On the construction of the HPFC for electricity prices

Transcription

1 On the construction of the HPFC for electricity prices Conference on Computational Management Science 2017/Bergamo Rüdiger Kiesel 1 Florentina Paraschiv 2 Audun Sætherø 1 1 Chair of Energy Trading and Financial Services, University Duisburg- Essen, Essen, Germany. 2 NTNU Business School, Norwegian University of Science and Technology, 7491 Trondheim, Norway Universitt Duisburg-Essen

2 Page 2 Construction of the HPFC Table of contents What is the HPFC Construction methods Empirical Results Conclusion References

3 Page 3 Construction of the HPFC What is the HPFC Introduction

4 Page 4 Construction of the HPFC What is the HPFC HPFC Definition Is the current price of electricity with delivery at a certain point (on an hourly scale) in the future. Is an OTC product used by producers of electricity to sell specialized electricity contracts Products traded on the exchanges are typically insufficient for most producers/consumers, making the HPFC crucial! Should reflect the believes about how electricity prices evolve, and be arbitrage free to traded Futures

5 Page 5 Construction of the HPFC What is the HPFC The goal of this talk is to explain how the HPFC is constructed We will present three different methods, two from the Literature and one novel approach We will make a comparative analyzes of these models explaining the strengths and weaknesses, and how these methods can be improved.

6 Page 6 Construction of the HPFC Construction methods Consists of two parts: Seasonality curve: Represents historical spot prices, weather etc. Adjustment function: Makes sure the curve is arbitrage free to traded Futures products

7 Page 7 Construction of the HPFC Construction methods Construction Methods

8 Page 8 Construction of the HPFC Construction methods Seasonality Curve (Blöchlinger, 2008, PHD-Thesis) [1]: Dummy Variables: 6 f 2 yd = a 0 + b i D di + 12 c i M di d i CDD di + e i HDD di i=1 i=1 i=1 i=1 Assigns different days into blocks and assigns a mean price to those blocks of days Problem: A non-smooth change between months

9 Page 9 Construction of the HPFC Construction methods Price (Euro/MWh) Days (1 Year) Seasonality curve Dummy Variables Price (Euro/MWh) Days (1 Year) Seasonality curve Dummy Variables (Without daily seasonality)

10 Page 10 Construction of the HPFC Construction methods Adjustment Curve Has as a primary focus to make sure that the PFC fits to the observed Futures products Our methods: Fleten et al. (2003) [2] Benth et al. (2007) [3] Novel approach based on a combined fitting of the seasonal directly to the Futures prices Our three main questions: Do they take care of the smoothing? What happens when the price of a Futures product change? What happens when a Futures product is cascaded into several smaller products?

11 Page 11 Construction of the HPFC Construction methods Price (Euro/MWh) Days (1 Year) Seasonality curve Dummy Variables Prices Mean of seasonality curve Futures prices Days Adjustment Function Days

12 Page 12 Construction of the HPFC Construction methods Fletens approach The approach suggested by Fleten et al. (2003)[2] reads as follows: For a seasonality curve s t min ft [ T ] T 1 (f t s t ) 2 + λ (f t 1 2f t + f t+1 ) 2 t=1 given: A f t = FuturesPrice(A) Problem: Suppresses the weekly/daily seasonality (Blöchlinger, 2008, PHD-Thesis) [1] λ seems arbitrary t=2 (1)

13 Page 13 Construction of the HPFC Construction methods Daily Profile price days price days

14 Page 14 Construction of the HPFC Construction methods Benth Approach Benth et al. (2007) [3] suggests a method as follow: FC(t) = s t + ε t ε t = a 1 t 4 + b 1 t 3 + c 1 t 2 + d 1 t + e 1 t [t 0, t 1 ) a 2 t 4 + b 2 t 3 + c 2 t 2 + d 2 t + e 2 t [t 1, t 2 ). a n t 4 + b n t 3 + c n t 2 + d n t + e n t [t n 1, t n ] x = {a 1,, b 1,, c 1, } min x tn t 0 [ε (t; x)] 2 dt

15 Page 15 Construction of the HPFC Construction methods Introducing a new Futures Product Euro/Mwh Original Curve Implied Curve Implied Futures Days (1 Year)

16 Page 16 Construction of the HPFC Construction methods Spline Curve FC(t) = C+ 6 a i sin( i=1 a Q(m) 4 sin( a Q(m) 12 sin( 2πi(t + S(m)) ) + b i cos( 12 M(m) 8π(t + S(m)) ) + b Q(m) 4 cos( 12 M(m) 24π(t + S(m)) ) + b Q(m) 12 cos( 12 M(m) 2πi(t + S(m)) ) + 12 M(m) 8π(t + S(m)) )+ 12 M(m) 24π(t + S(m)) ) 12 M(m) T (m) + S(m) M(m) = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

17 Page 17 Construction of the HPFC Construction methods minimize x subject to Ax y 2 Cx = d where x are the 26 coefficients,c and d assures the resulting curve is arbitrage free with respect to the Futures products x = (a 1,..., b 1,..., a 1 4,...a 4 4, b 1 4,..., b 4 4, a 1 12,...a 4 12, b 1 12,..., b 4 12) Requires a higher than normal number of parameters May lead to overfitting! Needs to pre-specify the number of Futures products

18 Page 18 Construction of the HPFC Construction methods Derivative of Adjustment Function derivative Fleten Method derivative Fred Method derivative Novel Method Figure: The derivative of the adjustment functions with respect to the March Future, with 3-12 monthly products as input.

19 Page 19 Construction of the HPFC Empirical Results Test Data Benth Novel Fleten 1 Fleten 2 MAPE IS 32% 29% 45% 32% MAPE OoS 67% 42% 57% 41% AD IS AD OoS AD IS AD OoS SD IS SD OoS Table: Comparing the different models to the realized spot prices, Test 1-4 is for a daily scale, while Test 5-8 is on an hourly scale. AD=Absolute Difference, SD=Square Difference, IS=In Sample, OoS=Out of sample

20 Page 20 Construction of the HPFC Conclusion Conclusion Important to know what your construction method does, and what you actually want it to do One should be careful about what the different parts of the seasonality curve does One should be careful about adding new parameters when the Futures are cascading (or when other new information appears) If your adjustment function has a smoothing term, you have to be sure what you want to smooth (and what not to smooth)

21 Page 21 Construction of the HPFC References References,Blöchlinger, Lea (2008). Power prices A regime-switching spot/forward price model with Kim filter estimation. PHD-Thesis Fleten, Stein-Erik and Lemming, Jacob (2003). Constructing forward price curves in electricity markets, Journal of Energy Economics, 5, Benth, Fred Espen and Koekkebakker, Steen and Ollmar, Fridthjof (2007).Extracting and applying smooth forward curves from average-based commodity contracts with seasonal variation, The Journal of Derivatives, 15, Sætherø, Audun Sviland and Paraschiv, Florentina and Kiesel, Ruediger, On the Construction of the Hourly Price Forward Curve for Electricity Prices (May 17, 2017). Available at SSRN. Thank you for your attention...