Modelling Power Futures Volatility: Comparison of ARMA and GARCH Models based on EEX Data

Transcription

1 Modelling Power Futures Volatility: Comparison of ARMA and GARCH Models based on EEX Data IAEE European Conference 2009, Wien Session 6-VI: Price Volatility Modelling Joachim Benatzky Chair for Management Science 10th September 2009 Introduction Models & Estimation Results Conclusion References 1 / 27

2 Overview Introduction Models & Estimation Results Conclusion Introduction Models & Estimation Results Conclusion References 2 / 27

3 Introduction Introduction Models & Estimation Results Conclusion Introduction Models & Estimation Results Conclusion References 3 / 27

4 Motivation Research interest What are the properties of power futures volatilities? Are there changes in the market behaviour (e.g. better efficiency through higher market liquidity)? Is it possible to detect changes in the behaviour of volatilities over time? How good are volatility forecasts? Why is this interesting? We can learn about the electricity market. Better volatility models can be used for risk management or option pricing purposes. Introduction Models & Estimation Results Conclusion References 4 / 27

5 Recent research in volatility Volatility research mostly in Oil Futures. Sadorsky (2006): Modeling and forecasting petroleum futures volatility WTI, heating oil #2, gasoline and natural gas futures different volatility models TGARCH fits well for heating oil and natural gas volatility GARCH model fits well for crude oil and unleaded gasoline volatility Agnolucci (2009): Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models WTI Futures GARCH type volatility implied volatility (IV) GARCH yields better results for forecasting than IV models Introduction Models & Estimation Results Conclusion References 5 / 27

6 Expectations and hypotheses Expectations from these studies for own research: GARCH models should be able to explain volatility also for electricity futures GARCH models could maybe even forecast volatility. Alternatively maybe an ARMA model could explain volatility behaviour. Further expectations From Efficient Market Hypothesis and standard risk models: constant volatility from Samuelson (1965): more volatility towards maturity Introduction Models & Estimation Results Conclusion References 6 / 27

7 Main differences between oil and power markets Electricity itself is not storable. Futures are traded as base and as peak (delivery Mo Fr, 0800h 2000h) products. More traded products than normally reported for oil futures: month quarter year Probably less speculative traders than in oil. Utilities that trade in the market are interested in a physical balance. Electricity trading is a young market with a short history. Introduction Models & Estimation Results Conclusion References 7 / 27

8 EEX Futures prices Financial Futures Underlying: German power spot price index Phelix for the corresponding time period. Futures are traded continuously during trading hours Monday to Friday. Six traded Futures (Month Base, Month Peak, Quarter Base, Quarter Peak, Year Base, Year Peak) Data used here: 1st October th September 2008 Products used: Month Products: 86; Quarter Products: 34; Year Products: 12 Data used here: closing prices of each trading day no usage of highest and lowest prices here no intraday data Introduction Models & Estimation Results Conclusion References 8 / 27

9 German Futures prices Front products / 1st October th September /MWh YEAR BASE QUARTER BASE MONTH BASE YEAR PEAK QUARTER PEAK MONTH PEAK Introduction Models & Estimation Results Conclusion References 9 / 27

10 Models & Estimation Results Introduction Models & Estimation Results Conclusion Introduction Models & Estimation Results Conclusion References 10 / 27

11 Choice of a volatility model Volatility models used successfully applied to Oil Futures: Daily volatility GARCH volatility Volatility models preferred by finance literature Realised Volatility usage of high-frequency data Implied Volatility usage of option prices but: Both not usable for EEX futures due to lacking intra-day data and missing exchange-traded options Classical volatility model Historical volatility 1 N ( σt = N 1 τ=1 (rτ r)2 ) Daily and GARCH volatility are used in this study. Introduction Models & Estimation Results Conclusion References 11 / 27

12 Daily Volatility σ 1 Log returns of Futures prices: r t = ln(p t ) ln(p t 1 ) (1) Volatility with r as σ 2 1 = r 2 t (2) similar to Sadorsky (2006) Introduction Models & Estimation Results Conclusion References 12 / 27

13 01/Okt/02 Introduction Models & Estimation Results Conclusion References 01/Aug/08 01/Jun/08 01/Apr/08 01/Feb/08 01/Dez/07 01/Okt/07 01/Aug/07 01/Jun/07 01/Apr/07 01/Feb/07 01/Dez/06 01/Okt/06 01/Aug/06 01/Jun/06 01/Apr/06 01/Feb/06 01/Dez/05 01/Okt/05 01/Aug/05 01/Jun/05 01/Apr/05 01/Feb/05 01/Dez/04 01/Okt/04 01/Aug/04 01/Jun/04 01/Apr/04 01/Feb/04 01/Dez/03 01/Okt/03 01/Aug/03 01/Jun/03 01/Apr/03 01/Feb/03 01/Dez/02 Chair for Management Science Volatility: Time Series Mean over all traded products MB MP QB 0.04 QP YB YP / 27

14 Illustration of σ 2 1 Time series / Mean over years MB MP QB QP YB YP Introduction Models & Estimation Results Conclusion References 14 / 27

15 Characteristics of Volatility Time Series Means for σ 2 1 : whole period and Period I (01/10/ /09/2005) and Period II (04/10/ /09/2008) mean std. dev. period I period II MB MP QB QP YB YP very persistence autocorrelation Seasonal influences? Introduction Models & Estimation Results Conclusion References 15 / 27

16 Methodology Including all available information for each product for the estimation. Parameter estimation for each day and day-ahead forecast with these estimations. Parameter estimations reported here are values for front products dated at the last trading day before maturity. Estimation with Eviews. Introduction Models & Estimation Results Conclusion References 16 / 27

17 ARMA(X) model σ 2 t = α 0 + α 1 σ 2 t 1 + β 1 ε t 1 + β X X (3) Following model configuration were being tested by using Eviews AR(1) MA(1) ARMA(1,1) AR(1) X with day to maturity as linear and as exponential function First results ARMA(1,1): no stable parameter estimations; estimations for α1 very near 1 and β 1 near 1 Introduction Models & Estimation Results Conclusion References 17 / 27

18 Parameter Estimations AR(1) α 0 α 0 t β 1 β 1 t MB whole sample Period I Period II MP whole sample Period I Period II QB whole sample Period I Period II QP whole sample Period I Period II YB whole sample YP whole sample Introduction Models & Estimation Results Conclusion References 18 / 27

19 Parameter Estimations AR(1)X α 0 α 0 t β X β X t β 1 β 1 t MB whole sample Period I Period II MP whole sample Period I Period II QB whole sample Period I Period II QP whole sample Period I Period II YB whole sample YP whole sample Introduction Models & Estimation Results Conclusion References 19 / 27

20 ARMA(X) models Volatility Forecast Forecasting routine rolling window minimum of observations: 20 daily parameter estimation one day ahead out-of-sample forecast four models t 1 model 1: σ 2 t = 1 t 1 i=0 σ2 i as a naive benchmark model 2: AR(1) model model 3: AR(1) X model Introduction Models & Estimation Results Conclusion References 20 / 27

21 Volatility Forecast / MSE model 1 model 2 model 3 MB full sample 6.820E E E-06 period I 5.297E E E-06 period II 8.029E E E-06 MP full sample 2.207E E E-06 period I 2.054E E E-06 period II 2.338E E E-06 QB full sample 1.267E E E-07 period I 8.307E E E-07 period II 2.231E E E-07 QP full sample 1.525E E E-07 period I 1.514E E E-07 period II 1.626E E E-07 YB full sample 5.647E E E-08 period I 2.721E E E-08 period II 9.811E E E-07 YP full sample 4.288E E E-08 period I 2.098E E E-08 period II 5.791E E E-08 Introduction Models & Estimation Results Conclusion References 21 / 27

22 GARCH model r t = c + ε t σ 2 GARCH,t = κ + γσ 2 t 1 + δε 2 t 1 (5) with γ + δ < 1; κ > 0; γ 0; δ 0 and r t as daily log return of futures prices; c is assumed to be 0. Following model configuration were being tested by using Eviews ARCH(1) GARCH(1,1) (4) Introduction Models & Estimation Results Conclusion References 22 / 27

23 Results for GARCH models In contrast to Oil Futures no success for simple GARCH models. Parameter estimations for ARCH(1) and GARCH(1,1) models often result in γ + δ > 1; same for ARCH(1). hopefully better results with EGARCH oder GARCH-in-mean Introduction Models & Estimation Results Conclusion References 23 / 27

24 Conclusion Introduction Models & Estimation Results Conclusion Introduction Models & Estimation Results Conclusion References 24 / 27

25 Conclusion Some expectations were disappointed: Electricity Futures do not have the same properties as Oil Futures possibility for further research. This study shows at least that an AR(1) and AR(1) X models can explain some movements of volatilities. Changing properties of EEX Futures between the two periods in period : higher volatility, less autoregression, but more Samuelson effect More volatility caused by higher liquidity? Day-ahead-forecast in second period worse than in first period. Further steps Deeper investigation in volatility persistence More research in other GARCH models Introduction Models & Estimation Results Conclusion References 25 / 27

26 Invitation to INREC st International Ruhr Energy Conference 5th 6th October 2009 Essen, Germany Introduction Models & Estimation Results Conclusion References 26 / 27

27 References Agnolucci, Paolo (2009). Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models. In: Energy Economics 31.2, Sadorsky, Perry (2006). Modeling and forecasting petroleum futures volatility. In: Energy Economics 28.4, pp issn: doi: DOI: /j.eneco url: 1/2/6d1abc1b0df5f f134c1293. Samuelson, Paul A. (1965). Proof that properly anticipated prices fluctuate randomly. In: Industrial Management Review 6.2, pp Introduction Models & Estimation Results Conclusion References 27 / 27