Volume and volatility in European electricity markets

Transcription

1 Volume and volatility in European electricity markets Roberto Renò Dipartimento di Economia Politica, Università di Siena Commodities Birkbeck, January 2007 p. 1/29

2 Joint work with: Francesca Fontana, now specializing at CORIPE, Torino, Italy Angelica Gianfreda, lecturing at University of York Davide Pirino, Ph.D. student, University of Pisa, Italy Commodities Birkbeck, January 2007 p. 2/29

3 Introduction and motivation We study the link between volatility and volume in European markets Commodities Birkbeck, January 2007 p. 3/29

4 Introduction and motivation We study the link between volatility and volume in European markets We analyze hourly and daily electricity prices and volumes of Germany, The Netherlands, France, Spain Commodities Birkbeck, January 2007 p. 3/29

5 Introduction and motivation We study the link between volatility and volume in European markets We analyze hourly and daily electricity prices and volumes of Germany, The Netherlands, France, Spain We study the drift and volatility of normal operational status with non-parametric techniques Commodities Birkbeck, January 2007 p. 3/29

6 Time series of prices Germany France The Netherlands Spain Commodities Birkbeck, January 2007 p. 4/29

7 Volume detrending We do not directly use volume as our regressor, but the detrended volume, defined after estimating the regression: V t = C+ αt + ε t, where V t is the observed volume at day t and ε t is IID noise. Commodities Birkbeck, January 2007 p. 5/29

8 Volume detrending We do not directly use volume as our regressor, but the detrended volume, defined after estimating the regression: V t = C+ αt + ε t, where V t is the observed volume at day t and ε t is IID noise. Ṽ t = V t ˆαt Commodities Birkbeck, January 2007 p. 5/29

9 Time series of detrended volumes Germany France The Netherlands Spain Commodities Birkbeck, January 2007 p. 6/29

10 First approach: GARCH modelling We use daily data (intraday data averaged with volumes). r t = logp t logp t 1 Commodities Birkbeck, January 2007 p. 7/29

11 First approach: GARCH modelling We use daily data (intraday data averaged with volumes). r t = logp t logp t 1 6 r t = µ+ δr t 1 + c i D i + ε t ht i=1 6 h t = ω+ d i D i + αrt βh t 1 + γ ˆV t i=1 Commodities Birkbeck, January 2007 p. 7/29

12 First approach: GARCH modelling We use daily data (intraday data averaged with volumes). r t = logp t logp t 1 6 r t = µ+ δr t 1 + c i D i + ε t ht i=1 6 h t = ω+ d i D i + αrt βh t 1 + γ ˆV t i=1 We exclude prices larger than a given threshold T = 50, 70, 90 (Euros/Megawatt). Commodities Birkbeck, January 2007 p. 7/29

13 Related literature Carnero, M. A., S. J. Koopman, and M. Ooms (2003). Periodic heteroskedastic RegARFIMA models for daily electricity spot prices. Working Paper. Escribano, A., J. Pena, and P. Villaplana (2002). Modelling electricity prices: International evidence. Working paper, Universidad Carlo III de Madrid. Goto, M. and G. Karolyi (2004). Understanding electricity price volatility within and across marketa. Working paper, Ohio University. Guirguis, H. and F. Felder (2004). Further advances in forecasting day-ahead electricity prices using time series models. KIEE International Transactions on PE 4-A(3), Hadsell, L., A. Marathe, and H. Shawky (2004). Estimating the volatility of wholesale electricity spot prices in the US. The Energy Journal 25(4), Karakatsani, N. V. and D. W. Bunn (2004). Modelling stochastic volatility in high-frequency spot electricity prices. Working paper, London Business School. Commodities Birkbeck, January 2007 p. 8/29

14 GARCH estimates - mean equation France Germany Threshold δ ( 0.049) ( 0.039) ( 0.037) ( 0.029) ( 0.028) ( 0.028) µ ( 0.024) ( 0.019) ( 0.018) ( 0.019) ( 0.016) ( 0.016) c c c c c c Commodities Birkbeck, January 2007 p. 9/29

15 GARCH estimates - variance equation France Germany Threshold ω α β γ ( 1.140) ( 1.680) ( 2.150) ( 0.320) ( 0.348) ( 0.365) d d d d d d Commodities Birkbeck, January 2007 p. 10/29

16 Regression-based approach log ˆσ t 2 = α+λ 1 log ˆσ t λ 2 log ˆσ t λ 3 log ˆσ t e i D i + γ ˆV t + ε t i=1 Commodities Birkbeck, January 2007 p. 11/29

17 Regression-based approach log ˆσ t 2 = α+λ 1 log ˆσ t λ 2 log ˆσ t λ 3 log ˆσ t e i D i + γ ˆV t + ε t i=1 To estimate ˆσ 2 t, we use realized volatility: ˆσ t 2 = (log pt 1 log pt 1) (log pt h log pt 1 h 1 )2 h=2 Commodities Birkbeck, January 2007 p. 11/29

18 Regression-based approach log ˆσ t 2 = α+λ 1 log ˆσ t λ 2 log ˆσ t λ 3 log ˆσ t e i D i + γ ˆV t + ε t i=1 To estimate ˆσ 2 t, we use realized volatility: ˆσ t 2 = (log pt 1 log pt 1) (log pt h log pt 1 h 1 )2 h=2 We cut intraday prices larger than a given threshold T. Commodities Birkbeck, January 2007 p. 11/29

19 Time series of realized volatilities Germany France The Netherlands Spain Commodities Birkbeck, January 2007 p. 12/29

20 Estimates - using intraday prices France Germany Threshold λ λ λ γ e e e e e e R Commodities Birkbeck, January 2007 p. 13/29

21 Discussion of results Why do we observe a null relation between volatility and volume? Commodities Birkbeck, January 2007 p. 14/29

22 Discussion of results Why do we observe a null relation between volatility and volume? In financial market, it takes volume to move prices. That is, the relation is positive (Karpoff, 1987) and driven by less informed agents (Daigler and Wiley, 1999). Commodities Birkbeck, January 2007 p. 14/29

23 Discussion of results Why do we observe a null relation between volatility and volume? In financial market, it takes volume to move prices. That is, the relation is positive (Karpoff, 1987) and driven by less informed agents (Daigler and Wiley, 1999). Many theoretical models explain this positive relation. Commodities Birkbeck, January 2007 p. 14/29

24 Theoretical models Mixture of Distributions Hyphotesis (Clark, 1973) Commodities Birkbeck, January 2007 p. 15/29

25 Theoretical models Mixture of Distributions Hyphotesis (Clark, 1973) Dispersion of beliefs (Tauchen and Pitts, 1983; Shalen, 1993) Commodities Birkbeck, January 2007 p. 15/29

26 Theoretical models Mixture of Distributions Hyphotesis (Clark, 1973) Dispersion of beliefs (Tauchen and Pitts, 1983; Shalen, 1993) Information asymmetry (Epps and Epps, 1976) Commodities Birkbeck, January 2007 p. 15/29

27 Theoretical models Mixture of Distributions Hyphotesis (Clark, 1973) Dispersion of beliefs (Tauchen and Pitts, 1983; Shalen, 1993) Information asymmetry (Epps and Epps, 1976) Strategic models (Admati and Pfleiderer, 1988; Foster and Viswanathan, 1990) Commodities Birkbeck, January 2007 p. 15/29

28 Theoretical models Mixture of Distributions Hyphotesis (Clark, 1973) Dispersion of beliefs (Tauchen and Pitts, 1983; Shalen, 1993) Information asymmetry (Epps and Epps, 1976) Strategic models (Admati and Pfleiderer, 1988; Foster and Viswanathan, 1990) Risk aversion (Wang, 1994) Commodities Birkbeck, January 2007 p. 15/29

29 Theoretical models Mixture of Distributions Hyphotesis (Clark, 1973) Dispersion of beliefs (Tauchen and Pitts, 1983; Shalen, 1993) Information asymmetry (Epps and Epps, 1976) Strategic models (Admati and Pfleiderer, 1988; Foster and Viswanathan, 1990) Risk aversion (Wang, 1994) Commodities Birkbeck, January 2007 p. 15/29

30 What happens in electricity markets? Electricity traders are risk averse, as shown in the term structure of forward contracts (Longstaff and Wang, 2002) Commodities Birkbeck, January 2007 p. 16/29

31 What happens in electricity markets? Electricity traders are risk averse, as shown in the term structure of forward contracts (Longstaff and Wang, 2002) Volume is influenced by seasonals and business cycles Commodities Birkbeck, January 2007 p. 16/29

32 What happens in electricity markets? Electricity traders are risk averse, as shown in the term structure of forward contracts (Longstaff and Wang, 2002) Volume is influenced by seasonals and business cycles Speculation is difficult in electriciy markets; substantial information simmetry between market partecipants Commodities Birkbeck, January 2007 p. 16/29

33 What happens in electricity markets? Electricity traders are risk averse, as shown in the term structure of forward contracts (Longstaff and Wang, 2002) Volume is influenced by seasonals and business cycles Speculation is difficult in electriciy markets; substantial information simmetry between market partecipants Most of trading is for liquidity reasons. Commodities Birkbeck, January 2007 p. 16/29

34 What happens in electricity markets? Electricity traders are risk averse, as shown in the term structure of forward contracts (Longstaff and Wang, 2002) Volume is influenced by seasonals and business cycles Speculation is difficult in electriciy markets; substantial information simmetry between market partecipants Most of trading is for liquidity reasons. Does volatility display heteroskedasticity? Commodities Birkbeck, January 2007 p. 16/29

35 Nonparametric estimation To answer this final question, we have first to separate the normal operational status from spikes, as in Geman and Roncoroni (2006). Commodities Birkbeck, January 2007 p. 17/29

36 Nonparametric estimation To answer this final question, we have first to separate the normal operational status from spikes, as in Geman and Roncoroni (2006). However, a simple threshold in price, as above, is not enough. Commodities Birkbeck, January 2007 p. 17/29

37 Nonparametric estimation To answer this final question, we have first to separate the normal operational status from spikes, as in Geman and Roncoroni (2006). However, a simple threshold in price, as above, is not enough. We use the above model in combination with threshold estimators. Commodities Birkbeck, January 2007 p. 17/29

38 The modulus of continuity Our idea to disentangle diffusion from jumps is based on the modulus of continuity of the Brownian motion: r(δ) = 2δlog 1 δ which has the following property, as established by Lévy: P lim sup δ 0 max W(t) W(s) t s δ r(δ) = 1 = 1 It measures the speed at which the BM shrinks to zero. Commodities Birkbeck, January 2007 p. 18/29

39 The intuition When δ 0, diffusive variations go to zero, while jumps do not. Moreover, we know the rate at which the diffusive variations shrink to zero: the modulus of continuity. Commodities Birkbeck, January 2007 p. 19/29

40 The intuition When δ 0, diffusive variations go to zero, while jumps do not. Moreover, we know the rate at which the diffusive variations shrink to zero: the modulus of continuity. Thus, we can identify the jumps as those variations which are larger than a suitable threshold ϑ(δ) which goes to zero, as δ 0, slower than r(δ). Commodities Birkbeck, January 2007 p. 19/29

41 The theorem (Mancini, 2004) Suppose X = Y + J, where Y is a Brownian martingale plus drift and J is a jump process with counting process N with E[N T ] < and time horizon T <. If ϑ(δ) is a real deterministic function such that lim ϑ(δ) = 0 and lim δ 0 δ 0 δlog 1 δ ϑ(δ) = 0 then for P-almost all ω, δ(ω) such that δ < δ(ω) we have i = 1,...,n, I { N=0} (ω) = I {( X) 2 ϑ(δ)}(ω). Commodities Birkbeck, January 2007 p. 20/29

42 The non-parametric model r t+1 = µ(r t )+σ(r t ) ε t + dj t Commodities Birkbeck, January 2007 p. 21/29

43 The non-parametric model r t+1 = µ(r t )+σ(r t ) ε t + dj t First we separate dj from continuous variations Commodities Birkbeck, January 2007 p. 21/29

44 The non-parametric model r t+1 = µ(r t )+σ(r t ) ε t + dj t First we separate dj from continuous variations Then we estimate the functions µ and σ. Commodities Birkbeck, January 2007 p. 21/29

45 Threshold estimation Jumps are detected using threshold estimation: r 2 t 9 ϑ t. Commodities Birkbeck, January 2007 p. 22/29

46 Threshold estimation Jumps are detected using threshold estimation: r 2 t 9 ϑ t. For the threshold, we use the above model as an auxiliary model: r t = µ+ δr t 1 + h t = ω+ 6 c i D i + ε t ht i=1 6 d i D i + αrt βh t 1 i=1 Commodities Birkbeck, January 2007 p. 22/29

47 Threshold estimation Jumps are detected using threshold estimation: r 2 t 9 ϑ t. For the threshold, we use the above model as an auxiliary model: r t = µ+ δr t 1 + h t = ω+ 6 c i D i + ε t ht i=1 6 d i D i + αrt βh t 1 i=1 We set ϑ t equal to the filtered values of h t. Commodities Birkbeck, January 2007 p. 22/29

48 Jump fast mean reversion We have to face the problem of fast jump mean-reversion. To accommodate for this problem, if we detect a jump at time t, do not modify the threshold for the next time instant, that is r 2 t 9h t = h t +1 = h t. Commodities Birkbeck, January 2007 p. 23/29

49 Jump fast mean reversion We have to face the problem of fast jump mean-reversion. To accommodate for this problem, if we detect a jump at time t, do not modify the threshold for the next time instant, that is r 2 t 9h t = h t +1 = h t. We iterate the filtering technique until no more jumps are detected. Commodities Birkbeck, January 2007 p. 23/29

50 Jump fast mean reversion We have to face the problem of fast jump mean-reversion. To accommodate for this problem, if we detect a jump at time t, do not modify the threshold for the next time instant, that is r 2 t 9h t = h t +1 = h t. We iterate the filtering technique until no more jumps are detected. It works! Commodities Birkbeck, January 2007 p. 23/29

51 Jump fast mean reversion We have to face the problem of fast jump mean-reversion. To accommodate for this problem, if we detect a jump at time t, do not modify the threshold for the next time instant, that is r 2 t 9h t = h t +1 = h t. We iterate the filtering technique until no more jumps are detected. It works! Few iterations are enough for convergence. Commodities Birkbeck, January 2007 p. 23/29

52 Nadaraya-Watson threshold estimators ˆµ(x) = N N 1 i=1 K( r i ) x h (ri+1 r i )I {r 2 T N i=1 K ( r i ) x h ) (ri+1 r i ) 2 I {r 2 ) ˆσ(x) = N N 1 i=1 K( r i x h T N i=1 K ( r i x h where K (.) is the standard Gaussian kernel: K (y) = 1 2π e y2 2. i ϑ i} i ϑ i} Commodities Birkbeck, January 2007 p. 24/29

53 The bandwidth parameter The bandwidth parameter h is set according to the typical thumb rule: h = h s σ N 5 Commodities Birkbeck, January 2007 p. 25/29

54 The bandwidth parameter The bandwidth parameter h is set according to the typical thumb rule: h = h s σ N 5 σ is the sample standard deviation (of the filtered data!) Commodities Birkbeck, January 2007 p. 25/29

55 The bandwidth parameter The bandwidth parameter h is set according to the typical thumb rule: h = h s σ N 5 σ is the sample standard deviation (of the filtered data!) You have to choose h s (here we set h s = 3.2). Commodities Birkbeck, January 2007 p. 25/29

56 Drift estimation Commodities Birkbeck, January 2007 p. 26/29

57 Volatility estimation Commodities Birkbeck, January 2007 p. 27/29

58 What did we neglect? Commodities Birkbeck, January 2007 p. 28/29

59 What did we neglect? Jumps! Commodities Birkbeck, January 2007 p. 28/29

60 What did we neglect? Jumps! Cartea, A. and M. G. Figueroa (2005). Pricing in electricity markets: A mean reverting jump diffusion model with seasonality. Applied Mathematical Finance 12(5), Geman, H. and A. Roncoroni (2006). Understanding the fine structure of electricity prices. Journal of Business 79(3). Huisman, R. and R. Mahieu (2003). Regime jumps in electricity prices. Energy Economics 25(5), Kanamura, T. and K. Ohashi (2004). A structural model for electricity prices with spikes. Working paper, Hitotsubashi University. Mount, T. D., Ning, Y. and Cai, X. (2006). Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters. Energy Economics 28, Commodities Birkbeck, January 2007 p. 28/29

61 Summary and conclusions It does not take volume to move electricity prices (at least, in European market) Commodities Birkbeck, January 2007 p. 29/29

62 Summary and conclusions It does not take volume to move electricity prices (at least, in European market) We use two different specifications: GARCH based and realized volatility based Commodities Birkbeck, January 2007 p. 29/29

63 Summary and conclusions It does not take volume to move electricity prices (at least, in European market) We use two different specifications: GARCH based and realized volatility based We discuss this result under the light of theories on informed trading borrowed by financial economics Commodities Birkbeck, January 2007 p. 29/29

64 Summary and conclusions It does not take volume to move electricity prices (at least, in European market) We use two different specifications: GARCH based and realized volatility based We discuss this result under the light of theories on informed trading borrowed by financial economics We propose a procedure to separate spikes from normal operation behaviour Commodities Birkbeck, January 2007 p. 29/29

65 Summary and conclusions It does not take volume to move electricity prices (at least, in European market) We use two different specifications: GARCH based and realized volatility based We discuss this result under the light of theories on informed trading borrowed by financial economics We propose a procedure to separate spikes from normal operation behaviour We estimate non-parametrically drift and volatility of electricity price returns Commodities Birkbeck, January 2007 p. 29/29

66 Summary and conclusions It does not take volume to move electricity prices (at least, in European market) We use two different specifications: GARCH based and realized volatility based We discuss this result under the light of theories on informed trading borrowed by financial economics We propose a procedure to separate spikes from normal operation behaviour We estimate non-parametrically drift and volatility of electricity price returns European markets are pretty similar! Commodities Birkbeck, January 2007 p. 29/29