Statistical Arbitrage in Balancing Markets and the Impact of Time Delay Stefan Kermer, Derek Bunn 1
Agenda • Introduction – Austrian Imbalance Settlement Design – Market Players‘ Perspectives • Predicting the Conditional Distribution of Imbalance – Quantile Regression Model – Results with different time delays • BackTesting Simulations 2
Austrian Imbalance Settlement Design System short System long 𝑉 𝑛𝑏𝑦 𝑞 𝐶𝐵 𝑞 𝐶𝑏𝑡𝑗𝑡 imb 𝑗𝑛𝑐 𝑛𝑏𝑦 Over Production Under Production Long position Short position min ptert,pID , pDA for imb<0 and activated tertary min pID, pDA for imb<0 and no tertiary 𝑞 𝐶𝑏𝑡𝑗𝑡 max p tert ,p ID , p DA for imb>0 and activated tertary max pID, pDA for imb>0 and no tertiary 𝑈 = min(𝑉 𝑛𝑗𝑜 + 𝑉 𝑛𝑏𝑦 − 𝑉 𝑛𝑗𝑜 × 𝑗𝑛𝑐 2 ; 𝑉 𝑛𝑏𝑦 ) 2 imb 𝑛𝑏𝑦 Source: APCS, July 2015 𝑞 𝐶𝐵 = 𝑞 𝐶𝑏𝑡𝑗𝑡 ± 𝑈 3
Market Player´s Perspectives Information perspective Decision perspective Physical Player e.g. gas turbine Information update IT Imbalance Wind and solar error IL EPEX spot last price D I DP I D I … decision and internal schedule transmission DP I … delivery period internal schedule changes (15 minutes) IL… TSO processing information lead time is 10 minutes for imbalance, furthe rmore we assume the same lead time for solar-, wind error IT… Information time delay + Non-Physical Player (external schedules) Pay off function for rational decisions IT PL E IL DP E2 DP E3 DP E4 D E DP E1 = ( − 𝑁𝐷) ∗ 𝑦 𝐶𝐵 𝑤 𝑦 𝑗𝑛𝑐 D E … decision and internal schedule transmission DP E … delivery period internal schedule 60 minutes à 15 minutes balancing prices IL… TSO processing Information lead tim10 minutes for imbalance, furthe rmore we Needs a rational expectation for 𝑗𝑛𝑐 assume the same lead time for solar-, wind error PL E … TSO processing lead time for external schedule nomination (45 minutes) IT… Information time delay 4
Quantile Regression Forecast imb i j = β i1 ∗ imb i j−r + β i2 ∗ EPEX i j−r + β i3 × wind_e i j−r + β i4 ∗ solar_e i j−r + c 𝑗 We identified 4 explanatory variables to describe the Information time delay in [minutes] response variable 𝑗𝑛𝑐 𝑗 𝑘 : 𝑗𝑛𝑐 𝑗 𝑘−𝑠 Imbalance(j-r) autoregressive parameter with a time lag of j-r. 𝐹𝑄𝐹𝑌 𝑗 𝑘−𝑠 Last price EPEX(j-r) EPEX spot intraday trading closes at j-r. 𝑥𝑗𝑜𝑒_𝑓 𝑗 𝑘−𝑠 Wind error(j-r) is calculated as the difference between the day ahead forecast and the actual measured. 𝑡𝑝𝑚𝑏𝑠_𝑓 𝑗 𝑘−𝑠 Solar error(j-r) is calculated as the difference between the day ahead forecast and the actual measured value. 𝐽𝑁𝐶 q2.5 q10 q20 q30 q40 q50 q60 q70 q80 iq90 q97.5 Time lags 1 to 8 Parametrizing 2 months (January and July) Outcome: A conditional distribution 5
Quantile Regression Forecast 𝑿𝒊𝒃𝒖 𝒆𝒑 𝒙𝒇 𝒉𝒇𝒖 𝒈𝒔𝒑𝒏 𝒖𝒊𝒃𝒖 𝒃𝒐𝒃𝒎𝒛𝒕𝒋𝒕? Lag 1 model Lag 8 model A more accurate portrayal of the relationship between the response variable and the observed explanatory variables 6
Expected Value Model Pay offs: Assumption : 𝑛𝑏𝑦 𝑙 𝐹𝑊(𝑦 𝑙 ) = 𝑤 𝑗 𝑙 𝜍(𝑡 𝑗 ) Physical player is in part-load Physical Player 𝑗∈𝐽 v 𝑚𝑝𝑜 = ( 𝑗𝑛𝑐 − 𝑁𝐷) ∗ 𝑦 The expected value for a given course of action is the weighted sum of possible pay offs for each v 𝑡ℎ𝑝𝑠𝑢 = 𝑁𝐷 𝐸𝐵 −𝑞 𝑏𝑡 𝑡ℎ𝑝𝑠𝑢 − 𝑞 𝑦 𝑗𝑛𝑐 ) ∗ 𝑦 alternative. It is obtained by summing the payoffs for each course of action multiplied by the probabilities 𝜍(𝑡 𝑗 ) associated with each state of Non-physical player nature 𝑡 𝑗 . The course of action 𝑦 𝑙 is chosen which has the highest expected value 𝐹𝑊(𝑦 𝑙 ) . 𝑞 𝑦. 𝑤 = 𝑗𝑛𝑐 − 𝑁𝐷 𝐹𝑄𝐹𝑌 ∗ 𝑦 Assumption : Non-Physical player trades last price at EPEX Spot OUR OBJECTIVE: Back Testing with observed data 𝑤 𝑗 𝑘 𝑙 ∗ 𝜍( ma k ( 𝑗𝑛𝑐 𝑗 ) ) winter and summer month 2015 𝑘 Benchmark and key performance 𝑗∈𝐽 indicators Index for time 𝑘 ∈ {T} Index for state of nature 𝑗 ∈ 𝐽𝑁𝐶 7 Index for position 𝑙 ∈ {−100 … 0. . +100} in MWh
Results Physical/Non-Physical Player 2.500.000 profit [EUR/month] 3.000.000 system costs in [EUR/mont] 2.000.000 2.500.000 1.500.000 2.000.000 1.000.000 500.000 1.500.000 - 1.000.000 realized expected realized expected 500.000 profit profit profit profit - summer summer winter winter summer winter physical player non-physical player observation physical player non-physical player standard deviation in [MWh] 32,00 66.000 30,00 absolute imbalance in [MWh] 64.000 28,00 62.000 60.000 26,00 58.000 24,00 56.000 54.000 22,00 52.000 20,00 50.000 48.000 summer winter winter summer observation physical player non-physical player observation physical player non-physical player 8
Results Physical/Non-Physical Player physical player non-physical player short positions winter 380 1641 short positions summer 271 1466 long positions winter 63 867 long positions summer 53 1050 9
Dynamic Analysis Hypothesis: Statistical Arbitrage is beneficial for both the market players (physical and non-physical) and the system, if short information time delays are provided . IT Short information time delays would need: PL E • IL instant imbalance information DP E2 DP E3 DP E4 D E DP E1 • short processing lead times for internal and external schedules D E … decision and internal schedule transmission DP E … delivery period internal schedule 60 minutes à 15 minutes balancing prices IL… TSO processing Information lead tim10 minutes for imbalance, furthe rmore we • Short delivery periods (15 minutes) assume the same lead time for solar-, wind error PL E … TSO processing lead time for external schedule nomination (45 minutes) IT… Information time delay Information time delay in [minutes] Comparison with observed imbalance 10
Dynamic Analysis Non-Physical Player System Costs and Parameters SUMMER WINTER System costs System costs System costs System costs Absolute imbalance Standard deviation Absolute imbalance Standard deviation Financial and system behavioural metrics show a win-win situation 11
Dynamic Analysis Non-Physical Player System Costs and Parameters SUMMER WINTER System costs System costs System costs System costs Absolute imbalance Absolute imbalance Standard deviation Standard deviation With long information time delays the actions are inefficient. 12
Dynamic Analysis Non-Physical Player How often did they take positions? How often do they 70% 70% quantity summer quantity summer 60% 60% spill/short the 50% 50% 40% 40% market? 30% 30% 20% 20% 10% 10% 0% 0% From 2683 15 minute intervals in short positions non-physical player winter short positions non-physical player winter short positions physical player winter short positions physical player winter winter/summer the long positions non-physical player winter long positions non-physical player winter long positions physical player winter long positions physical player winter physical player traded less than 20 percent 100% 90% of time intervals 80% percentage of positions quantity of positions non-physical player summer whereas the non- 70% quantity of positions non-physical player winter 60% physical EPEX Spot 50% quantity of positions physical player summer trading model 40% quantity of positions physical player winter 30% suggested over 90% 20% of the time to take a 10% 0% imbalance position. 13
Dynamic Analysis Non-Physical Player Imbalance Extremes SUMMER WINTER System short System long 𝑉 𝑛𝑏𝑦 𝑞 𝐶𝐵 System long >70 MWh decreased significantly 𝑞 𝐶𝑏𝑡𝑗𝑡 System Short >70 MWh remained constant for physical player and increased slightly for non-physical player imb 𝑗𝑛𝑐 𝑛𝑏𝑦 Over Production Under Production Short position Long position 14
Dynamic Analysis Non-Physical Player Imbalance Half-cycles 1.000 900 imbalance half cycles [-] 800 700 600 500 400 300 200 100 - half cycles winter half cycles summer Half cycles in case of participation of the physical player increased by 80% for the lag 1 model For the physical player only a slight increase is observed. 15
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