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.     

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.     

The forward premium in electricity futures

Understanding the nature of the forward premium is particularly crucial, but rather elusive, for a non-storable commodity such as wholesale electricity. Whilst forward prices emerge as the expectation of spot plus, or minus, an ex ante premium for risk, the manifestation and empirical analysis must focus upon realised ex post premiums. This presents modelling requirements to control for shocks to the spot expectation as well as the endogeneity of ex post premia with spot price outcomes. In addition, because electricity is a derived commodity in the sense that market prices are often set by technologies that convert gas or coal into power, it is an open question whether much of the premia in power may actually be a pass-through of the premia in gas (or coal). Using a four dimensional VAR model we are able to distinguish fundamental and behavioural aspects of price formation in both the daily and monthly forward premia from the British market. We present new evidence on daily and seasonal sign reversals, associated with demand cycles, the greater importance of behavioural adaptations in the risk premia than fundamental or spot market risk measures, and the substantial fuel risk pass-through. We also show the value of a nonlinear specification in this context.     

The Forward Premium in the Nord Pool Power Market

This article investigates the forward premium of futures contracts in the Nordic power market for the time period from January 2004 to December 2013. We find that futures prices are biased predictors of the subsequent spot prices and that there is a significant forward premium in the Nord Pool market, particularly during the winter and autumn. We analyze the impact from several factors on the forward premium. The spot price, and the deviation of water inflow from its usual level, positively affect the forward premium. The variance of the spot price also has a positive effect on the forward premium, but only for the contract closest to delivery.     

Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periods.     

Optimal Portfolio Choices, House Risk Hedging and the Pricing of Forward House Transactions

This paper develops a utility indifference model for evaluating various prices associated with forward transactions in the housing market, based on the equivalent principle of expected wealth utility derived from the forward and spot real estate markets. Our model results show that forward transactions in the housing market are probably not due to house sellers?? and buyers?? heterogeneity, but to their demand for hedging against house price risk. When the imperfections of real estate markets and the risk preferences of market participants are taken into consideration, we are able to show that the idiosyncratic risk premium, which mainly depends on the participants?? risk preferences and the correlation between the traded asset and the real estate, is a remarkable determinant of house sellers?? and buyers?? forward reservation prices. In addition, we also find that the market clearing forward price usually will not converge toward the expected risk-neutral forward price. The sellers?? or buyers?? risk aversion degrees and market powers are also identified to play crucial roles in determining the clearing forward price.     

Beyond Basis Basics: Liquidity Demand and Deviations from the Law of One Price

Deviations from the law of one price between futures and spot prices—the futures-cash basis—capture information about liquidity demand for equity market exposure in global markets. We show that the basis comoves with dealer and investor futures positions, is contemporaneously positively correlated with futures and spot market returns, and negatively predicts futures and spot returns. These findings are consistent with the futures-cash basis reflecting liquidity demand that is common to futures and cash equity markets. We find persistent supply-demand imbalances for equity index exposure reflected in the basis, giving rise to an annual premium of 5% to 6%.     

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.     

The skewness risk premium in equilibrium and stock return predictability

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.     

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.     

The information content of the term structure of risk-neutral skewness

We seek to reconcile the debate about the price effect of risk-neutral skewness (RNS) on stocks. We document positive predictability from short-term skewness, consistent with informed-trading demand, and negative predictability from long-term skewness, consistent with skewness preference. A term spread on RNS captures different information from long- and short-term contracts, resulting in stronger predictability. The quintile portfolio with the lowest spread outperforms that with highest spread by 14.64% annually. The term structure of RNS predicts earnings surprises and price crashes. We extract the slope factor from RNS term structure, estimate its risk premium, and explore its relation with several macroeconomic variables.     

Can Companies Use Hedging Programs to Profit from the Market? Evidence from Gold Producers*

In this article, the authors summarize the findings of their recent study of the hedging activities of 92 North American gold mining companies during the period 1989‐1999. The aim of the study was to answer two questions: (1) Did such hedging activities increase corporate cash flows? (2) And if yes, were such increases the result of management's ability to anticipate price movements when adjusting their hedge ratios? Although the author's answer to the first question is “yes,” their answer to the second is “no.” More specifically, the authors concluded that:

• ? During the 1989‐1999 period, the gold derivatives market was characterized by a persistent positive risk premium— that is, a positive spread between the forward price and the realized future spot price—that caused short forward positions to generate positive cash flows. The gold mining companies that hedged their future gold production realized an average total cash flow gain of $11 million, or $24 per ounce of gold hedged, per year, as compared to average annual net income of only $3.5 million. Because of the positive risk premium, short derivatives positions did not generate significant losses even during those subperiods of the study when the gold price increased.
• ? There was considerable volatility in corporate hedge ratios during the period of the study, which is consistent with managers incorporating market views into their hedging programs and attempting to time the market by hedging selectively. But after attempting to distinguish between derivatives activities designed to hedge and those designed to profit from a view, the authors conclude that corporate efforts to time the market through selective hedging were largely if not completely futile. In fact, the companies' adjustments of hedge ratios appeared to consistently lag instead of leading the market.

     

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.     

Transformations to normality and selectivity bias in hedonic price functions

Zuehlke and Rasmussen (1988) presented an investigation of selectivity bias in hedonic price functions estimated from sold subsamples. The empirical findings were sensitive to the degree of skewness allowed by the choice of offer distribution. With the generalized model presented in this paper, the degree of skewness present in the offer distribution is determined empirically, rather than imposed by assumption. This allows a test of the hypothesis advanced in Zuehlke and Rasmussen, that by failing to allow for an upward skew in offers, the normal distribution incorrectly attributes skewness in observed selling prices to censoring.     

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.     

Effects of skewness and kurtosis on production and hedging decisions: a skewed t distribution approach

This paper assumes that the spot price follows a skewed Student t distribution to analyze the effects of skewness and kurtosis on production and hedging decisions for a competitive firm. Under a negative exponential utility function, the firm will not over-hedge (under-hedge) when the spot price is positively (negatively) skewed. The extent of under-hedge (over-hedge) decreases as the forward price increases. Compared with the mean-variance hedger, the producer will hedge more (less) when negative (positive) skewness prevails. In addition, an increase in the skewness reduces the demand for hedging. The effect of the kurtosis, however, depends on the sign of the skewness. When the spot price is positively (negatively) skewed, an increase in kurtosis leads to a smaller (larger) futures position.     

From boom ‘til bust: How loss aversion affects asset prices

This article studies the impact of heterogeneous loss averse investors on asset prices. In very good states loss averse investors become gradually less risk averse as wealth rises above their reference point, pushing up equity prices. When wealth drops below the reference point the investors become risk seeking and demand for stocks increases drastically, eventually leading to a forced sell-off and stock market bust in bad states. Heterogeneity in reference points and initial wealth of the loss averse investors does not change the salient features of the equilibrium price process, such as a relatively high equity premium, high volatility and counter-cyclical changes in the equity premium.     

A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.     

The Effect of Errors in Variables on Tests for a Risk Premium in Forward Exchange Rates

Conventional tests for a risk premium in the price of forward exchange use the subsequently realized spot rate as a proxy for prior expectations. Use of this proxy creates a serious errors-in-variables problem which makes it difficult to reject the null hypothesis of zero risk premium. Use of a better proxy for expectations indicates the presence of a risk premium in the forward exchange rate of all countries analyzed.