options on futures at different strike prices are available. The design of the first‐best hedging instrument is first derived and then it is used to examine the optimal hedging strategy in futures and options markets. The role of options as useful hedging tools is highlighted from the shape of the first‐best solution. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:59–72, 2002     

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     

Pricing VIX futures: Evidence from integrated physical and risk‐neutral probability measures

This study derives closed‐form solutions to the fair value of VIX (volatility index) futures under alternate stochastic variance models with simultaneous jumps both in the asset price and variance processes. Model parameters are estimated using an integrated analysis of integrated volatility and VIX time series from April 21, 2004 to April 18, 2006. The stochastic volatility model with price jumps outperforms for the short‐dated futures, whereas additionally including a state‐dependent volatility jump can further reduce out‐of‐sample pricing errors for other futures maturities. Finally, adding volatility jumps enhances hedging performance except for the short‐dated futures on a daily‐rebalanced basis. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:1175–1217, 2007     

Forecasting oil price movements: Exploiting the information in the futures market

Relying on the cost of carry model, the long‐run relationship between spot and futures prices is investigated and the information implied in these cointegrating relationships is used to forecast out of sample oil spot and futures price movements. To forecast oil price movements, a vector error correction model (VECM) is employed, where the deviations from the long‐run relationships between spot and futures prices constitute the equilibrium error. To evaluate forecasting performance, the random walk model (RWM) is used as a benchmark. It was found that (a) in‐sample, the information in the futures market can explain a sizable portion of oil price movements; and (b) out‐of‐sample, the VECM outperforms the RWM in forecasting price movements of 1‐month futures contracts. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:34–56, 2008     

Causality in the VIX futures market

This study examines the price‐discovery function and information efficiency of a fast growing volatility futures market: the Chicago Board of Option Exchange VIX futures market. A linear Engle–Granger cointegration test with an error correction mechanism (ECM) shows that during the full sample period, VIX futures prices lead spot VIX index, which implies that the VIX futures market has some price‐discovery function. But a modified Baek and Brock nonlinear Granger test detects bi‐directional causality between VIX and VIX futures prices, suggesting that both spot and futures prices react simultaneously to new information. Quarter‐by‐quarter investigations show that, on average, the estimated parameters are not significantly different from zero, thus providing further evidence supporting information efficiency in the VIX futures market. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Do small traders contribute to price discovery? Evidence from the Hong Kong Hang Seng Index markets

Using one‐contract‐size trades in the Mini Hang Seng Index futures to proxy the activities of small traders, this study empirically investigates the information contribution of small futures traders to price discovery on the Hang Seng Index (HSI) markets. Estimated with the models of Gonzalo, J., and Granger, C. W. J. ( 1995 ) and Hasbrouck, J. ( 1995 ), the results show that small traders contribute about 16.8% to price discovery, a disproportionately high share considering their relatively low trading volume. The results also indicate that the Hang Seng Index futures (HSIF) market still has the largest information share (about 71.0%), whereas the HSI spot market has a 12.2% share. Our results suggest that small traders are not uninformed in the HSIF markets, and play an important role in price discovery. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:156–174, 2010     

The evolution of price discovery in us equity and derivatives markets

This study considers the evolution of price discovery in the S&P 500 E-mini futures and the corresponding exchange traded fund (SPY ETF) over the period January 2002 through December 2013. The study reports evidence that the E-mini futures dominate price discovery at the beginning of the sample period. However, from 2007 onward both the SPY ETF and E-mini futures contribute similar portions to the price discovery process. The level of price discovery is significantly influenced by volume measures and relative levels of transaction costs for both securities.     

Delivery risk and the hedging role of options

Multiple delivery specifications exist on nearly all commodity futures contracts. Sellers typically are allowed to deliver any of several grades of the underlying commodity and at any of several locations. On the delivery day, the futures price as such needs not converge to the spot price of the par‐delivery grade at the par‐delivery location, thereby imposing an additional delivery risk on hedgers. This article derives the optimal hedging strategy for a risk‐averse hedger in the presence of delivery risk. In particular, it is shown that the hedger optimally uses options on futures for hedging purposes. This article provides a rationale for the hedging role of options when futures markets allow for multiple delivery specifications. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:339–354, 2002     

Do futures lead price discovery in electronic foreign exchange markets?

Using intraday data, this study investigates the contribution to the price discovery of Euro and Japanese Yen exchange rates in three foreign exchange markets based on electronic trading systems: the CME GLOBEX regular futures, E‐mini futures, and the EBS interdealer spot market. Contrary to evidence in equity markets and more recent evidence in foreign exchange markets, the spot market is found to consistently lead the price discovery process for both currencies during the sample period. Furthermore, E‐mini futures do not contribute more to the price discovery than the electronically traded regular futures. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:137–156, 2009     

Valuing real options using implied binomial trees and commodity futures options

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market‐implied probability distributions for commodity prices. In addition, the existence of long‐dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. A detailed out‐of‐sample test is included that shows how IBT option pricing errors evolve on subtrees emanating from future levels of the underlying asset. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:203–226, 2007     

The effect of the introduction of Cubes on the Nasdaq‐100 index spot‐futures pricing relationship

This paper examines the impact of the introduction of the Nasdaq‐100 Index Tracking Stock (referred to as Cubes) on the pricing relationship between Nasdaq‐100 futures and the underlying index. Observations obtained from tick‐by‐tick Nasdaq‐100 futures transactions and index value data support the hypothesis that the introduction of Cubes in March 1999 has led to improvements in the Nasdaq‐100 index futures pricing efficiency. Both the size and frequency of violations in futures price boundaries appear to be reduced. Furthermore, there appears to be an increase in the speed of the market response to observed violations. These results are attributed to the increased ease in establishing a spot Nasdaq‐100 index position after the introduction of the tracking stock. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22: 197–218, 2002     

A maximal affine stochastic volatility model of oil prices

This study develops and estimates a stochastic volatility model of commodity prices that nests many of the previous models in the literature. The model is an affine three‐factor model with one state variable driving the volatility and is maximal among all such models that are also identifiable. The model leads to quasi‐analytical formulas for futures and options prices. It allows for time‐varying correlation structures between the spot price and convenience yield, the spot price and its volatility, and the volatility and convenience yield. It allows for expected mean‐reversion in the short term and for an increasing expected long‐term price, and for time‐varying risk premia. Furthermore, the model allows for the situation in which options' prices depend on risk not fully spanned by futures prices. These properties are desirable and empirically important for modeling many commodities, especially crude oil. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:101–133, 2010     

The cost of carry model and regime shifts in stock index futures markets: An empirical investigation

This article examines empirically the dynamic relationship between spot and futures prices in stock index futures markets employing a class of nonlinear, regime‐switching‐vector‐equilibrium‐correction models, which is novel in this context. Using data for the S&P 500 and the FTSE 100 over the post‐1987 crash period, it is shown that a long‐run relationship between spot and futures prices exists, which implies mean reversion of the basis. After providing strong evidence against the hypothesis of linear dynamics in the relationship under investigation, regime‐switching‐vector‐equilibrium‐correction models for spot and futures price movements are developed and shown to capture well the time‐series properties of our data, consistent with a large theoretical and empirical literature. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:603–624, 2000.     

Do futures prices help forecast the spot price?

This study proposes a futures‐based unobserved components model for commodity spot prices. Prices quoted at the same time incorporate the same information, but are affected differently, resulting in the different shapes of futures curves. This model utilizes information from part of the futures curve to improve forecasting accuracy of the spot price. Applying this model to oil market data, I find that the model forecasts outperform the literature benchmark (the no‐change forecast) and futures prices forecasts in multiple dimensions, with smaller average error variation over the sample period and higher chance of smaller absolute error in each period.     

Pricing Eurodollar Futures Options with the Heath—Jarrow—Morton Model

This article uses the algorithm developed by Ritchken and Sankarasubramanian (1995) to make comparisons among the Heath—Jarrow—Morton (HJM) models (Heath, Jarrow, & Morton, 1992) with different volatility structures in pricing the Eurodollar futures options. We show that the differences among the HJM models as well as the difference between the HJM models and Black's model can be insignificant when the volatility of the forward rate is relatively small. Moreover, our findings imply that the difference between the American‐style and European‐style options is insignificant for options with a life of less than 1 year. However, the difference can be significant for options with a 1‐year maturity, the difference depending on the exercise price. Finally, our tests indicate that the difference between the forward price and the futures price is insignificant if the volatility parameter is low enough and when the volatility of the spot rate is proportional to the spot rate. A higher volatility parameter can lead to a significant difference between the forward price and the futures price, although its impact on the price of the options will still be trivial. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 655–680, 2001     

Price discovery and investor structure in stock index futures

Previous literature on price discovery in stock index futures and spot markets neglects the role of different investor groups. This study relates time‐varying spot‐futures linkages studied within a VECM‐DCC‐GARCH framework to changes in the investor structure of the futures market over time. Empirical results suggest that during the dominance of presumably uninformed private investors, the futures market does not contribute to price discovery. By contrast, there is evidence of information flows from futures to spot markets and a significant increase in conditional correlation between both markets as institutional investors' share in trading volume increases. We derive implications for the design of emerging futures markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark31:282–306, 2011     

Price discovery in bitcoin spot or futures?

In December 2017, both the Chicago Board Options Exchange and the Chicago Mercantile Exchange introduced futures contracts on bitcoin. We investigate to what extent they provide useful information for the price discovery of bitcoin. We rely on the information share methodology of Hasbrouck (1995, J Finance, 50, pp. 1175–1199) and Gonzalo and Granger (1995, J Bus Econ Stat, 13, pp. 27–35) and find that the spot price leads the futures price. We attribute this result to the higher trading volume and the longer trading hours of the globally distributed bitcoin spot market, compared to the relatively restricted access to the US-based futures markets.     

Price discovery in the foreign exchange futures market

Examination is made of the relative contributions to price discovery of the floor and electronically traded euro FX and Japanese yen futures markets and the corresponding retail on‐line foreign exchange spot markets. GLOBEX electronic futures contracts provide the most price discovery in the euro; the on‐line trading spot market provides the most in the Japanese yen. The floor‐traded futures markets contribute the least to price discovery in both the euro and the Japanese yen markets. The overall results show that electronic trading platforms facilitate price discovery more efficiently than floor trading. Futures traders may also extract information from on‐line spot prices. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1131–1143, 2006     

Information transmission in electronic versus open‐outcry trading systems: An analysis of U.S. equity index futures markets

In this article the intraday price discovery process between regular index futures (floor trading) and E‐mini index futures (electronic trading) in the S&P 500 and Nasdaq 100 index futures markets is examined, using intraday data from the introduction of the E‐mini index futures to 2001. Using both information shares (Hasbrouck, J., 1995) and common long‐memory factor weights (Gonzalo, J., & Granger, C. W. J., 1995) techniques, we find that both E‐mini index futures and regular index futures contribute to the price discovery process. However, since September 1998, the contribution made by E‐mini index futures has been greater than that provided by regular index futures. Based on regression analysis, we have also found direct empirical evidence to support the hypothesis that the joint effects of operational efficiency and relative liquidity determine the greater contribution made towards price discovery by electronic trading relative to open‐outcry trading over time. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25: 679–715, 2005     

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