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Computaonal +Finance:+ARoad+ Map+ForTheNext Ten +Years
23
Computa(onal Finance: A Road Map For The Next Ten Years Richard Olsen
Transcript of Computaonal +Finance:+ARoad+ Map+ForTheNext Ten +Years
Computa(onal Finance: A Road Map For The Next Ten Years
Richard Olsen
November 2012 – p. 2 Richard Olsen
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Our Track Record
Performance of product profile AF, gross of fees, including transac;on cost, leverage, interest and monthly reinvestment. Past performance is no guarantee for future results. The value of investments may fall as well as rise. Data sources: see disclaimer.
Parker
Olsen AF
HFRX
November 2012 – p. 3 Richard Olsen
Short-‐term Vola(lity Is Bigger Than We Think
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Price move up/down?
Sum of price moves up and down?
November 2012 – p. 4 Richard Olsen
Financial Markets As Energy Source
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Over one day: 0.5% plus/minus price move 6% coastline (at threshold of 0.05% after deducting transaction costs) Over one year: 30% plus/minus price move 1600% coastline
November 2012 – p. 5 Richard Olsen
How to approach problem?
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Fundamental analysis Neural networks Technical analysis Time series analysis ……
?
November 2012 – p. 6 Richard Olsen
Physical (me introduces bias
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Physical Time
Price
November 2012 – p. 7 Richard Olsen
What is problem?
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Observer
Complex process
Observer influences object by choosing time scale.
November 2012 – p. 8 Richard Olsen
What is (me?
Events are turning points.
November 2012 – p. 9 Richard Olsen
Event Based Intrinsic Time
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Physical Time
Price
DC
OS
Direc;onal Change
Overshoot 1. Overshoot
Threshold
Intrinsic Time
Endogenous time scale: more radical than Mandelbrot’s transaction clock
November 2012 – p. 10 Richard Olsen
Intrinsic Time: Threshold + Overshoot
0 10 20 30 40 50 60 70
1.26
1.28
1.30
1.32
Events
Mid
pric
e
0 10 20 30 40 50 60 70
1.26
1.28
1.30
1.32
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0 10 20 30 40 50 60 70
1.26
1.28
1.30
1.32
EUR_USD 0.4: 2010−05−03 00:08:20 − 2010−05−09 23:37:49
0 50 100 150 200
1.26
1.28
1.30
1.32
Events
Mid
pric
e
0 50 100 150 200
1.26
1.28
1.30
1.32
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0 50 100 150 200
1.26
1.28
1.30
1.32
EUR_USD 0.2: 2010−05−02 21:12:12 − 2010−05−09 23:59:09 0 5 10 15
1.26
1.28
1.30
1.32
Events
Mid
pric
e
0 5 10 15
1.26
1.28
1.30
1.32
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1.26
1.28
1.30
1.32
EUR_USD 0.8: 2010−05−03 01:20:39 − 2010−05−09 23:37:49
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Physical Time
Price
DC
OS
Direc;onal Change Overshoot 1. Overshoot
Threshold
Original Price Curve Threshold 0.8%
Threshold 0.4% Threshold 0.2% Intrinsic Time
Event Time Price
November 2012 – p. 11 Richard Olsen
How Big Is Price Overshoot On Average?
Price Overshoot is approx. = Threshold
November 2012 – p. 12 Richard Olsen
Scaling Laws: Mathema(cal Descrip(on
ln y = ln� x
C
�E= E lnx− E lnC
y = Ex + C
y0 =�x0
C
�E
x1 = αx0 → y1 =�αx0
C
�E= αEy0
Invariance of scales
Elegant: a couple of constants summarizes the rela;on
No point of reference
November 2012 – p. 13 Richard Olsen
Tick Scaling Law
�N(∆xtck)� =�
∆x
CN,tck
�EN,tck
where ∆xtck = 0.02%
AUD-JPY
AUD-USD
CHF-JPY
EUR-AUD
EUR-CHF
EUR-GBP
EUR-JPY
EUR-USD
GBP-CHF
GBP-JPY
GBP-USD
GRW
USD-CHF
USD-JPY
10-210-210-210-210-210-210-210-210-210-210-210-210-210-2 10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
100
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Tick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling lawTick-count scaling law
∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)
Ave
rage
num
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
sA
vera
genum
ber
oftick
s
Kernel density estimation
Kernel density estimation
∆x = 0.1%(Density vs. number of ticks)
∆x = 3.0%(Density vs. no. of ticks)
02e
-24e
-2
0
0 200 400 600 800
20000 40000 60000 80000
02e
-54e
-56e
-5
November 2012 – p. 14 Richard Olsen
A Set of Scaling Laws
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
100
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101
102102102102102102102102102102102102102102 103103103103103103103103103103103103103103 104104104104104104104104104104104104104104 105105105105105105105105105105105105105105 106106106106106106106106106106106106106106
10−
210
−2
10−
210
−2
10−
210
−2
10−
210
−2
10−
210
−2
10−
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−2
10−
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−2
Mean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveMean price moveaaaaaaaaaaaaaa
∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
〈|∆
x|〉 1
(%)
Law (0a), p = 1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
100
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102102102102102102102102102102102102102102 103103103103103103103103103103103103103103 104104104104104104104104104104104104104104 105105105105105105105105105105105105105105 106106106106106106106106106106106106106106
10−
210
−2
10−
210
−2
10−
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−2
10−
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−2
10−
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−2
10−
210
−2
10−
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−2
Quadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price moveQuadratic mean price movebbbbbbbbbbbbbb
∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
Law (0a), p = 2
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100
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10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Directional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countDirectional change countcccccccccccccc
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
N(∆
x dc)
Law (0b)
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100
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10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Price move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countPrice move countdddddddddddddd
∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
N(∆
x)N
(∆x)
Law (2)
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
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−1
10−
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−1
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102102102102102102102102102102102102102102 103103103103103103103103103103103103103103 104104104104104104104104104104104104104104 105105105105105105105105105105105105105105 106106106106106106106106106106106106106106
10−
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−2
10−
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−2
10−
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−2
10−
210
−2
10−
210
−2
Maximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveMaximum price moveeeeeeeeeeeeeee
∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
〈∆x m
ax〉
(%)
Law (3), p = 110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
−1
10−
110
010
010
010
010
010
010
010
010
010
010
010
010
010
010
110
110
110
110
110
110
110
110
110
110
110
110
110
1
102102102102102102102102102102102102102102 103103103103103103103103103103103103103103 104104104104104104104104104104104104104104 105105105105105105105105105105105105105105 106106106106106106106106106106106106106106
10−
210
−2
10−
210
−2
10−
210
−2
10−
210
−2
10−
210
−2
10−
210
−2
10−
210
−2
Quadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveQuadratic mean max price moveffffffffffffff
∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)∆t (s)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
〈∆x〉
2(%
)〈∆
x〉2
(%)
Law (3), p = 2
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100100100100100100100100100100100100100100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
103
103
103
103
103
103
103
103
103
103
103
103
103
103
105
105
105
105
105
105
105
105
105
105
105
105
105
105
107
107
107
107
107
107
107
107
107
107
107
107
107
107
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Mean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price moveMean time of price movegggggggggggggg
∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)∆x (%)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
〈∆t x〉 1
(s)
Law (4)
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100100100100100100100100100100100100100100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
105
105
105
105
105
105
105
105
105
105
105
105
105
105
106
106
106
106
106
106
106
106
106
106
106
106
106
106
107
107
107
107
107
107
107
107
107
107
107
107
107
107
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Time during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changesTime during directional changeshhhhhhhhhhhhhh
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
〈∆t d
c〉
(s)
Law (5)
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Total price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveTotal price moveiiiiiiiiiiiiii
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
〈∆xt
o〉
(%)
Law (9), ∗ = to
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100100100100100100100100100100100100100100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
105
105
105
105
105
105
105
105
105
105
105
105
105
105
106
106
106
106
106
106
106
106
106
106
106
106
106
106
107
107
107
107
107
107
107
107
107
107
107
107
107
107
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Time of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total moveTime of total movejjjjjjjjjjjjjj
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
〈∆tt
o〉
(s)
Law (10), ∗ = to
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
105
105
105
105
105
105
105
105
105
105
105
105
105
105
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Total-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countTotal-move tick countkkkkkkkkkkkkkk
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Num
ber
oftick
sto
tal
Law (11), ∗ = to
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100100100100100100100100100100100100100100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)Coastline (cum. total move)llllllllllllll
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
∆x c
oast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)∆
x coast(%
)
Law (12), ∗ = to
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
Directional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change moveDirectional-change movemmmmmmmmmmmmmm
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
〈∆xd
c〉
(%)
Law (9), ∗ = dc
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
105
105
105
105
105
105
105
105
105
105
105
105
105
105
106
106
106
106
106
106
106
106
106
106
106
106
106
106
107
107
107
107
107
107
107
107
107
107
107
107
107
107
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Time of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changeTime of directional changennnnnnnnnnnnnn
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
〈∆td
c〉
(s)
Law (10), ∗ = dc
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
10−210−
2
Directional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countDirectional-change tick countoooooooooooooo
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
〈N(∆
xdc
tck)〉
Law (11), ∗ = dc
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Cumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changeCumulative directional changepppppppppppppp
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
∆xd
ccoast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)∆
xdc
coast(%
)
Law (12), ∗ = dc
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
10−1
10−
1
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
10−2
10−
2
Overshoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveOvershoot moveqqqqqqqqqqqqqq
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
〈∆xo
s〉
(%)
Law (9), ∗ = os
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100100100100100100100100100100100100100100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
105
105
105
105
105
105
105
105
105
105
105
105
105
105
106
106
106
106
106
106
106
106
106
106
106
106
106
106
107
107
107
107
107
107
107
107
107
107
107
107
107
107
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Time of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootTime of overshootrrrrrrrrrrrrrr
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
〈∆to
s〉
(s)
Law (10), ∗ = os
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
10−110−
1
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
102
102
102
102
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
105
105
105
105
105
105
105
105
105
105
105
105
105
105
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Overshoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countOvershoot tick countssssssssssssss
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
ber
oftick
sov
ersh
oot
Num
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oftick
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Num
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oot
Num
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Num
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Num
ber
oftick
sov
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oot Law (11), ∗ = os
10−110−110−110−110−110−110−110−110−110−110−110−110−110−1 100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
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100
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101
101
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102
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102
102
102
102
102
102
102
102
102
103
103
103
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103
103
103
103
103
103
104
104
104
104
104
104
104
104
104
104
104
104
104
104
10−210−210−210−210−210−210−210−210−210−210−210−210−210−2
Cumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshootCumulative overshoottttttttttttttt
∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)∆xdc (%)
∆xo
scoast(%
)∆
xos
coast(%
)∆
xos
coast(%
)∆
xos
coast(%
)∆
xos
coast(%
)∆
xos
coast(%
)∆
xos
coast(%
)∆
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
)∆
xos
coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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coast(%
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xos
coast(%
)∆
xos
coast(%
)∆
xos
coast(%
)
Law (12), ∗ = os
November 2012 – p. 15 Richard Olsen
Imbalances Of Supply And Demand Cause Price Overshoots
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
Agent based modeling: we configure agents as virtual traders with simple trading rules.
November 2012 – p. 16 Richard Olsen
Trading the Coastline
November 2012 – p. 17 Richard Olsen
Interac(ng Agents Trade The Coastline Long And Short
EUR_USD
Price
Price
1.250
1.265
1.280
1.295
1.310
1.325
03 04 05 06 07 08 092010−05−02 18:58:28 2010−05−09 23:59:17
1
1
1
1
1
2
2
2
1
1
2
2
3
3
3
1 1 1 1
2
2 2 2 1 1
1
2 1 3 3 1 2 3
open
long
open
sho
rt
increase long
take profit sho
rt
open
long
open
sho
rt
take profit sho
rt
1 gets advantage
open
sho
rt
increase long
coastline
trading
increase sho
rt
take profit sho
rt
take profit long
take profit long 2
1 gets advantage
long trade
short trade
close long
close short
coastline trading
Each number corresponds to an independent trading agent.
November 2012 – p. 18 Richard Olsen
! "#$ %&' (#) *+) (#, "-$& "-., *-/ 0&+1 231 456 7&3 8&#) 9#):&) ;%<=
>??@ ?ABC ?ADC ?ABB ?AED ?AFF G?A?E >AB> G>ABC EABC
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>?B> G?AIF ?AIE BADC BAD@ GBAH> BAHE G?AH? BAFI ?A?B DA>? G?ADB >AD>
Return Is Reward for Providing Liquidity And Stabilizing Prices.
Performance of product profile AF, gross of fees, including transac;on cost, leverage, interest and monthly reinvestment. Past performance is no guarantee for future results. The value of investments may fall as well as rise. Data sources: see disclaimer.
Parker
Olsen AF
HFRX
November 2012 – p. 19 Richard Olsen
Context
45 trillion USD: World Global Product 60 trillion USD: Market Capitalization of equity markets 160 trillion USD: Global Debt
• Crash of 1987 • Crash of 2008 • Flash Crash • Interest Rate Bubble
Errors and omissions in computational finance translate into losses of 10+ trillion of USD.
November 2012 – p. 20 Richard Olsen
Financial Markets Are A Mirror For Real Economy
Outdated middle and back office of financial industry with based processing and daily interest rate payments
Revamping of financial market infrastructure: electronic certificates for financial assets and Internet exchange
Global information system with real time forecasts, risk measures as a Wikipedia-like project.
Price stabilizing investment strategies
November 2012 – p. 21 Richard Olsen
Research And Development Agenda
• Collecting big data and making data accessible
• Online Wikipedia for global information system
• Dynamic model of emerging systems
• Theory of scaling laws
• Modeling of market processes
• Emergent social structures
• Financial engines: alpha generating trading models
• Weather maps of financial markets
• Risk modeling
• iPhone like financial products
November 2012 – p. 22 Richard Olsen
www.futurict.eu
FuturICT pitches for a 10 year 1 billion EUR program:
….integrating adaptive information and communication technologies, Complexity Science and Social Sciences will create a paradigm shift….
Prof. Dirk Helbing, ETH Zurich
November 2012 – p. 23 Richard Olsen
Centre for Computa(onal Finance and Economic Agents
More powerful than all the armies of the world, is an idea whose time has come. ........Victor Hugo
