Optimal hedging under biased energy futures markets

Optimal futures hedging positions for those agents trying to maximize their expected utility will depend on their view about the evolution of the market and on how risk adverse they are. The most risk adverse agents will probably decide to full-cover their positions. But when a futures bias exists, hedgers with moderate or low degree of risk aversion can alter their strategy depending on the expected gains in futures markets. In our application to the UK natural gas market, we find a statistically significant time-varying negative futures bias that can be forecasted with confidence. As a result of this bias, most effective and best performing hedging strategies for moderate risk-averse agents are those involving short (long) hedging in winter (summer) with a hedging ratio above (below) the minimum variance hedge ratio. These findings are of great interest to practitioners in the UK natural gas markets and the methodology can be extrapolated to other energy markets.     

Crude oil price shocks and hedging performance: A comparison of volatility models

From a practical perspective, it is crucial to hedge the crude oil price risk in periods of dramatic price change. In this study, we directly investigate the performance of crude oil hedge portfolios in the five periods in which the largest oil price shocks in history occurred. We use stochastic volatility (SV), GARCH, and the diagonal BEKK model to estimate the minimum variance hedge ratio of hedge portfolios. Our empirical results provide evidence that hedging strategies based on the SV model are able to outperform the GARCH and BEKK models in terms of variance reduction. Our results are also consistently valid for various hedge horizons. Interestingly, although it is important to estimate variance and covariance accurately when constructing minimum variance portfolios, we find that reducing the mean squared and mean absolute errors does not guarantee superior hedge performance.     

Is hedging the crack spread no longer all it's cracked up to be?

The traditional approach to hedging the crude oil refining margin (crack spread) adopts a fixed 3:2:1 ratio between the futures positions of crude oil, gasoline, and heating oil. However, hedging the latter in arbitrary proportions might be more effective under some conditions. The paper constructs optimal hedging strategies for both scenarios during the periods of relatively stable and volatile oil prices observed in recent years. Minimization of downside risk (LPM₂) and variance are used as alternative hedging objectives. The joint distribution of spot and futures price log returns is modeled using a kernel copula method. The hedging performance of the constructed strategies is compared using hedging effectiveness, expected profit, and expected shortfall. The results show that allowing for arbitrary proportions in the sizes of futures positions generally achieves a better hedging performance. The advantage becomes particularly important during periods characterized by greater variation of the cross-dependence between the price log returns of individual commodities. In addition, using LPM₂ as a hedging criterion can help hedgers to better track downside risk as well as lead to higher expected profit and lower expected shortfall.     

The (de)merits of minimum-variance hedging: Application to the crack spread

We study the empirical performance of the classical minimum-variance hedging strategy, comparing several econometric models for estimating hedge ratios of crude oil, gasoline and heating oil crack spreads. Given the great variability and large jumps in both spot and futures prices, considerable care is required when processing the relevant data and accounting for the costs of maintaining and re-balancing the hedge position. We find that the variance reduction produced by all models is statistically and economically indistinguishable from the one-for-one “naïve” hedge. However, minimum-variance hedging models, especially those based on GARCH, generate much greater margin and transaction costs than the naïve hedge. Therefore we encourage hedgers to use a naïve hedging strategy on the crack spread bundles now offered by the exchange; this strategy is the cheapest and easiest to implement. Our conclusion contradicts the majority of the existing literature, which favours the implementation of GARCH-based hedging strategies.     

Strips of hourly power options—Approximate hedging using average-based forward contracts

We study approximate hedging strategies for a contingent claim consisting of a strip of independent hourly power options. The payoff of the contingent claim is a sum of the contributing hourly payoffs. As there is no forward market for specific hours, the fundamental problem is to find a reasonable hedge using exchange-traded forward contracts, e.g. average-based monthly contracts. The main result is a simple dynamic hedging strategy that reduces a significant part of the variance. The idea is to decompose the contingent claim into mathematically tractable components and to use empirical estimations to derive hedging deltas. Two benefits of the method are that the technique easily extends to more complex power derivatives and that only a few parameters need to be estimated. The hedging strategy based on the decomposition technique is compared with dynamic delta hedging strategies based on local minimum variance hedging, using a correlated traded asset.     

European natural gas seasonal effects on futures hedging

This paper is the first to discuss the design of futures hedging strategies in European natural gas markets (NBP, TTF and Zeebrugge). A common feature of energy prices is that conditional mean and volatility are driven by seasonal trends due to weather, demand, and storage level seasonalities. This paper follows and extends the Ederington and Salas (2008) framework and considers seasonalities in mean and volatility when minimum variance hedge ratios are computed. Our results show that hedging effectiveness is much higher when the seasonal pattern in spot price changes is approximated with lagged values of the basis (futures price minus spot price). This fact remains true for short (a week) and long (one, three and six months) hedging periods. Furthermore, volatility of weekly price changes also has a seasonal pattern and is higher in winter than in summer. A simple volatility seasonal model that is based on sinusoidal functions on the basis improves the risk reduction obtained by strategies in which hedging ratios are estimated with linear regressions. Seasonal hedging strategies, linear regression based strategies, or even a naïve position, perform better than more sophisticated statistical methods.     

Timing strategy performance in the crude oil futures market

The rewards to speculative trading in the crude oil futures market are assessed. For investors who adopt timing strategies that maximise their (iso-elastic) utility during each trading session, the rewards can be economically significant providing that transaction costs are small. Moreover, we are able to show via a decomposition of performance that the bulk of this benefit is due to their ability to predict realised volatility (that is, the second realised moment). The benefits derived from predicting other realised moments either require unrealistic levels of skill (all odd moments) or an infeasible degree of risk aversion (the fourth moment and higher even moments).     

Minimum variance hedging with bivariate regime-switching model for WTI crude oil

This paper proposes a four-regime bivariate Markov regime-switching model to estimate the daily time-varying minimum variance hedge ratios for West Texas Intermediate (WTI) crude oil, and evaluates its in- and out-of-sample hedging performances with two-regime model, CC-GARCH, TVC-GARCH, and OLS models. Empirical results reveal that the four-regime Markov switching model outperforms the other models for both in- and out-of-sample hedging performance. Based on Hansen’s SPA test (2005), the four-regime model significantly outperforms the other models for only in-sample hedging.     

Hedging local volume risk using forward markets: Nordic case

With focus on the Nordic electricity market, this paper develops hedging strategies for an electricity distributor who manages price and volume risk from fixed price agreements on stochastic electricity load. Whereas the distributor trades in the spot market at area prices, the financial contracts used for hedging are settled against the system price. Area and system prices are correlated with electricity load, as are price differences. In practice, however, this is often disregarded. Here, we develop a joint model for the area price, the system price and the load, accounting for correlations, and we suggest various strategies for hedging in the presence of local volume risk. We benchmark against a strategy that ignores correlation and hedges at expected load, as is common practice in the industry. Using data from 2013 and 2014 for two Danish bidding areas, we show that our best hedging strategy reduces gross loss by 5.8% and 13.6% and increases gross profit by 3.8% and 9.5%, respectively. Although this is partly due to the inclusion of correlation, we show that performance improvement is mainly driven by the choice of risk measure.     

Pure martingale and joint normality tests for energy futures contracts

In this study, we empirically analyze to see if the pure martingale hypothesis holds for three energy-related commodities: crude oil, heating oil and natural gas. We also test this hypothesis for five different hedging horizons: 1-day, 1-week, 4-week, 8-week and 12-week. Our empirical results show that the pure martingale hypothesis holds for all three commodities and all five horizons. This implies that the expected return on futures contract can be ignored in determining the optimal hedge ratio. We also test to see if the joint normality between futures and spot returns holds for the same three commodities and five hedging horizons. We reject the joint normality hypothesis for all three commodities and five hedging horizons. This implies that hedgers with different utility function have different optimal hedge ratios. Thus, in general, one needs to take into account of hedger's utility function when deriving optimal hedge ratio. Our results are robust to pre- and post-financial crisis as well as some other specifications considered in the paper.     

A regime switching approach for hedging tanker shipping freight rates

Tanker shipping is the primary means for the transportation of petroleum and petroleum products around the world and thus plays a crucial role in the energy supply chain. However, the high volatility of tanker freight rates has been a major concern for market participants and led to the development of the tanker freight derivatives in the form of forward freight agreements (FFAs). The aim of this paper is to investigate the performance of these instruments in managing tanker freight rate risk. Using a data set for six major tanker routes covering the period between 2005 and 2013, we examine the effectiveness of alternative hedging methods, including a bivariate Markov Regime Switching GARCH model, in hedging tanker freight rates. The regime switching GARCH specification links the concept of equilibrium freight rate determination underlying different market conditions and the dynamics of the conditional second moments across high and low volatility regimes. Overall, we find evidence supporting the argument that the tanker freight market is characterized by different regimes. However, while the use of a regime switching model allows for a significant improvement in the performance of the hedge in-sample, out-of-sample results are mixed.     

Risk and unit commitment decisions in scenarios of wind power uncertainty

This paper addresses the problem of decision making in Unit Commitment in systems with a significant penetration of wind power. Traditional approaches to Unit Commitment are inadequate to fully deal with the uncertainties associated to wind, represented by scenarios of forecasted wind power qualified by probabilities. Departing from a critique of planning paradigms, the paper argues that a stochastic programming approach, while a step in the good direction, is insufficient to model all aspects of the decision process and therefore proposes the adoption of models based on a Risk Analysis paradigm. A case study is worked out reinforcing this perspective. In a multi-objective context, the properties of the cost vs. risk Pareto-optimal fronts are analyzed, where risk may be represented by aversion to a worst scenario or a worst event. It is shown that the Pareto-optimal front may not be convex, which precludes a simplistic use of tradeoff concepts. It is also shown that decisions based on stochastic programming may in fact put the system at risk. An evaluation of risk levels and cost of hedging against undesired events is proposed as the paradigm to be followed in Unit Commitment decision making.     

Electricity procurement for large consumers based on Information Gap Decision Theory

In the competitive electricity market, consumers seek strategies to meet their electricity needs at minimum cost and risk. This paper provides a technique based on Information Gap Decision Theory (IGDT) to assess different procurement strategies for large consumers. Supply sources include bilateral contracts, a limited self-generating facility, and the pool. It is considered that the pool price is uncertain and its volatility around the estimated value is modeled using an IGDT model. The proposed method does not minimize the procurement cost but assesses the risk aversion or risk-taking nature of some procurement strategies with regard to the minimum cost. Using this method, the robustness of experiencing costs higher than the expected one is optimized and the related strategy is determined. The proposed method deals with optimizing the opportunities to take advantage of low procurement costs or low pool prices. A case study is used to illustrate the proposed technique.     

Risk assessment of new pricing strategies in the district heating market: A case study at Sundsvall Energi AB

The price structure of district heating has been no major scientific issue for the last decades in energy-related research. However, today trends in district heating pricing tend to move towards a more customer-oriented approach with predetermined prices under a longer periods, leading to a more complex price structure. If a district heating supplier offers district heating with predetermined prices in order to compete with similar electricity offers, the financial risk of the new price structure is significantly higher than the risk of an ordinary variable cost offer based on short-run marginal cost. In contrary to an electricity seller, the district heating company cannot transfer all of the risk of predetermined prices to the financial market, instead the company is thrown upon its own ability to handle the risk by, e.g., hedging its own energy purchase. However, all uncertainties cannot be coped with in this manner. Thus, there is a need for a methodology that can be used to estimate the financial risk of different price structures and to value different opportunities to reduce the risk. In this article, we propose a methodology, implemented in prototype software, to evaluate the risk associated with new price structures in district heating.     

An equilibrium pricing model for weather derivatives in a multi-commodity setting

Many industries are exposed to weather risk. Weather derivatives can play a key role in hedging and diversifying such risk because the uncertainty in a company's profit function can be correlated to weather condition which affects diverse industry sectors differently. Unfortunately the weather derivatives market is a classical example of an incomplete market that is not amenable to standard methodologies used for derivative pricing in complete markets. In this paper, we develop an equilibrium pricing model for weather derivatives in a multi-commodity setting. The model is constructed in the context of a stylized economy where agents optimize their hedging portfolios which include weather derivatives that are issued in a fixed quantity by a financial underwriter. The supply and demand resulting from hedging activities and the supply by the underwriter are combined in an equilibrium pricing model under the assumption that all agents maximize some risk averse utility function. We analyze the gains due to the inclusion of weather derivatives in hedging portfolios and examine the components of that gain attributable to hedging and to risk sharing.     

Locational price spreads and the pricing of contracts for difference: Evidence from the Nordic market

In electricity markets, not only does the risk of substantial price variations over time exist, but so does the risk of price variations over space, as prices between locations can differ due to transmission congestion. To manage this risk, Contracts for Difference (CfDs), i.e., forwards on the spread between a particular area price and the (unconstrained) system price, were introduced at the Scandinavian electricity exchange Nord Pool at the end of 2000. We empirically investigate the pricing of these CfDs over the period 2001 through 2006 and find that CfD prices contain significant risk premia. Their sign and magnitude, however, differ substantially between areas and delivery periods, because areas are subject to transmission congestion to a varying extent. While the relation between risk premia and time-to-maturity is not uniform for CfDs, there is a negative relation for implied area and system forwards, which can be explained by the relative hedging demand of market participants. In addition, we find that risk premia of CfDs and implied area forwards vary systematically with the variance and skewness of the underlying spot prices. This confirms both implications of the Bessembinder and Lemmon [Bessembinder, H., Lemmon, M.L., 2002. Equilibrium pricing and optimal hedging in electricity forward markets. Journal of Finance, 57, 1347–1382] model.     

Downside risk and the energy hedger's horizon

In this paper, we explore the impact of investor time-horizon on an optimal downside hedged energy portfolio. The optimal heating oil hedge ratio is first calculated for a variety of downside risk objective functions at different time-horizons using the wavelet transform. Next, associated hedging effectiveness is contrasted for a range of risk metrics, with all metrics showing increasing hedging effectiveness at longer horizons. Moreover, decreased hedging effectiveness is demonstrated for increased levels of uncertainty at higher confidence intervals. While small differences in effectiveness are found across the different hedging objectives, time-horizon effects are found to dominate confirming the importance of the hedging horizon. The findings suggest that while downside risk measures are useful in determining an optimal futures hedge encompassing negative returns, hedging horizon and confidence intervals should also be given careful consideration by the energy hedger.     

Analyzing volatility spillovers and hedging between oil and stock markets: Evidence from wavelet analysis

This paper examines the linkage of crude oil market (WTI) and stock markets of the G-7 countries. We study the mean and volatility spillovers of oil and stock market prices over various time horizons. We propose a new approach incorporating both multivariate GARCH models and wavelet analysis: wavelet-based MGARCH approach. We combine a bivariate GARCH-BEKK model with wavelet multiresolution analysis in order to capture the multiscale features of mean and volatility spillovers between time series. For optimal portfolio allocation decisions, we analyze the multiscale behavior of hedge ratio. Empirical results show strong evidence of significant volatility spillovers between oil and stock markets, as well as time-varying correlations for various market pairs. However, results of wavelet coherence indicate that in most, the WTI market was leading. In addition, it is stated that the decomposed volatility spillovers permit investors to adapt their hedging strategies.     

Trading wind power through physically settled options and short‐term electricity markets

Wind power producers participating in today's electricity markets face significant variability in revenue streams, with potential high losses mostly due to wind's limited predictability and the intermittent nature of the generated electricity. In order to further expand wind power generation despite such challenges, it is important to maximize its market value and move decisively towards economically sustainable and financially viable asset management. In this paper, we introduce a decision‐making framework based on stochastic optimization that allows wind power producers to hedge their position in the market by trading physically settled options in futures markets in conjunction with their participation in the short‐term electricity markets. The proposed framework relies on a series of two‐stage stochastic optimization models that identify a combined trading strategy for wind power producers actively participating in both financial and day‐ahead electricity markets. The proposed models take into consideration penalties from potential deviations between day‐ahead market offers and real‐time operation and incorporates different preferences of risk aversion, enabling a trade‐off between the expected profit and its variability. Empirical analysis based on data from the Nordic region illustrates high efficiency of the stochastic model and reveals increased revenues for both risk neutral and risk averse wind producers opting for combined strategies.     

Effects of stochastic energy prices on long-term energy-economic scenarios

In view of the currently observed energy prices, recent price scenarios, which have been very moderate until 2004, also tend to favor high future energy prices. Having a large impact on energy-economic scenarios, we incorporate uncertain energy prices into an energy systems model by including a stochastic risk function. Energy systems models are frequently used to aid scenario analysis in energy-related studies. The impact of uncertain energy prices on the supply structures and the interaction with measures in the demand sectors is the focus of the present paper.

For the illustration of the methodological approach, scenarios for four EU countries are presented. Including the stochastic risk function, elements of high energy price scenarios can be found in scenarios with a moderate future development of energy prices. In contrast to scenarios with stochastic investment costs for a limited number of technologies, the inclusion of stochastic energy prices directly affects all parts of the energy system. Robust elements of hedging strategies include increasing utilization of domestic energy carriers, the use of CHP and district heat and the application of additional energy-saving measures in the end-use sectors. Region-specific technology portfolios, i.e., different hedging options, can cause growing energy exchange between the regions in comparison with the deterministic case.