Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange

This paper examines the importance of the regular pattern in the behavior of electricity prices, and its implications for the purposes of derivative pricing. We analyze the Nordic Power Exchange's spot, futures, and forward prices. We conclude that the seasonal systematic pattern throughout the year, in particular, is of crucial importance in explaining the shape of the futures/forward curve. Moreover, in the context of the oneand two factor models analyzed in this paper, a simple sinusoidal functionis adequate in order capture the seasonal pattern of the features and forwardcurve directly implied by the seasonal behavior of spot electricity prices.     

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.     

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.     

Arbitrage, Risk Premium, and Cointegration Tests of the Efficiency of Futures Markets

This article provides a new perspective on the efficiency of futures markets in a cointegration framework. Under the conventional risk premium hypothesis, if futures and spot prices are non-stationary, they must be cointegrated if futures markets are efficient. Alternatively, the cost-of-carry model implies that there should be a cointegration relationship among spot prices, futures prices and interest rates assuming all the series contain a unit root. Market efficiency further implies specific parameter restrictions under these two models. Using data on the futures markets for gold, silver, palladium and platinum, this article first establishes that interest rates, spot and futures prices are unit root non-stationary. The evidence on cointegration is somewhat mixed: the gold futures market is consistent with the cost-of-carry model, and the silver futures market satisfies the risk premium hypothesis, but the evidence for the other two markets is inconclusive.     

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.     

Informed Futures Trading and Price Discovery: Evidence from Taiwan Futures and Stock Markets

This article focuses on the information effects between the futures market and its spot market. Intraday data are used to investigate the lead-lag relationships between the returns and trading activity of Taiwan stock index futures and the spot returns. We focus on the transmission direction and the sources of information. Consistent with most previous studies, our results show that other than the contemporaneous relationship predicted by carry-cost theory and efficient market theory, futures returns significantly lead spot returns, which implies that informed trades may occur in the futures market. Using private transaction information, net open buy, as a proxy for futures trading activity and distinguishing different types of futures traders, we find that foreign institutional traders are the major source of informed trades because their trading has predictive power for future movements in both spot and futures prices. Traders in other categories are information laggards.     

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 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.     

Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure

We use the term structure of futures prices to test whether investors anticipate mean reversion in spot asset prices. The empirical results indicate mean reversion in each market we examine. For agricultural commodities and crude oil the magnitude of the estimated mean reversion is large; for example, point estimates indicate that 44 percent of a typical spot oil price shock is expected to be reversed over the subsequent eight months. For metals, the degree of mean reversion is substantially less, but still statistically significant. We detect only weak evidence of mean reversion in financial asset prices.     

Modelling electricity prices: a time change approach

To capture mean reversion and sharp seasonal spikes observed in electricity prices, this paper develops a new stochastic model for electricity spot prices by time changing the Jump Cox-Ingersoll-Ross (JCIR) process with a random clock that is a composite of a Gamma subordinator and a deterministic clock with seasonal activity rate. The time-changed JCIR process is a time-inhomogeneous Markov semimartingale which can be either a jump-diffusion or a pure-jump process, and it has a mean-reverting jump component that leads to mean reversion in the prices in addition to the smooth mean-reversion force. Furthermore, the characteristics of the time-changed JCIR process are seasonal, allowing spikes to occur in a seasonal pattern. The Laplace transform of the time-changed JCIR process can be efficiently computed by Gauss–Laguerre quadrature. This allows us to recover its transition density through efficient Laplace inversion and to calibrate our model using maximum likelihood estimation. To price electricity derivatives, we introduce a class of measure changes that transforms one time-changed JCIR process into another time-changed JCIR process. We derive a closed-form formula for the futures price and obtain the Laplace transform of futures option price in terms of the Laplace transform of the time-changed JCIR process, which can then be efficiently inverted to yield the option price. By fitting our model to two major electricity markets in the US, we show that it is able to capture both the trajectorial and the statistical properties of electricity prices. Comparison with a popular jump-diffusion model is also provided.     

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.     

Returns to Speculators and the Theory of Normal Backwardation

A nonparametric statistical procedure is employed to examine the returns to speculators in wheat, corn, and soybeans futures markets. We find that the theory of normal backwardation is supported. Moreover, the presence of the risk premiums to speculators tends to be more prominent in recent years than in earlier years. We also find that large wheat speculators as a whole possessed some superior forecasting ability. The evidence is inconsistent with the hypothesis that commodity futures prices are unbiased estimates of the corresponding future spot prices.     

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.     

Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets

Spot power prices are volatile and since electricity cannot be economically stored, familiar arbitrage-based methods are not applicable for pricing power derivative contracts. This paper presents an equilibrium model implying that the forward power price is a downward biased predictor of the future spot price if expected power demand is low and demand risk is moderate. However, the equilibrium forward premium increases when either expected demand or demand variance is high, because of positive skewness in the spot power price distribution. Preliminary empirical evidence indicates that the premium in forward power prices is greatest during the summer months.     

Electricity Forward Prices: A High-Frequency Empirical Analysis

We conduct an empirical analysis of forward prices in the PJM electricity market using a high‐frequency data set of hourly spot and day‐ahead forward prices. We find that there are significant risk premia in electricity forward prices. These premia vary systematically throughout the day and are directly related to economic risk factors, such as the volatility of unexpected changes in demand, spot prices, and total revenues. These results support the hypothesis that electricity forward prices in the Pennsylvania, New Jersey, and Maryland market are determined rationally by risk‐averse economic agents.     

Limits to arbitrage and hedging: Evidence from commodity markets

We build an equilibrium model of commodity markets in which speculators are capital constrained, and commodity producers have hedging demands for commodity futures. Increases in producers' hedging demand or speculators' capital constraints increase hedging costs via price-pressure on futures. These in turn affect producers' equilibrium hedging and supply decision inducing a link between a financial friction in the futures market and the commodity spot prices. Consistent with the model, measures of producers' propensity to hedge forecasts futures returns and spot prices in oil and gas market data from 1979 to 2010. The component of the commodity futures risk premium associated with producer hedging demand rises when speculative activity reduces. We conclude that limits to financial arbitrage generate limits to hedging by producers, and affect equilibrium commodity supply and prices.     

Risk management in the energy markets and Value-at-Risk modelling: a hybrid approach

This paper proposes a set of Value-at-Risk (VaR) models appropriate to capture the dynamics of energy prices and subsequently quantify energy price risk by calculating VaR and expected shortfall measures. Amongst the competing VaR methodologies evaluated in this paper, besides the commonly used benchmark models, a Monte Carlo (MC) simulation approach and a hybrid MC with historical simulation approach, both assuming various processes for the underlying spot prices, are also being employed. All VaR models are empirically tested on eight spot energy commodities that trade futures contracts on the New York Mercantile Exchange (NYMEX) and the constructed Spot Energy Index. A two-stage evaluation and selection process is applied, combining statistical and economic measures, to choose amongst the competing VaR models. Finally, both long and short trading positions are considered as it is of utmost importance for energy traders and risk managers to be able to capture efficiently the characteristics of both tails of the distributions.     

Examining the forward pricing function of the Australian equity index futures contract

The relationship between the Australian equity index futures and spot prices is examined. Tests indicate that futures prices with one, two and three months to maturity are unbiased predictors of the spot and hence provide an efficient hedging mechanism for Australian equity index market participants, while six‐, nine‐ and twelve‐month futures prices are biased predictors of spot prices, indicating that speculative opportunities may exist in futures contracts for these time spreads. An analysis of the short‐run dynamic properties of the long‐run equilibrium relationship found that for all time spreads the futures prices respond to changes in the long‐run equilibrium, and for the twelve‐month contract, both futures and spot prices adjust to return to the long‐run equilibrium.     

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。     

Cojumping: Evidence from the US Treasury bond and futures markets

The basis between spot and future prices will be affected by jump behavior in each asset price, challenging intraday hedging strategies. Using formal cojumping tests this paper considers the cojumping behavior of spot and futures prices in high frequency US Treasury data. Cojumping occurs most frequently at shorter maturities and higher sampling frequencies. We find that the probability of cojumping is altered by the presence of an anticipated macroeconomic news announcement. The probability of cojumping is particularly affected by news surprises in non-farm payrolls, CPI, GDP and retail sales. However, the two cojumping tests are also more likely to provide contradictory results in the presence of surprises in non-farm payrolls. On these occasions the market does not clearly signal its short term pricing behavior.