Review of Models and Empirical Analysis of Power Markets in Europe

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. Review of Models
•Fundamental modelling
•Cost based modelling
•Economic equilibrium
•Agent based modelling
•Quantitative modelling
- Based on stochastic models ( finance )
- Finance & « physical »

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. 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

6. 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

7. 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)

10. 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

11. 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

13. 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

14. 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

15. Market Data
Daily average of 24 hourly spot prices
Characteristics of weekly seasonality
then Spot after normalisation

16. Powernext EEX Spot
EEX-Powernext +80

17. Powernext & EEX
Average Spot Price on Different Days
Sunday
Monday
Monday
Sunday
Daily average Daily variance

18. Powernext, EEX: Variograms
Before normalisation
After normalisation

19. APX Spot
Before
After

20. APX Spot
Variogram before
normalisation
Variogram after
normalisation

21. Powernext Price & Temperature
T+50°

22. 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]

23. Simulating price knowing Temperature
Price | Temp
Price

24. 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

25. Copulas
Two bivariate distributions with Gaussian margins
and correlation =0.6
Bigaussian Copula

26. A Copula based co-simulation.
Copula Gaussian

27. 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!