FORECASTING ENERGY FUTURES VOLATILITY USING INTRADAY DATA Julien Chevallier, Imperial College London, UK, +44(0)20.7594.5796, firstname.lastname@example.org Florian Ielpo, Pictet Asset Management, Switzerland, +41 583231204, email@example.com Benoit Sevi, University of Angers, France, +33(0)184.108.40.206.34, firstname.lastname@example.org 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 Agnolucci, P., 2009. Volatility in crude oil futures: a comparison of the predictive ability of GARCH and implied volatility models. Energy Economics 31, 316-321. Andersen, T.G., Benzoni, L., 2009. Realized volatility. In: Andersen, T.G., Davis, R.A., Kreiss, J.-P., Mikosch, Th. (Eds.) Handbook of Financial Time Series, Springer. Andersen, T.G., Bollerslev, T., 1998. Answering the skeptics: yes, standard volatility models do provide accurate forecasts. International Economic Review 39, 885-905. Andersen, T.G., Bollerslev, T., Diebold, F.X., Ebens, H., 2001a. The distribution of stock return volatility. Journal of Financial Economics 61, 43-76. Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2001b. The distribution of exchange rate volatility. Journal of the American Statistical Association 96, 42-55. Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2003. Modeling and forecasting realized volatility. Econometrica 71, 579- 625. Andersen, T.G., Bollerslev, T., Diebold, F.X., 2007. Roughing it up: including jump components in the measurement, modeling and forecasting of return volatility. Review of Economics and Statistics 89, 701-720. Awartani, B.M.A., 2008. Forecasting volatility with noisy jumps: an application to the Dow Jones Industrial Average stocks. Journal of Forecasting 27, 267-278. Awartani, B.M.A., Corradi, V., Distaso, W., 2009. Testing market microstructure effect with an application to the Dow Jones Industrial Average stocks. Journal of Business and Economic Statistics, forthcoming. Bandi, F., Russell, J., 2006. Microstructure Noise, Realized Variance, and Optimal Sampling. The Review of Economic Studies 75, 339-369. Bontemps, C., Meddahi, N., 2005. Testing normality: a GMM approach. Journal of Econometrics 124, 149-186. Chan, K., Chung, Y.P., Fong, W.-M., 2002. The informational role of stock and option volume. Review of Financial Studies 15, 1049-1075. Chen, W.W., Deo, R.S., 2004. Power transformations to induce normality and their applications. Journal of the Royal Statistical Association B 66, 117-130. Corsi, F., 2004. A simple approximate long memory model of realized volatility. Journal of Financial Econometrics, forthcoming. Corsi, F., Mittnik, S., Pigorsch, C., Pigorsch, U., 2008. The volatility of realized volatility. Econometric Reviews 27, 46-78. Deo, R., Hurvich, C., Lu, Y., 2006. Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment. Journal of Econometrics 131, 29-58. Duong, H.N., Kalev, P.S., 2008. The Samuelson Hypothesis in futures markets: an analysis using intraday data. Journal of Banking and Finance 32, 489-500. Fong, W.M., See, K.H., 2002. A Markov switching model of the conditional volatility of crude oil futures prices. Energy Economics 24, 71-95. Giot, P., Laurent, S., 2003. Value-at-Risk for long and short positions. Journal of Applied Econometrics 18, 641-664. Giot, P., Laurent, S., 2004. Modelling daily Value-at-Risk using realized volatility and ARCH type models. Journal of Empirical Finance 11, 379-398. Gonçalves, S., Meddahi, N., 2008. Box-Cox transforms for realized volatility. Unpublished manuscript. Gonçalves, S., Meddahi, N., 2009. Bootstrapping realized volatility. Econometrica 77, 283-306. Hull, J.C., White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance 42, 281-300. Jiang, G.J., Tian, Y.S., 2005. The Model-Free Implied Volatility and Its Information Content. The Review of Financial Studies 18, 1305-1342. Kalev, P.S., Duong, H.N., 2008. A Test of the Samuelson Hypothesis Using Realized Range. Journal of Futures Markets 28, 680- 696. Koopman, S.J., Jungbacker, B., Hol, E., 2005. Forecasting daily variability of the S\&P 100 stock index using historical, realised and implied volatility measurements, Journal of Empirical Finance 12, 445-475. Martens, M., Zein, J., 2004. Predicting Financial Volatility: High-Frequency Time-Series Forecasts Vis-à-Vis Implied Volatility. Journal of Futures Markets 24, 1005-1029. McAleer, M., Medeiros, M.C., 2008. Realized volatility: a review. Econometric Reviews 27, 10-45. Timmermann, A., 2006. Forecast Combinations. in Handbook of Economic Forecasting 1, edited by Elliott, G., Granger, C., Timmermann, A., Elsevier. Wang, T., Wu, J., Yang, J., 2008. Realized Volatility and Correlation in Energy Futures Markets. Journal of Futures Markets 28, 993-1011. Yang, C., Bandi, F.M., Russell, J.R., 2008. Realized volatility forecasting and option pricing. Journal of Econometrics 147, 34-46.
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