Statistical Arbitrage in Balancing Markets - TU Wien · Results Physical/Non-Physical Player...
Transcript of Statistical Arbitrage in Balancing Markets - TU Wien · Results Physical/Non-Physical Player...
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
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Austrian Imbalance Settlement Design
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Source: APCS, July 2015
imb
𝑝𝐵𝐴
𝑝 𝐵𝑎𝑠𝑖𝑠
𝑖𝑚𝑏𝑚𝑎𝑥
𝑈𝑚𝑎𝑥
System long System short
Under Production
Short position
Over Production
Long position
𝑝𝐵𝑎𝑠𝑖𝑠
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
𝑇 = min(𝑈𝑚𝑖𝑛 +𝑈𝑚𝑎𝑥 − 𝑈𝑚𝑖𝑛
imb𝑚𝑎𝑥2 × 𝑖𝑚𝑏2 ; 𝑈𝑚𝑎𝑥)
𝑝𝐵𝐴 = 𝑝𝐵𝑎𝑠𝑖𝑠 ± 𝑇
Market Player´s Perspectives
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+
𝑣 = ( 𝑥 𝑖𝑚𝑏 −𝑀𝐶) ∗ 𝑥𝐵𝐴
Pay off function for rational decisions
Needs a rational expectation for 𝑖𝑚𝑏
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 DP
E3 DP
E4
PLE
IT
Non-Physical Player (external schedules)
Information perspectiveDecision perspective
Quantile Regression Forecast
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imbi j = βi1 ∗ imbi j−r + βi2 ∗ EPEXi j−r + βi3 × wind_ei j−r + βi4 ∗ solar_ei j−r + c𝑖
We identified 4 explanatory variables to describe the
response variable 𝑖𝑚𝑏𝑖 𝑗:
𝑖𝑚𝑏𝑖 𝑗−𝑟 Imbalance(j-r) autoregressive parameter with
a time lag of j-r. 𝐸𝑃𝐸𝑋𝑖 𝑗−𝑟Last price EPEX(j-r) EPEX spot intraday
trading closes at j-r. 𝑤𝑖𝑛𝑑_𝑒𝑖 𝑗−𝑟Wind error(j-r) is calculated as the
difference between the day ahead forecast and the actual measured. 𝑠𝑜𝑙𝑎𝑟_𝑒𝑖 𝑗−𝑟Solar error(j-r) is calculated as the
difference between the day ahead forecast and the actual measured value.
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
Information time delay in [minutes]
Quantile Regression Forecast
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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
Expected Value Model
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𝑚𝑎𝑥𝑘 𝐸𝑉(𝑥𝑘) =
𝑖∈𝐼
𝑣𝑖 𝑘 𝜌(𝑠𝑖)
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(𝑠𝑖) associated with each state of nature 𝑠𝑖. The course of action 𝑥𝑘 is chosen which has the highest expected value 𝐸𝑉(𝑥𝑘).
Physical Player
Non-physical player
v𝑙𝑜𝑛𝑔 = ( 𝑖𝑚𝑏 −𝑀𝐶) ∗ 𝑥
v𝑠ℎ𝑜𝑟𝑡 = 𝑀𝐶𝐷𝐴 −𝑝𝑔𝑎𝑠𝑠ℎ𝑜𝑟𝑡 − 𝑝 𝑥 𝑖𝑚𝑏 ) ∗ 𝑥
𝑣 = 𝑝 𝑥. 𝑖𝑚𝑏 − 𝑀𝐶𝐸𝑃𝐸𝑋 ∗ 𝑥
ma k(𝑗
𝑖∈𝐼
𝑣𝑖 𝑗 𝑘 ∗ 𝜌( 𝑖𝑚𝑏𝑖) )
Pay offs:
OUR OBJECTIVE:
Index for time 𝑗 ∈ {T}
Index for state of nature 𝑖 ∈𝐼𝑀𝐵
Index for position 𝑘 ∈ {−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 datawinter and summer month 2015Benchmark and key performanceindicators
Results Physical/Non-Physical Player
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-
500.000
1.000.000
1.500.000
2.000.000
2.500.000
realizedprofit
expectedprofit
realizedprofit
expectedprofit
summer summer winter winter
pro
fit
[EU
R/m
on
th]
physical player non-physical player
-
500.000
1.000.000
1.500.000
2.000.000
2.500.000
3.000.000
summer wintersyst
em
co
sts
in [
EUR
/mo
nt]
observation physical player non-physical player
20,00
22,00
24,00
26,00
28,00
30,00
32,00
summer winterstan
dar
d d
evi
atio
n in
[M
Wh
]
observation 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
abso
lute
imb
alan
ce in
[M
Wh
]
observation physical player non-physical player
Results Physical/Non-Physical Player
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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
Dynamic Analysis
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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 DP
E3 DP
E4
PLE
IT
Information time delay in [minutes] Comparison withobserved imbalance
Dynamic Analysis Non-Physical PlayerSystem Costs and Parameters
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Financial and system behavioural metrics show a win-win situation
WINTER SUMMERSystem costs System costs
Absolute imbalance Standard deviation
System costs System costs
Absolute imbalance Standard deviation
Dynamic Analysis Non-Physical PlayerSystem Costs and Parameters
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With long information time delays the actions are inefficient.
WINTER SUMMERSystem costs System costs
Absolute imbalance Standard deviation
System costs System costs
Absolute imbalance Standard deviation
Dynamic Analysis Non-Physical PlayerHow often did they take positions?
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0%10%20%30%40%50%60%70%
qu
anti
ty s
um
me
r
short positions non-physical player wintershort positions physical player winterlong positions non-physical player winterlong positions physical player winter
0%10%20%30%40%50%60%70%
qu
anti
ty s
um
me
r
short positions non-physical player wintershort positions physical player winterlong positions non-physical player winterlong positions physical player winter
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
pe
rce
nta
ge o
f p
osi
tio
ns
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 theyspill/short themarket?
From 2683 15 minute intervals in winter/summer thephysical player traded less than 20 percent of time intervals whereas the non-physical EPEX Spot trading model suggested over 90% of the time to take a imbalance position.
Dynamic Analysis Non-Physical PlayerImbalance Extremes
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WINTER SUMMER
imb
𝑝𝐵𝐴
𝑝 𝐵𝑎𝑠𝑖𝑠
𝑖𝑚𝑏𝑚𝑎𝑥
𝑈𝑚𝑎𝑥
System long System short
Under Production
Short position
Over Production
Long position
System long >70 MWh decreased significantlySystem Short >70 MWh remained constant for physicalplayer and increased slightly for non-physical player
Dynamic Analysis Non-Physical PlayerImbalance Half-cycles
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- 100 200 300 400 500 600 700 800 900
1.000
imb
alan
ce h
alf
cycl
es
[-]
half cycles winter half cycles summer
Half cycles in case of participation of the physical player increased by 80% for the lag 1 modelFor the physical player only a slight increase is observed.
Conclusion
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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 wouldbe able to help the system, but the frequency of trades in this single player simulationwas very high, which potentially would lead to overreactions in the market in a multiplayer setting.
BACK UP
• In August, 2 short extremes can be described by LAST Epex spot price extremes
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REF Time
OLS IMB
EST
OLS_pBA_i
mb_est_N
O_x
OLS_pBA_d
ec x-decision imbalance_obs imb_obs+x obs_pBA_BASE
obs_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