Ederington's ratio with production flexibility

The impact of flexibility upon hedging decision is examined for a competitive firm under demand uncertainty. We show that if the firm can adapt its production subsequently to its hedging decision, the standard minimum variance hedge ratio from Ederington (Journal of Finance 34, 1979) is systematically biased. This resulting bias depends on the statistical relation between demand and futures prices.

On the volatility-volume relationship in energy futures markets using intraday data

This paper investigates the relationship between trading volume and price volatility in the crude oil and natural gas futures markets when using high-frequency data. By regressing various realized volatility measures (with/without jumps) on trading volume and trading frequency, our results feature a contemporaneous and largely positive relationship. Furthermore, we test whether the volatility-volume relationship is symmetric for energy futures by considering positive and negative realized semivariance. We show that (i) an asymmetric volatility-volume relationship indeed exists, (ii) trading volume and trading frequency significantly affect negative and positive realized semivariance, and (iii) the information content of negative realized semivariance is higher than for positive realized semivariance.Trading Volume; Price Volatility; Crude Oil Futures; Natural Gas Futures; High-Frequency Data; Realized Volatility; Bipower Variation; Median Realized Volatility; Realised Semivariance; Jump

A special case of self-protection: The choice of a lawyer

Considering self-protection, it is a well-known result that an increase in risk aversion does not unambiguously lead to a higher level of effort. In this paper, we consider a particular case of self-protection, the choice of a lawyer, assuming a positive relation between legal expenses and probability of success. In this context, level of effort is strictly monotone in risk aversion. We show that, paradoxically, the level of effort is not systematically higher for an indemnified more risk-averse agent than for a non-indemnified less risk-averse agent.increase in risk aversion

A reassessment of the risk-return tradeoff at the daily horizon

This note makes two contributions by extending the analysis in Bali and Peng (2006) which investigates the risk-return tradeoff at the daily horizon using high-frequency data. Our first contribution is to show that the empirical relation between returns and risk is not validated for recent years. Our second contribution is to assess the importance of disentangling jumps from the continuous component using high-frequency data and recent nonparametric methods. We show that similar results are obtained using either realized variance or an alternative measure of realized variance which is robust to jumps thereby providing evidence that jumps do not improve significantly the explanatory power in the risk-return relation.risk-return tradeoff, ICAPM, realized volatility, bipower variation, jumps.

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

The recent implementation of the EU Emissions Trading Scheme (EU ETS) in January 2005 created new financial risks for emitting firms. To deal with these risks, options are traded since October 2006. Because the EU ETS is a new market, the relevant underlying model for option pricing is still a controversial issue. This article improves our understanding of this issue by characterizing the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European Climate Exchange (ECX), which is valid during Phase II (2008-2012) of the EU ETS. The realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-distributions hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability. Our conclusions indicate that (i) the standard Brownian motion is not an adequate tool for option pricing in the EU ETS, and (ii) a jump component should be included in the stochastic process to price options, thus providing more efficient tools for risk-management activities.CO2 Price, Realized Volatility, HAR-RV, GARCH, Futures Trading, Emissions Markets, EU ETS, Intraday data, Forecasting

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

The recent implementation of the EU Emissions Trading Scheme (EU ETS) in January 2005 created new financial risks for emitting firms. To deal with these risks, options are traded since October 2006. Because the EU ETS is a new market, the relevant underlying model for option pricing is still a controversial issue. This article improves our understanding of this issue by characterizing the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European Climate Exchange (ECX), which is valid during Phase II (2008-2012) of the EU ETS. The realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-distributions hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability. Our conclusions indicate that (i) the standard Brownian motion is not an adequate tool for option pricing in the EU ETS, and (ii) a jump component should be included in the stochastic process to price options, thus providing more efficient tools for risk-management activities.CO2 Price; Realized Volatility; HAR-RV; GARCH; Futures Trading; Emissions Markets; EU ETS; Intraday data; Forecasting

Revisiting the excess co-movements of commodity prices in a data-rich environment.

We reinvestigate the issue of excess comovements of commodity prices initially raised in Pindyck and Rotemberg (1990). While Pindyck and Rotemberg and following contributions consider this issue using an arbitrary set of control variables, we develop our analysis using recent development in large approximate factor models so that a richer information set can be considered. This ensures that fundamentals, a necessary concept for any excess comovement analysis, are modelled as well as possible. We then consider different measures of correlation to assess comovement and we provide evidence of excess comovement for a set of 8 seemingly unrelated commodities. Our results indicate that excess comovement in returns does exist even when the issue of heteroscedasticity is considered. We extend our analysis to the excess comovement of volatilities and show that, contrary to the case of returns, comovement vanishes once the effect of fundamentals have been taken out.spillover index; heteroscedasticity-corrected correlation; factor models; commodity excess comovement hypothesis;

Do jumps help in forecasting the density of returns?.

The estimation of the jump component in asset pricing has witnessed a considerably growing body of literature. Of particular interest is the decomposition of total volatility between its continuous and jump components. Recent contributions highlight the importance of the jump component in forecasting the volatility at different horizons. In this paper, we extend the methodology developed by Maheu and McCurdy (2011) to measure the information content of intraday data in forecasting the density of returns at horizons up to sixty days. We extract jumps as in Andersen, Bollerslev, Frederiksen and Nielsen (2010) to have a measure of the jumps in returns. Then, we estimate a bivariate model of returns and volatilities where the jump component is indepen- dently modeled. Our empirical results for S&P 500 futures, WTI crude oil futures, the USD/JPY exchange rate and the MacDonald’s stock confirm the importance of considering the continuous/jump decomposition for density forecasting.bivariate model; median realized volatility; bipower variation; realized volatility; jumps; density forecasting;

Volatility transmission and volatility impulse response functions in European electricity forward markets.

A  l’aide de données quotidiennes  sur  la période mars  2001 à  juin  2005, nous estimons un modèle VAR‐BEKK  et montrons  l’existence  de  transmissions  au  niveau  des  rendements  et  des  volatilités  entre  les marchés  forward  de  l’électricité  pour  l’Allemagne,  les  Pays‐Bas  et  la  Grande‐Bretagne. Nous  appliquons  la fonction VIRF de Hafner and Herwartz [2006, Journal of  International Money and Finance 25, 719‐740] afin de mesurer  l’impact  d’un  choc  sur  la  volatilité  conditionnelle. Nous  observons  qu’un  choc  a  un  impact  positif important seulement si son amplitude est grande en regard du niveau de la volatilité à cet instant. Finalement, nous estimons  la densité des  fonctions VIRF pour différents horizons de prévisions.  Ces distributions lissées  sont asymétriques  et montrent que des  évènements extrêmes sont  possibles même si leur  probabilité est faible. Ces résultats ont des implications intéressantes pour les participants au marché dont la politique de gestion des risques est basée sur les prix des options, eux‐mêmes dépendant du niveau de volatilité.Using daily data from March 2001 to June 2005, we estimate a VAR-BEKK model and find evidence of return and volatility spillovers between the German, the Dutch and the British forward electricity markets. We apply Hafner and Herwartz [2006, Journal of International Money and Finance 25, 719–740] Volatility Impulse Response Function (VIRF) to quantify the impact of shock on expected conditional volatility. We observe that a shock has a high positive impact only if its size is large compared to the current level of volatility. The impact of shocks are usually not persistent, which may be a consequence of the non-storability of power. Finally, we estimate the density of the VIRF at different forecast horizons. These fitted distributions are asymmetric and show that large increases in expected conditional volatilities are possible even if their probability is low. These results have interesting implications for market participants whose risk management policy depends on option prices which themselves depend on the characteristics of volatility.volatility spillovers; electricity forward markets; multivariate GARCH; volatility impulse response function; transmission de volatilité; marché forward de l’électricité; GARCH multivarié; Fonction impulsion réponse de volatilité;

On the realized volatility of the ECX CO2 emissions 2008 futures contract: distribution, dynamics and forecasting

The recent implementation of the EU Emissions Trading Scheme (EU ETS) in January 2005 created new financial risks for emitting firms. To deal with these risks, options are traded since October 2006. Because the EU ETS is a new market, the relevant underlying model for option pricing is still a controversial issue. This article improves our understanding of this issue by characterizing the conditional and unconditional distributions of the realized volatility for the 2008 futures contract in the European Climate Exchange (ECX), which is valid during Phase II (2008-2012) of the EU ETS. The realized volatility measures from naive, kernel-based and subsampling estimators are used to obtain inferences about the distributional and dynamic properties of the ECX emissions futures volatility. The distribution of the daily realized volatility in logarithmic form is shown to be close to normal. The mixture-of-distributions hypothesis is strongly rejected, as the returns standardized using daily measures of volatility clearly departs from normality. A simplified HAR-RV model (Corsi, 2009) with only a weekly component, which reproduces long memory properties of the series, is then used to model the volatility dynamics. Finally, the predictive accuracy of the HAR-RV model is tested against GARCH specifications using one-step-ahead forecasts, which confirms the HAR-RV superior ability. Our conclusions indicate that (i) the standard Brownian motion is not an adequate tool for option pricing in the EU ETS, and (ii) a jump component should be included in the stochastic process to price options, thus providing more efficient tools for risk-management activities