Markets and the Impact of Time Delay Stefan Kermer, Derek Bunn 1 - - PowerPoint PPT Presentation

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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

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SLIDE 1

Statistical Arbitrage in Balancing Markets

and the Impact of Time Delay Stefan Kermer, Derek Bunn

1

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SLIDE 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

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SLIDE 3

Austrian Imbalance Settlement Design

3

Source: APCS, July 2015

imb 𝑞𝐶𝐵 𝑞 𝐶𝑏𝑡𝑗𝑡

𝑗𝑛𝑐𝑛𝑏𝑦

𝑉𝑛𝑏𝑦

System long System short Under Production Short position Over Production Long position

𝑞𝐶𝑏𝑡𝑗𝑡 min ptert,pID , pDA for imb<0 and activated tertary min pID, pDA for imb<0 and no tertiary max ptert,pID , pDA for imb>0 and activated tertary max pID, pDA for imb>0 and no tertiary 𝑈 = min(𝑉𝑛𝑗𝑜 + 𝑉𝑛𝑏𝑦 − 𝑉𝑛𝑗𝑜 imb𝑛𝑏𝑦

2

× 𝑗𝑛𝑐2 ; 𝑉𝑛𝑏𝑦) 𝑞𝐶𝐵 = 𝑞𝐶𝑏𝑡𝑗𝑡 ± 𝑈

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SLIDE 4

Market Player´s Perspectives

4

+

𝑤 = ( ෣ 𝑦 𝑗𝑛𝑐 − 𝑁𝐷) ∗ 𝑦𝐶𝐵 Pay off function for rational decisions Needs a rational expectation for 𝑗𝑛𝑐

Information update Imbalance Wind and solar error EPEX spot last price DPI IL DI DI … decision and internal schedule transmission DPI… 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 IT

Physical Player  e.g. gas turbine

IL DE DE … decision and internal schedule transmission DPE… 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 PLE… TSO processing lead time for external schedule nomination (45 minutes) IT… Information time delay DPE1 DPE2 DPE3 DPE4 PLE IT

Non-Physical Player (external schedules)

Information perspective Decision perspective

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SLIDE 5

Quantile Regression Forecast

5

෣ imbi j = βi1 ∗ imbi j−r + βi2 ∗ EPEXi j−r + βi3 × wind_ei j−r + βi4 ∗ solar_ei j−r + c𝑗

We identified 4 explanatory variables to describe the response variable 𝑗𝑛𝑐𝑗 𝑘: 𝑗𝑛𝑐𝑗 𝑘−𝑠 Imbalance(j-r) autoregressive parameter with a time lag of j-r. 𝐹𝑄𝐹𝑌𝑗 𝑘−𝑠Last price EPEX(j-r) EPEX spot intraday trading closes at j-r. 𝑥𝑗𝑜𝑒_𝑓𝑗 𝑘−𝑠Wind error(j-r) is calculated as the difference between the day ahead forecast and the actual measured. 𝑡𝑝𝑚𝑏𝑠_𝑓𝑗 𝑘−𝑠Solar 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

Information time delay in [minutes]

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SLIDE 6

Quantile Regression Forecast

6

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

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SLIDE 7

Expected Value Model

7

𝑛𝑏𝑦𝑙 𝐹𝑊(𝑦𝑙) = ෍

𝑗∈𝐽

𝑤𝑗 𝑙 𝜍(𝑡𝑗)

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 𝜍(𝑡𝑗) associated with each state of nature 𝑡𝑗. The course of action 𝑦𝑙 is chosen which has the highest expected value 𝐹𝑊(𝑦𝑙).

Physical Player Non-physical player

v𝑚𝑝𝑜𝑕 = ( 𝑗𝑛𝑐 − 𝑁𝐷) ∗ 𝑦 v𝑡ℎ𝑝𝑠𝑢 = 𝑁𝐷𝐸𝐵 −𝑞𝑕𝑏𝑡𝑡ℎ𝑝𝑠𝑢 − 𝑞 𝑦 𝑗𝑛𝑐 ) ∗ 𝑦 𝑤 = 𝑞 𝑦. 𝑗𝑛𝑐 − 𝑁𝐷𝐹𝑄𝐹𝑌 ∗ 𝑦

ma k(

𝑘

෍

𝑗∈𝐽

𝑤𝑗 𝑘 𝑙 ∗ 𝜍( 𝑗𝑛𝑐𝑗) ) Pay offs: OUR OBJECTIVE:

Index for time 𝑘 ∈ {T} Index for state of nature 𝑗 ∈ ෣ 𝐽𝑁𝐶

Index for position 𝑙 ∈ {−100 … 0. . +100} in MWh

Assumption: Physical player is in part-load 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

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SLIDE 8

Results Physical/Non-Physical Player

8

  • 500.000

1.000.000 1.500.000 2.000.000 2.500.000 realized profit expected profit realized profit expected profit summer summer winter winter profit [EUR/month] physical player non-physical player

  • 500.000

1.000.000 1.500.000 2.000.000 2.500.000 3.000.000 summer winter system costs in [EUR/mont]

  • bservation

physical player non-physical player 20,00 22,00 24,00 26,00 28,00 30,00 32,00 summer winter standard deviation in [MWh]

  • bservation

physical player non-physical player 48.000 50.000 52.000 54.000 56.000 58.000 60.000 62.000 64.000 66.000 winter summer absolute imbalance in [MWh]

  • bservation

physical player non-physical player

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SLIDE 9

Results Physical/Non-Physical Player

9

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

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SLIDE 10

Dynamic Analysis

10

Hypothesis: Statistical Arbitrage is beneficial for both the market players (physical and non-physical) and the system, if short information time delays are provided.

Short information time delays would need:

  • instant imbalance information
  • short processing lead times for internal and

external schedules

  • Short delivery periods (15 minutes)

IL DE DE … decision and internal schedule transmission DPE… 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 PLE… TSO processing lead time for external schedule nomination (45 minutes) IT… Information time delay DPE1 DPE2 DPE3 DPE4 PLE IT

Information time delay in [minutes]

Comparison with

  • bserved imbalance
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SLIDE 11

Dynamic Analysis Non-Physical Player System Costs and Parameters

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Financial and system behavioural metrics show a win-win situation

WINTER SUMMER

System costs System costs Absolute imbalance Standard deviation System costs System costs Absolute imbalance Standard deviation

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SLIDE 12

Dynamic Analysis Non-Physical Player System Costs and Parameters

12

With long information time delays the actions are inefficient.

WINTER SUMMER

System costs System costs Absolute imbalance Standard deviation System costs System costs Absolute imbalance Standard deviation

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SLIDE 13

Dynamic Analysis Non-Physical Player How often did they take positions?

13

0% 10% 20% 30% 40% 50% 60% 70% quantity summer short positions non-physical player winter short positions physical player winter long positions non-physical player winter long positions physical player winter 0% 10% 20% 30% 40% 50% 60% 70% quantity summer short positions non-physical player winter short positions physical player winter long positions non-physical player winter long positions physical player winter 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% percentage of positions 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

How often do they spill/short the market? From 2683 15 minute intervals in winter/summer the physical player traded less than 20 percent

  • f time intervals

whereas the non- physical EPEX Spot trading model suggested over 90%

  • f the time to take a

imbalance position.

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SLIDE 14

Dynamic Analysis Non-Physical Player Imbalance Extremes

14

WINTER SUMMER

imb 𝑞𝐶𝐵 𝑞 𝐶𝑏𝑡𝑗𝑡

𝑗𝑛𝑐𝑛𝑏𝑦

𝑉𝑛𝑏𝑦 System long System short Under Production Short position Over Production Long position

System long >70 MWh decreased significantly System Short >70 MWh remained constant for physical player and increased slightly for non-physical player

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SLIDE 15

Dynamic Analysis Non-Physical Player Imbalance Half-cycles

15

  • 100

200 300 400 500 600 700 800 900 1.000 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.

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SLIDE 16

Conclusion

16

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.

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SLIDE 17

BACK UP

  • In August, 2 short extremes can be described

by LAST Epex spot price extremes

17

REF Time OLS IMB EST OLS_pBA_i mb_est_N O_x OLS_pBA_d ec x-decision imbalance_obs imb_obs+x

  • bs_pBA_BASE
  • bs_pBA_Op

timized_no_t ert expected spread spread p_ID 20908 557 8,63 60,03

  • 00

100,00 0,71 100,71 59,54 96,54

  • 180,00

83,46 180,00 22851 2500

  • 15,83

13,35

  • 00

100,00

  • 37,08

62,92 5,95 66,42

  • 198,00

131,58 198,00