Commodity price modelling that matches current observables: a new approach

We develop a stochastic model of the spot commodity price and the spot convenience yield such that the model matches the current term structure of forward and futures prices, the current term structure of forward and futures volatilities, and the inter-temporal pattern of the volatility of the forward and futures prices. We let the underlying commodity price be a geometric Brownian motion and we let the spot convenience yield have a mean-reverting structure. The flexibility of the model, which makes it possible to simultaneously achieve all these goals, comes from allowing the volatility of the spot commodity price, the speed of mean-reversion parameter, the mean-reversion parameter, and the diffusion parameter of the spot convenience yield all to be time-varying deterministic functions.     

Price dynamics in refined petroleum spot and futures markets

This article characterizes the spot and futures price dynamics of two important physical commodities, gasoline and heating oil. Using a non-linear error correction model with time-varying volatility, we demonstrate many new results. Specifically, the convergence of spot and futures prices is asymmetric, non-linear, and volatility inducing. Moreover, spreads between spot and futures prices explain virtually all spot return volatility innovations for these two commodities, and spot returns are more volatile when spot prices exceed futures prices than when the reverse is true. Furthermore, there are volatility spillovers from futures to spot markets (but not the reverse), futures volatility shocks are more persistent than spot volatility shocks, and the convergence of spot and futures prices is asymmetric and non-linear. These results have important implications. In particular, since the theory of storage implies that spreasd vary with fundamental supply and demand factors, the strong relation between spreads and volatility suggests that these fundamentals — rather than trading induced noise — are the primary determinants of spot price volatility. The volatility spillovers, differences in volatility persistence, and lead-lag relations are consistent with the view that the futures market is the primary locus of informed trading in refined petroleum product markets. Finally, our finding that error correction processes may be non-linear, asymmetric, and volatility inducing suggests that traditional approaches to the study of time series dynamics of variables that follow a common stochastic trend that ignore these complexities may be mis-specified.     

Oil convenience yields estimated under demand/supply shock

This paper extends the call option model of Milonas and Thomadakis (1997) to estimate oil convenience yields with futures prices. We define the business cycle of a seasonal commodity with demand/supply shocks and find that the convenience yield for crude oil exhibits seasonal behavior. The convenience yield for West Texas Intermediate (WTI) crude oil is the highest in the summer, while that for Brent crude oil is the highest in the winter. This implies that WTI crude oil is more sensitive to high summer demand and that Brent crude oil is more sensitive to shortages in winter supply. Convenience yields are negatively related to the inventory level of the underlying crude oil and positively related to interest rates due to the business cycle. We also show that convenience yields may explain price spread between WTI crude oil and Brent crude oil. Our computed convenience yields are consistent with Fama and French (1988) in that oil prices are more volatile than futures prices at low inventory level, verifying the Samuelson (1965) hypothesis that future prices are less variables than spot prices at lower inventory levels.

News announcements and price discovery in foreign exchange spot and futures markets

This paper studies competition in price discovery between spot and futures rates for the EUR–USD and JPY–USD markets around scheduled macroeconomic announcements. Using both the information shares approach and the common factor component weight approach for futures prices from the Chicago Mercantile Exchange (CME), as well as deal prices from spot trading on the Electronic Broking Services (EBS), we gauge how foreign exchange spot and futures markets respond to news surprises. The results show that the spot rates provide more price discovery than do the CME futures rates overall; however, the contribution of the futures rates to price discovery increases in the time surrounding macroeconomic announcement releases.     

限制交易政策如何影响期现关系?——对股指期货价格发现功能的实证检验

本文利用2015年中国股市大幅下跌期间,对股指期货严格限制交易政策这一独特事件前后的高频数据,研究限制交易政策对股指期货与股票市场价格引导关系的影响。利用I-S模型和分位数回归方法的实证结果表明:限制交易政策实施前,股指期货对股票市场的价格影响更强,尤其表现在价格急剧下跌时期;限制交易政策显著增加了期货市场交易成本,从而降低了期货市场的信息份额,削弱了其对股票市场的价格影响,并且改变了期货价格对现货价格“助跌强于助涨”的影响模式,增强了股指期货在价格上涨时对股票市场的影响。研究结果一方面直接量化了期货交易成本变动对其价格发现功能的负面影响,另一方面也从价格引导关系的视角提供了股市危机时期股指期货限制交易政策监管效果的实证证据。     

Price Discovery,Causality and Forecasting in the Freight Futures Market

This paper investigates the causal relationship between futures and spot prices in the freight futures market. Being a thinly traded market whose underlying asset is a service, sets it apart from other markets investigated so far in the literature. Causality tests, generalised impulse response analysis and forecasting performance evaluation indicate that futures prices tend to discover new information more rapidly than spot prices. Revisions in the composition of the underlying index to make it more homogeneous, have strengthened the price discovery role of futures prices. The information incorporated in futures prices, when formulated as a VECM, produces more accurate forecasts of spot prices than the VAR, ARIMA and random-walk models, over several steps ahead. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pricing Efficiency and Arbitrage in the Bitcoin Spot and Futures Markets

This study examines the pricing efficiency for the leading cryptocurrency, Bitcoin using spot prices and all CBOE and CME futures contracts traded from January 2018 to March 2019. We find that the futures basis provide some predictive power for future changes in the spot price and in the risk premium. However, the basis of Bitcoin is a biased predictor of the future spot price changes. Cointegration tests also demonstrate that futures prices are biased predictors of spot prices. Deviations from no-arbitrage between spot and futures markets are persistent and widen significantly with Bitcoin thefts (hacks, frauds) as well as alternative cryptocurrency issuances.     

Hedging Multiperiod Forward Commitments: The Case of Period-by-Period Quantity Uncertainty

This article considers the hedging problem of a producer with along-term forward commitment to deliver a commodity at multiple futurepoints in time. The aggregate quantity to be delivered over time is knownwith certainty; however, the period-by-period quantity is determined bythe customer and is unknown to the producer. A minimum-variancemultiperiod futures position that considers both price uncertainty andperiod-by-period quantity uncertainty is derived. The following resultsare obtained: The individual effects of price uncertainty and quantityuncertainty on the multiperiod minimum-variance are separable. In thetwo-period case, if the spot price is expected to decrease over time, therisk-minimizing hedge considering both price and quantity uncertaintiesis greater than that which considers price uncertainty only. If the spotprice is expected to increase over time, then the hedger would beover-hedged if only price uncertainty were considered. Convenience yieldpromotes a larger risk-minimizing futures position, whereas storage costsand financial costs reduce the size of the risk-minimizing futuresposition. In the multiperiod case, if forward prices are unbiasedestimators of future spot prices, or if spot prices are expected todecrease over time, then quantity uncertainty increases the size of therisk-minimizing hedge. If spot prices are expected to increase, then theeffect of period-by-period quantity uncertainty isindeterminate.     

中国饲料工业期货的价格发现实证研究

本文借助向量自回归模型、协整检验、误差修正模型、方差分解、脉冲响应函数等方法,以中国唯一的饲料工业期货———大连商品交易所豆粕期货品种为例,研究了期货价格与现货价格之间的动态关系,定量刻画了期货市场在价格发现中的作用。研究结果显示:豆粕期货价格与现货价格存在相互引导关系,并且期货与现货价格之间存在长期均衡关系,对豆粕期货来说,期货市场在价格发现功能中起到主导作用。     

The Traditional Hedging Model Revisited with a Nonobservable Convenience Yield

This article examines the hedging of constrained commodity positions with futures contracts. We extend the study of Adler and Detemple (1988a, 1988b) to include a partial information framework where the convenience yield is not observable. As a consequence, futures prices depend on investor's beliefs regarding the value of the convenience yield, and every component of the hedge is impacted by these beliefs. We achieve a decomposition of the demand that clarifies the impact on the optimal hedge of the beliefs, the spot price and the risk‐free rate as well as the hedging horizon.     

Backwardation in Oil Futures Markets: Theory and Empirical Evidence

Oil futures prices are often below spot prices. This phenomenon, known as strong backwardation, is inconsistent with Hotelling's theory under certainty that the net price of an exhaustible resource rises over time at the rate of interest. We introduce uncertainty and characterize oil wells as call options. We show that (1) production occurs only if discounted futures are below spot prices, (2) production is non-increasing in the riskiness of future prices, and (3) strong backwardation emerges if the riskiness of future prices is sufficiently high. The empirical analysis indicates that U.S. oil production is inversely related and backwardation is directly related to implied volatility.     

No-arbitrage conditions for storable commodities and the modeling of futures term structures

One distinguishable feature of storable commodities is that they relate to two markets: cash market and storage market. This paper proves that, if no arbitrage exists in the storage-cash dual markets, the commodity convenience yield has to be non-negative. However, classical reduced-form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield. To avoid negative convenience yield, this paper proposes a semi-affine arbitrage-free model, which prices futures analytically and fits futures term structures reasonably well. Importantly, our model prices commodity-related contingent claims (such as calendar spread options) quite differently with classical models.     

The response of U.S. natural gas futures and spot prices to storage change surprises: Fundamental information and the effect of escalating physical gas production

We study the behavior of U.S. natural gas futures and spot prices on and around the weekly announcements by the U.S. Energy Information Administration of the amount of natural gas in storage. We identify an inverse empirical relation between changes in futures prices and surprises in the change in natural gas in storage and that this relation is not driven by the absolute size of the surprise. The evidence also indicates prices react first in the futures market for natural gas with that information then flowing to the spot market. Post 2005, corresponding to a period of significant increases in the production of natural gas in the United States, the response of prices to storage surprises was larger in absolute value. No evidence is found of economically meaningful reactions to the surprise other than on the date the storage news is released. The results demonstrate the importance of fundamental information in the formation of natural gas prices.     

Spot and derivative pricing in the EEX power market

Using spot and futures price data from the German EEX Power market, we test the adequacy of various one-factor and two-factor models for electricity spot prices. The models are compared along two different dimensions: (1) We assess their ability to explain the major data characteristics and (2) the forecasting accuracy for expected future spot prices is analyzed. We find that the regime-switching models clearly outperform its competitors in almost all respects. The best results are obtained using a two-regime model with a Gaussian distribution in the spike regime. Furthermore, for short and medium-term periods our results underpin the frequently stated hypothesis that electricity futures quotes are consistently greater than the expected future spot, a situation which is denoted as contango.     

What role do futures markets play in Bitcoin pricing? Causality,cointegration and price discovery from a time-varying perspective?

Recent papers that have explored spot and futures markets for Bitcoin have concluded that price discovery takes place either in the spot, or the futures market. Here, we consider the robustness of previous price discovery conclusions by investigating causal relationships, cointegration and price discovery between spot and futures markets for Bitcoin, using appropriate daily data and time-varying mechanisms. We apply the time-varying Granger causality test of Shi, Phillips, and Hurn [2018]; time-varying cointegration tests of Park and Hahn [1999], and time-varying information share methodologies, concluding that futures prices Granger cause spot prices and that futures prices dominate the price discovery process.     

基于波动效应与价格发现的期指仿真交易研究

沪深300股指期货仿真交易的推出,对我国现货市场的影响如何以及这种影响是否有利于现货效率的改进。首次采用修正的GARCH模型和向量误差修正模型（VEC）将股指期货推出后现货市场波动性的变化和股指期货与现货市场的价格发现功能结合起来进行对比研究。结果表明,期指仿真交易的推出对于现货市场效率的改进确实存在正面的影响。其引入在短期内加大了现货市场的波动,但这一波动正是市场信息流动加速的反映,因而提高了市场信息的传递效率。同时期货价格领先于现货价格,存在由期货市场到现货市场长期的单向因果关系,说明期货价格具有引导现货价格向均衡方向调整的功能,从而在经验上支持了股指期货市场的开放政策。     

Stochastic Convenience Yield and the Pricing of Oil Contingent Claims

This paper develops and empirically tests a two-factor model for pricing financial and real assets contingent on the price of oil. The factors are the spot price of oil and the instantaneous convenience yield. The parameters of the model are estimated using weekly oil futures contract prices from January 1984 to November 1988, and the model's performance is assessed out of sample by valuing futures contracts over the period November 1988 to May 1989. Finally, the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time.     

Analysis of DJIA,S&P 500, S&P 400, NASDAQ 100 and Russell 2000 ETFs and their influence on price discovery

This study examines the temporal behavior of price discovery in the spot, ETF and futures markets of the DJIA, S&P 500, S&P 400, NASDAQ 100 and Russell 2000. We document an increasing trend in the price discovery metrics of exchange traded funds for all indexes but the DJIA. Contrary to past studies, our findings show that the spot market rather than the futures market leads the price discovery. The arbitrage process that links exchange traded funds to spot prices, and not the futures prices might explain the results. This daily arbitrage that ensures exchange traded funds prices equal net asset values appear to promote spot market price discovery especially with the popularity of exchange traded funds in more recent years. We additionally document that the temporal behavior of the exchange traded funds price discovery metric affects differently price discovery in the spot and futures markets across indexes.     

PRICING CURRENCY OPTIONS UNDER STOCHASTIC INTEREST RATES AND JUMP‐DIFFUSION PROCESSES

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forwards, and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term‐structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Bates's and Black's models underprice the European currency futures options in both the presence and the absence of jumps. The mispricing increases with the volatilities of interest rates and futures prices. JEL classification: G13     

The Impact of Futures Trading on the Spot Market for Treasury Bonds

Critics of futures markets contend that futures trading destabilizes spot prices and raises price levels of the underlying treasury bonds, while the proponents claim that futures trading improves the information content and stability of spot prices. To investigate these conflicting viewpoints, this paper examines the price behavior of treasury bonds at three critical time points: a) as they enter, retain, and exit the cheapest-to-deliver status; b) as they approach the futures delivery date; and, c) as they cease to be deliverable. An empirical analysis based on a rich data set of daily bond prices over thirty-four delivery quarters reveals little support for the critics’ view of futures trading.