Towards a Better Design of Electricity Transmission Rights - a Monte - PowerPoint PPT Presentation

Towards a Better Design of Electricity Transmission Rights - a Monte Carlo based option valuation Matthias Janssen (with Thomas Niedrig and Magnus Wobben) 10 th INFRADAY Conference, Berlin, 08 Oct 2011

Imagine you operated a power plant in Germany… …and wanted to provide electricity for a factory in NL Transmission capacity is You‘ll need a limited transmission right ( TR )  auction How much would you be willing to pay? Frontier Economics 2

Transmission rights are options on hourly price spreads ● Your power plant operates baseload  physically long ● You have a TR for the next month Example ● You sell a base contract to a factory in NL for next month  long position closed In hours where P NL < P GE  don‘t use TR In hours where P NL ≥ P GE  use TR • Sell in Germany • Buy in NL Lesson Value of the TR = sum of cross-border spot price spreads during next month! Spot prices in the future unknown and no traded expectations Problem (forward products) on hourly spot prices… A B Use historic spot price data to Use all available market data that reveal simulate the spot price characteristics price expectations for the delivery month Frontier Economics 3

● Data ● Model ● Results ● Conclusion Frontier Economics 4

Data Available IC capacity ● Explicit auction ● Explicit auction Explicit /Implicit day-ahead auction ● Yearly TRs ● Monthly TRs 11 monthly PTR auctions November 2009 to October 2010 Data sources: APX, EEX, Endex, Entso-E, Casc EU Frontier Economics 5

● Data ● Model ● Results ● Conclusion Frontier Economics 6

Timeline of used data Example: Auction for November 2009 transmission right Delivery month A TR auction in November 2009 preceding month (21 2 preceding years for October 2009) spot price modeling 600 600 Price difference Germany ‐ Netherlands (€/MWh) Price difference Germany ‐ Netherlands (€/MWh) B 400 400 Price difference of month- ahead futures at the time 200 200 of TR auction 0 0 01/2007 01/2007 04/2007 04/2007 07/2007 07/2007 10/2007 10/2007 01/2008 01/2008 04/2008 04/2008 07/2008 07/2008 10/2008 10/2008 01/2009 01/2009 04/2009 04/2009 07/2009 07/2009 10/2009 10/2009 C ‐ 200 ‐ 200 Monte Carlo simulation ‐ 400 ‐ 400 ‐ 600 ‐ 600 ‐ 800 ‐ 800 ‐ 1000 ‐ 1000 …same procedure for all 11 monthly PTRs Frontier Economics 7

A Estimation of stochastic spot price process P t 3 1 2 Entire timeseries* 140 Deterministic part Jump process Y t Diffusion process X t 120 100 80 €/MWh 60 P t = f(t) + Yt + Xt Monte Carlo 40 20 simulation 0 MO TU WE TH FR Estimate season Estimate jump process 140 75 70 120 65 100 60 80 55 €/MWh €/MWh 60 50 45 40 40 20 35 0 30 MO TU WE TH FR MO TU WE TH FR dY t = - β Y t dt + J u dN u – J d dN d , dX t = - κ X t dt + σ dW t 1 Deterministic part 3 2 Jump filtration Diffusion estimation 60 20 Deseasonalise 50 15 Substitue 40 10 process 30 5 spikes €/MWh €/MWh 20 0 MO TU WE TH FR 10 ‐ 5 0 ‐ 10 MO TU WE TH FR ‐ 10 ‐ 15 ‐ 20 ‐ 20 ‐ 30 ‐ 25 Frontier Economics 8 For visualisation purposes: Exemplary spot price work week (not price spreads).

A 1 Estimating the deterministic component f(t) Now: Cross-border spreads GE-NL Systematic pattern in spreads? ● No overall level ≠ 0 ● No trend Exemplary: Spreads GE-NL September 2009 ● No systematic pattern (season) 50 40 □ No season of the year 30 □ No week/weekend pattern 20 €/MWh 10 □ No pattern during the day (e.g. 0 peak/off-peak) ‐ 10  Nothing that reveals information for ‐ 20 spot price spreads during the ‐ 30 forthcoming delivery month ‐ 40 Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday  f(t) = 0 Use in MC simulation Frontier Economics 9

A 2 Filtering and estimating jumps Iterative Repeat procedure until no more jumps remain jump Calibrate threshold such filter that remaining diffusion process X t is Identify jump Substitute jump characterised by normally increments increments distributed increments (increments > threshold) 20 Feed into 15 10 5 €/MWh 0 next step ‐ 5 MO TU WE TH FR ‐ 10 ‐ 15 ‐ 20 ‐ 25 140 120 100 80 €/MWh 60 Estimated parameter 40 20 0 MO TU WE TH FR Frequency of neg. jumps 3.38% Maximum-Likelihood estimation of Mean size of neg. jumps -10.12 €/MWh jump processes Yt Frequency of pos. jumps 3.94% ● Positive jumps Mean size of pos. jumps 9.38 €/MWh ● Negative jumps Mean reversion speed β 1.03 Use in MC simulation Frontier Economics 10

A 3 Estimating the residual diffusion process X t 20 15 10 5 €/MWh 0 MO TU WE TH FR ‐ 5 ‐ 10 ‐ 15 ‐ 20 ‐ 25 Increments approximately normally distributed after filtration Estimated parameter Mean reversion speed 0.24 κ of diffusion process Maximum-Likelihood estimation Volatility σ of diffusion 3.03 process (€/MWh) Use in MC simulation Frontier Economics 11

B Integrating information on expected price spreads No forward products traded on hourly prices or spreads Forwards on hours Still, spread in prices of month-ahead base forward reveal Forwards on month information about expected spot price spreads on average For every TR, ● we set the deterministic part f(t) to the month-ahead base Use in simulation future price spread ● traded on the day of the TR auction Example: for TR Nov 2009: • f(t) = 0.51 €/MWh • Traded on 21 Oct 2009 Frontier Economics 12

C Monte-Carlo (MC) simulation Simulation of 10,000 simulation paths by generating random MC simulation numbers according to the estimated parameters MC ‐ Path 1 MC ‐ Path 2 MC ‐ Path 3 MC ‐ Path 4 100 Payoff in a MC path = sum of all positive hourly spreads 50 0 €/MWh ‐ 50 ‐ 100 ‐ 150 ‐ 200 Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday Monday Tuesday TR value Value of transmission right = average of all 10,000 payoffs Frontier Economics 13

● Data ● Model ● Results ● Conclusion Frontier Economics 14

Modelled values > auction results 16 Modelled TR values exceed actual 14 auction results by far! Model results 12 Transmission right value in €/MWh Intrinsic Value Even though: Actually 10 Auction results realisable profit (ex-post) 8 = 3,4 €/MWh 6 4 Potential 2 institutional 0 reasons ‐ 15 ‐ 10 ‐ 5 0 5 10 15 Price spread month ‐ ahead futures in €/MWh Timing of option exercise Non-firmness of tranmission rights Nomination of Day-ahead long-term auction PTRs TSOs with the right to curtail transport if available transmission capacity is lower than expected 8 am 12 am 0 am 12 pm Day-ahead Delivery day Now we take nomination uncertainty into account Frontier Economics 15

Are PTRs underprice? Current European market design No payoff in case of non-nomination Assumption  Physical transmission right (PTR) with UIO L I* 6 Model results with "perfect option exercise" PTRs with “best guess Model results with "best guess option exercise" 5 exercise” worth much less Intrinsic Value Transmission right value in €/MWh Auction results 4 Actual PTRs still cheaper 3 than modelled PTRs with “best guess exercise” 2 1 0 Potential reasons ‐ 5 ‐ 4 ‐ 3 ‐ 2 ‐ 1 0 1 2 3 4 5 Price spread month ‐ ahead futures in €/MWh Institutional reasons Model failures Market preferences ● Non-firmness of ● Constant volatility ● Players don‘t value PTRs as PTRs options  buy PTRs as ● … they‘re a bargain! Frontier Economics 16 * UIOLI = Use-it-or- lose -it  we assume that a potential manual resell does not reveal any payoffs.

● Data ● Model ● Results ● Conclusion Frontier Economics 17

In short… ● Valuation of hourly exercisable transmission rights is challenging, but possible ● Nomination uncertainty depresses the option value What did significantly we learn?  Use-it-or- sell -it or Financial TRs are preferrable ● PTRs could well be underpriced  in that case there are arbitrage potentials ● Improve the model Further research ● Analyse other borders Frontier Economics 18

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