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					FORECASTING ENERGY FUTURES VOLATILITY USING INTRADAY DATA
                                 Julien Chevallier, Imperial College London, UK, +44(0)20.7594.5796, j.chevallier@imperial.ac.uk
                                           Florian Ielpo, Pictet Asset Management, Switzerland, +41 583231204, fielpo@pictet.com
                                           Benoit Sevi, University of Angers, France, +33(0)2.40.14.17.34, benoit.sevi@gmail.com




       Overview
Using NYMEX intraday (tick-by-tick) data for the light sweet crude oil and natural gas futures, we use realized volatility measures
to forecast the volatility of crude oil and natural gas at an horizon of 1, 5 and 10 days (Awartani, 2008). The use of realized
volatility measures for oil and natural gas appears especially important for three reasons. First, data at an ultra high frequency
allows us to obtain better volatility forecasts compared with those derived from daily data (see Corsi et al., 2008, Andersen et al.
(2001a, b, 2003, 2007)) when the true volatility process is thought to the diffusive component of a stochastic process of general
form thus measured by the integrated volatility (see the surveys of Andersen and Benzoni (2008) or McAleer and Medeiros (2008)
for an introduction to this topics). Second, realized volatility measures appear to be useful for option pricing. The issue of
stochastic volatility in this setting has been raised by Hull and White (1987) and many measures of volatility have been proposed in
the literature to accommodate this assumption. Realized volatility appears to be the most successful candidate for this purpose as
shown recently in Yang et al. (2008) (see also references therein for an overview of this literature). Third, realized volatility
measures appear central to risk management strategies as well as for portfolio selection (see Giot and Laurent (2003, 2004) for
developments about Value-at-Risk and Fleming et al. (2003) for the comparative advantage of using realized measures for
investing). Fourth, the measure of realized volatility allows a broader comparison of several volatility measures including implied
volatility and volatility extracted from daily data using parametric such as GARCH or SV models (Koopman et al., 2005).

       Methods
Previous literature on volatility forecasting using energy data may be broadly characterized in three strands. The first strand
(Martens and Zein, 2004) compares the predictive power of ultra high-frequency time-series forecasts with implied volatility
measures for several forward exchanges rates, equity and energy futures including light sweet crude oil, but not natural gas. The
authors show that volatility forecasts based on intraday returns tend to provide superior results. However, their study does not allow
for a comparison of several criteria for forecasting techniques. In addition, the authors do not consider the possible presence of
jumps which may considerably impact the measure of the diffusive component of the process, what we do (see Andersen et al.
(2007) and Awartani (2008) for similar contributions on this issue). The second strand (Wang et al., 2008) concentrates on realized
volatility and correlation in energy futures markets, including the NYMEX light sweet crude oil and the Henry-Hub natural gas
futures. The authors focus on the distributional properties of futures data but the dynamic properties are not studied, precluding any
forecasting exercise. The third strand (Kalev and Duong (2008), Duong and Kalev (2008)) provides an analysis of the Samuelson
hypothesis in futures markets using intraday data including, among many other contracts, crude oil but not natural gas. These papers
concentrate on the volatility level near contracts' expiration, what we also consider in our paper, but have two main drawbacks.
First, the possible presence of jumps is ignored and second, no thorough analysis of the optimal sampling frequency is provided, in
spite of the lower liquidity of energy futures markets compared with financial futures markets.

       Results
Our contribution to the literature of volatility forecasting for energy markets may be summarized as follows: (i) we provide a
complete study of the realized volatility measures on both the oil and gas markets, including optimal sampling frequency tests
(Bandi and Russell (2006), Awartani et al. (2009)). The normality of standardized residuals, which is necessary assumption for the
use of Black and Scholes pricing formulae, is tested using the method of moments as in Bontemps and Meddahi (2005) (ii) our
forecasting results include a comparison of several criteria (MSE, RMSE, MAD) to obtain best forecasts when forecast
combination is used (see Timmermann, 2006)); (iii) we investigate different techniques to derive implied volatility measures (first
by inverting numerically the Black-Scholes formula as in Agnolucci (2009) and then by applying model-free estimators as
proposed recently in Jiang and Tian (2005)); (iv) we test for the relative merits of the Heterogenous Autoregressive Model (HAR)
introduced in Corsi (2004) and commonly used in the literature yet and long memory (ARFIMA) models in modeling the dynamics
of realized volatility for oil and natural gas futures, after a transformation of our series, as in Chen and Deo (2004) or Gonçalves
and Meddahi (2008), to better approximate Gaussianity. Collectively, our results aim at documenting the properties of oil and
natural gas futures in terms of volatility using different frequencies, and at improving forecasting performance using long memory
components (Deo et al., 2006).




References

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Andersen, T.G., Bollerslev, T., Diebold, F.X., Ebens, H., 2001a. The distribution of stock return volatility. Journal of Financial
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