Modelling Electricity Spot Prices A Regime-Switching Approach

Transcription

1 Modelling Electricity Spot Prices A Regime-Switching Approach Dr. Gero Schindlmayr EnBW Trading GmbH Financial Modelling Workshop Ulm September 2005 Energie braucht Impulse

2 Agenda Model Overview Daily Price Process Hourly Profile Process Backtesting Applications Outlook 2

3 Electricity Spot Prices Features seasonality (yearly, weekly, daily) spikes Explanation power not efficiently storable => no cash-and-carry arbitrage inelastic demand curve seasonal weather-dependent demand pattern events can cause market shocks (plant outages, low water levels, extreme temperature) 3

4 Marginal Costs of Generation costs include CO2 emission certificates Demand??? brown coal nuclear coal oil equilibrium price gas 4

5 Historical Hourly Spot Prices EEX 5

6 Fundamental and Stochastic Approaches Fundamental model system generation and load price = marginal generation costs needs fuel prices and data about generation capacity many sources of uncertainty (generation, import/export, ) Stochastic view power prices as time series choose appropriate stochastic process calibrate to price data needs only prices as input data Hybrid use both approaches (e.g. SMaPS 1 ) Here we concentrate on the stochastic approach! 1 M.Burger, B.Klar, A.Müller, G.Schindlmayr A spot market model for pricing derivatives in electricity markets, Quantitative Finance 4 (2004)

7 Model Overview Notation: hourly log prices regime-switching AR(1)-process daily mean log price s(t) daily log profile h(t) PCA-decomposition + ARMA-process Different processes for business days and non-business days 7

8 Daily Price Process: Seasonality Seasonal component: dummy variables for weekdays, holidays, vacation periods (1,..,N d ) sin/cos regressors for yearly seasonality linear trend 8

9 Daily Price Process: Seasonal Component EEX 9

10 Daily Price Process: Regime-Switching AR(1) Model: r k = regime at time k transition matrix (for two regimes): calibration: Hamilton filter (max. likelihood optimization) example: EEX (Jan 01 May 05) 10

11 Daily Price Process: Regime Identification residuals probability spike regime 11

12 Daily Price Process: Autocorrelation of Residuals 12

13 Daily Price Process: Q-Q Plot of Residuals 13

14 Hourly Profiles: PCA Decomposition Regression: seasonal component PCA decomposition for 24h-residuals stochastic model for factor loads ARMA(p,q) for z i k For spike regime: take random historical profile according to season and weekday 14

15 Hourly Profiles: Seasonal Component 15

16 Hourly Profiles: Principal Component Vectors 16

17 Hourly Profiles: PCA Explained Variance 17

18 Hourly Profiles: Factor Load Autocorrelation of Residuals 18

19 The Long-Term Dynamics Model: f(t) : seasonal (deterministic) component y t : regime-switching process h t : hourly profile process l t : long term process t Future price: for T>>t short term dynamics: long term dynamics long-term approximation: Black s future price model Calibration s = f ( t) + y + h + l t t t t t l µ + "! = ( t # 2 " l ) [ yt ]! E[ yt ], Et[ ht ] E[ ht ] = E [ S ]! C( T ) [ exp( l )] E! F t, T t T Et l l t t 19 historical volatility or implied volatility (depending on application)

20 Simulation Results: Sample Paths 20

21 Simulation Results: Histogram Prices /MWh 21

22 Backtesting: Calibration Stability moving two-year calibration period parameter base regime parameter spike regime transition probabilities 22

23 Backtesting: 1-Day-Forecasting Quality (excl. Holidays) Holidays 23

24 Backtesting: Quantile-Statistics How do the probability distributions compare? histogram to analyze, how often the real spot price falls into which quantile of the model distribution period: calibration off-sample (uses data from ) frequency 24 quantile

25 Applications: Option Pricing Electricity Option Option on Forwards Underlying: Forward contract for delivery month/quarter/year Swing Option Daily/hourly exercise energy constraints Daily/Hourly Option Virtual Power Plants Hourly exercise multi-commodity technical constraints Strip of options for daily/hourly exercise Underlying: daily product (base/peak) or single hour 25

26 Applications: Option Pricing and Hedging Hourly call option period: 01/01/ /01/2007 strike: 60 /MWh capacity: 10 MW Pricing results price: inner value: profit-at-risk (95%): mean exercise 16 GWh (1600 h) 26

27 Applications: Mean Exercise Schedule MW January

28 Applications: Hedging Strategies energetic hedging calculate mean exercise schedule sell energetic equivalent base and peak contracts delta hedging calculate delta sensitivities with respect to base/peak forward prices construct delta neutral portfolio variance-minimizing hedge calculate hedge ratios by minimizing portfolio variance 28

29 Applications: Analyzing Hedging Strategies 350 frequency no hedge delta hedge energy hedge P&L [EUR] 29

30 Outlook better coupling of business days and non-business days improve dynamics of hourly profiles, especially during spike regime integration of spot and future price models multi-commodity model: integrate fuel and CO2 prices 30