Power Market and Models Convergence ?

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Review of Models and Empirical Analysis of Power Markets in Europe

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Power Market and Models Convergence ?

  1. 1. Power Markets and Models: Convergence ? Alain Galli, Nicolas Rouveyrollis & Margaret Armstrong ENSMP Web Site: www.cerna.ensmp.fr Presented at Le printemps de la recherche -EDF, 20 May 2003 CERNA, Centre d’économie industrielle Ecole Nationale Supérieure des Mines de Paris - 60, bld St Michel - 75272 Paris cedex 06 - France Téléphone : (33) 01 40 51 9314 - Télécopie : (33) 01 44 07 10 46 - E-mail : galli@cerna.ensmp.fr
  2. 2. Review of Models •Fundamental modelling •Cost based modelling •Economic equilibrium •Agent based modelling •Quantitative modelling - Based on stochastic models ( finance ) - Finance & « physical »
  3. 3. Models derived from finance •Black & Scholes •Mean reverting (OU) exp (OU) •Multifactor type models • HJM type models •Jumps models •Stochastic volatility models •Garch •Levy processes •Switching models
  4. 4. Multifactor models Variants of Brennan’s model (for interest rates) or Gibson-Schwartz extended by Schwartz (for commodity) dS = ( µ − C )dt + σ S dW S S dC = κ (α − C )dt + σ C dWC dW S dWC = ρ dt Drawback: Pilipovic • C non observable S ~ OU • 6 parameters C ~ GBM
  5. 5. HJM type (multifactor) Clewlow &Strikland (1999) dF ( t , T ) n = ∑ σ i ( t , T )dWt i F ( t , T ) i =1 dS(t) ∂Log(F(0,t) n  t ∂σi (u,t) t ∂σi (u, t) i  n = − ∑∫0σi (u,t) du + ∫0 dWu  dt + ∑σi (t,t)dWti S(t)  ∂t i=1  ∂t ∂t  i=1
  6. 6. Jump models Electricity spot prices show strong variations Strong variations = Jumps •Jumps « mean reverting » •Positive and negative Jumps Examples •OU +Jumps (Villaplana - 2003) •GS two factors +Jumps •Jump +switching (Roncoroni - 2002)
  7. 7. Stochastic volatility Example dS = µ dt + ν ( t )dW S S Heston ν ( t ) = κ (θ − ν ( t ))dt + ξ ν ( t )dWν dW S dWν = ρ dt
  8. 8. Switching Models Ln( St ) = µ r + ε t t ε t ~ N (0,σ r ) t rt is a Markov Chain Example (Elliott, Sick & Stein, 2003) Markov chain = the number of active generators at time t
  9. 9. Bid based Stochastic Models Skantze, P., Gubina, A., & Ilic, M. (2000) S ( t ) = e aL( t )+ b( t ) L(t) = Stochastic Load b(t) = Stochastic shift with jumps due to outage
  10. 10. Comments on Models •Most models (except the last ones) are transposed directly from finance •Seasonality is considered not a problem •From practical point of view similar results can be obtained from Jumps, Switching and Volatility -If Jump amplitude ~Vol- •Still few models consider external variables (eg Temperature,Capacity, Outage,..) • Many practical studies on markets but few proposals for market driven diffusion models
  11. 11. Market Data Daily average of 24 hourly spot prices Characteristics of weekly seasonality then Spot after normalisation
  12. 12. Powernext EEX Spot EEX-Powernext +80
  13. 13. Powernext & EEX Average Spot Price on Different Days Sunday Monday Monday Sunday Daily average Daily variance
  14. 14. Powernext, EEX: Variograms Before normalisation After normalisation
  15. 15. APX Spot Before After
  16. 16. APX Spot Variogram before normalisation Variogram after normalisation
  17. 17. Powernext Price & Temperature T+50°
  18. 18. Powernext Price & Temperature ρ = 0.43 exp(-Temp) Normalised Price ρ=0.52 Price Skew (1% >2 0% <-2) 25 % in [-2,-0.5] 12% in [0.5 2]
  19. 19. Simulating price knowing Temperature Price | Temp Price
  20. 20. Price & Temperature: Is correlation enough ? Cor(P,T) = 0.43 but visually high peaks of Temperature are strongly correlated to high prices. •Switching models •Copulas
  21. 21. Copulas Two bivariate distributions with Gaussian margins and correlation =0.6 Bigaussian Copula
  22. 22. A Copula based co-simulation. Copula Gaussian
  23. 23. Conclusion Initially models were taken directly from finance. Studies have demonstrated the complexity of these markets and the similarities and differences between them. Better suited models are starting to be developed, for example, by incorporating the impact of temperature. But much work still remains to be done!

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