Statistical Arbitrage in Balancing Markets

Size: px

Start display at page:

Download "Statistical Arbitrage in Balancing Markets"

Leslie Fox
6 years ago
Views:

1 Statistical Arbitrage in Balancing Markets and the Impact of Time Delay Stefan Kermer, Derek Bunn 1

2 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 long p BA U max System short p

position p Basis min p tert,p ID, p DA for imb<0 and activated tertary min

activated tertary max p ID, p DA for imb>0 and no tertiary T = min(u min +

3 Austrian Imbalance Settlement Design System long p BA U max System short p Basis imb imb max Under Production Short position Over Production Long position p Basis min p tert,p ID, p DA for imb<0 and activated tertary min p ID, p DA for imb<0 and no tertiary max p tert,p ID, p DA for imb>0 and activated tertary max p ID, p DA for imb>0 and no tertiary T = min(u min + U max U min 2 imb 2 ; U imb max ) max Source: APCS, July 2015 p BA = p Basis ± T 3

4 Market Player s Perspectives Decision perspective Information perspective Physical Player e.g. gas turbine Information update Imbalance Wind and solar error EPEX spot last price IL DI IT 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, furthermore we assume the same lead time for solar-, wind error IT Information time delay + Pay off function for rational decisions Non-Physical Player (external schedules) IT v = ( x imb MC) x BA IL DE PL E DP E1 DP E2 DP E3 DP E4 Needs a rational expectation for imb 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, furthermore we 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 i We identified 4 explanatory variables to describe the response variable

wind_e i j r Wind error(j-r) is calculated as the difference between the day ahead forecast and the actual measured.

5 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 i We identified 4 explanatory variables to describe the response variable imb i j : imb i j r Imbalance(j-r) autoregressive parameter with a time lag of j-r. EPEX i j r Last price EPEX(j-r) EPEX spot intraday trading closes at j-r. wind_e i j r Wind error(j-r) is calculated as the difference between the day ahead forecast and the actual measured. solar_e i j r Solar error(j-r) is calculated as the difference between the day ahead forecast and the actual measured value. Information time delay in [minutes] IMB 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

6 Quantile Regression Forecast What do we get from that analysis? Lag 1 model Lag 8 model A more accurate portrayal of the relationship between the response variable and the observed explanatory variables 6

7 Expected Value Model max k EV(x k ) = v i k ρ(s i ) i I The expected value for a given course of action is the weighted sum of possible pay offs for each alternative. It is obtained by summing the payoffs for each course of action multiplied by the probabilities ρ(s i ) associated with each state of nature s i. The course of action x k is chosen which has the highest expected value EV(x k ). Index for time j {T} ma k ( v i j k ρ( imb i ) ) j i I Index for state of nature i IMB OUR OBJECTIVE: Index for position k { } in MWh Pay offs: Physical Player v long = ( imb MC) x v short = MC DA p gas short p x imb Non-physical player Assumption: Physical player is in part-load v = p x. imb MC EPEX x ) x Assumption: Non-Physical player trades last price at EPEX Spot Back Testing with observed data winter and summer month 2015 Benchmark and key performance indicators 7

8 standard deviation in [MWh] absolute imbalance in [MWh] profit [EUR/month] system costs in [EUR/mont] Results Physical/Non-Physical Player ,00 30,00 28,00 26,00 24,00 22,00 20,00 realized profit expected profit realized profit expected profit summer summer winter winter physical player summer non-physical player winter observation physical player non-physical player summer winter observation physical player non-physical player winter summer observation physical player non-physical player 8

9 Results Physical/Non-Physical Player physical player non-physical player short positions winter short positions summer long positions winter long positions summer

10 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. IL DE PL E IT DP E1 DP E2 DP E3 DP E4 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, furthermore we 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 Short information time delays would need: instant imbalance information short processing lead times for internal and external schedules Short delivery periods (15 minutes) Information time delay in [minutes] Comparison with observed imbalance 10

11 Dynamic Analysis Non-Physical Player System Costs and Parameters System costs WINTER System costs System costs SUMMER System costs Absolute imbalance Standard deviation Absolute imbalance Standard deviation Financial and system behavioural metrics show a win-win situation 11

12 Dynamic Analysis Non-Physical Player System Costs and Parameters System costs WINTER System costs System costs SUMMER System costs Absolute imbalance Standard deviation Absolute imbalance Standard deviation With long information time delays the actions are inefficient. 12

13 percentage of positions quantity summer quantity summer Dynamic Analysis Non-Physical Player How often did they take positions? 70% 60% 50% 40% 30% 20% 10% 0% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% short positions non-physical player winter short positions physical player winter long positions non-physical player winter long positions physical player winter 70% 60% 50% 40% 30% 20% 10% 0% quantity of positions non-physical player summer quantity of positions non-physical player winter quantity of positions physical player summer quantity of positions physical player winter short positions non-physical player winter short positions physical player winter long positions non-physical player winter long positions physical player winter How often do they spill/short the market? From minute intervals in winter/summer the physical player traded less than 20 percent of time intervals whereas the nonphysical EPEX Spot trading model suggested over 90% of the time to take a imbalance position. 13

Dynamic Analysis Non-Physical Player Imbalance Extremes WINTER SUMMER System long System short p Basis imb p BA U max imb max System long >70 MWh decreased significantly

14 Dynamic Analysis Non-Physical Player Imbalance Extremes WINTER SUMMER System long System short p Basis imb p BA U max imb max System long >70 MWh decreased significantly System Short >70 MWh remained constant for physical player and increased slightly for non-physical player Under Production Short position Over Production Long position 14

15 imbalance half cycles [-] Dynamic Analysis Non-Physical Player Imbalance Half-cycles 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

16 Conclusion Research Questions: Does statistical arbitrage help the system to decrease system imbalance and system costs? What is the impact of information time delay? For the physical player YES! Short time delays decrease system costs and stabilize the system significantly. For the non-physical player a more differentiated point of view is necessary: The current nomination regulation offers arbitrage potential for the non-physical player (profitpotential), but it is not as beneficial from system perspective In the dynamic analysis we observed a significant reduction of imbalance extremes if the system imbalance was long, but a slight increase for short imbalance extremes Furthermore we saw that up to a time lag of 30 minutes the non-physical player would be able to help the system, but the frequency of trades in this single player simulation was very high, which potentially would lead to overreactions in the market in a multiplayer setting. 16

17 BACK UP In August, 2 short extremes can be described by LAST Epex spot price extremes REF Time OLS_pBA_i mb_est_n O_x obs_pba_op timized_no_t ert expected spread spread p_id OLS IMB EST OLS_pBA_d ec x-decision imbalance_obs imb_obs+x obs_pba_base ,63 60, ,00 0,71 100,71 59,54 96,54-180,00 83,46 180, ,83 13, ,00-37,08 62,92 5,95 66,42-198,00 131,58 198,00 17

Ex-ante trade of balancing power reserves in German electricity markets The cure to the missing money or a new disease?*

Ex-ante trade of balancing power reserves in German electricity markets The cure to the missing money or a new disease?* Joonas Päivärinta and Reinhard Madlener Chair of Energy Economics and Management