1. 1 Lecture Plan 1400-1530 Factor models for spot electricity markets (modelling and predicting prices and price distributions). Part II. Building fundamental models for the UK, Nordpool and the EEX spot market using quantile regression. Predicting prices distributions. Fundamental quantile regression models for electricity spot price distributions Non-linear sensitivities to fundamentals and risk analysis Scenario analysis (e.g. how does a change in demand forecast influence the price distribution?)

2. 2 Introduction Quantile Regression 2 How can be establish fundamental models for the electricity spot prices that allows for the following: Capturing the spiky behaviour of electricity prices Analyse how non-linear sensitivities of different risk factors (e.g. the reserve margin / capacity forecasts will influence the el prices much more in a regime of high prices versus a regime of low prices) Risk analysis (VaR and CVaR) with forecasts of the price distribution at various horizons Scenario analysis for specific values of the risk factors

3. 3 Quantile Regression The Concept and Theory Regression Quantiles” Koenker R. and Bassett G., Econometrica, vol. 46 (1978), 33-51. Roger Koenker is still teaching at University of Illinois Urbana Champaign

4. 4 4 Demand for electricity is rather in-elastic for “normal” sets of prices ranges in the short run The supply function is well-known to be convex and steeply increasing. The supply function reflects the merit order of short- run marginal costs, which increase steeply as plant move from baseload to peakload Fundamental analysis of electricity spot price formation Total production of electricity (MWh) Price / Marginal cost (£/MWh) Demand curve Supply curve Renewables Nuclear Coal Gas Oil

5. 5 5 Fundamental analysis of electricity spot price formation The implications for the exogenous price drivers: Demand elasticity is positive and increases nonlinearly with higher quantiles Reserve margin elasticity is negative and decrease nonlinearly with higher quantiles

6. 6 6 Fundamental analysis of electricity spot price formation The implications for the exogenous price drivers: Fuel (including carbon allowance prices) elasticity's will be positive but have nonlinear, non monotonic functional relation across quantiles

7. 7 7 Quantile regression was introduced in an econometrica paper by Koenker and Bassett (1978) and is now fully described in these books: Koenker (2005) and Hao and Naiman (2007). Applications in financial risk management (stocks / currency markets) can be found for example in Engle and Manganelli (2004), Alexander (2008), Taylor (2008). Quantile regression

8. 8 8 If you think of OLS as simply modelling the mean of the electricity prices as the dependent variable, then quantile regression can model the median, the 1%, 5%, 10%, 90%, 95%, and 99% percentiles, etc., or a whole set of them to effectively describe the full distribution. Quantile regression

9. 9 9 0.1, 0.5, and 0.9 quantile regression lines. The lines are found by the following minimizing the weighted absolute distance to the q th regression line: Y q t = α q +β q X t +ε q t

10. 10 Quantile regression Example 90% Quantile Y 0.9 t = α 0.9 +β 0.9 X t +ε 0.9 t |ε 1 | is weighted 0.9 |ε 2 | is weighted 0.1 We minimize the sum of all weighted residuals for a given quantile curve

11. 11 Quantile regression Excel (UK) (One independent variable)

12. 12 Quantile regression (UK) Example Excel (more dependent variables)

13. 13 Quantile regression Example Excel UK (more dependent variables)

14. 14 –Demand forecast –Significant positive effect, Generally increasing with quantiles. –Reserve margin –Significant negative effect, Generally increasing effect with quantiles. Price distribution modelling

15. 15 –Coal –Significant positive effect. Decreasing effect with quantile –Gas prices –Significant positive effect. Rather constant effect –Co2 –Very little effect Price distribution modelling

16. 16 Scenario Analysis / Sensitivity Analysis –From an expected base scenario, how does the predicted price distribution look like? –From this scenario, how will lets say changes in demand forecast influence the predicted price distribution?

17. 17 Scenario Analysis UK / Sensitivity Analysis

18. 18 Scenario Analysis UK / Sensitivity Analysis

19. 19 Using a fundamental quantile regression model we can: Quantify the non-linear sensitivities of different risk factors (coal-, gas-, co2 prices, forecast of demand and reserve margins) Predict the price distribution given a set of values for the different risk factors Conclusion

20. 20 From the base scenario, analyze how changes in these variables influence the 1%, 5%, 10%, 50%, 90%, 95%,99% quantiles Coal price Gas price Co 2 price Forecast of demand Forecast of reserve margins Take the Min and Max values for the variables and construct an interval of 10 values. Use the Excel Datatables Exercises

21. 21 Build similar models for all periods/hours for these markets: UK NP EEX Perform scenario analysis changing one/more variables at a time Exercises