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Annihilation of Information Destabilizes Speculative Markets
Klaus Pawelzik with Felix Patzelt Institute for Theoretical Physics University Bremen
Destabilizes Speculative Markets Klaus Pawelzik with Felix Patzelt - - PowerPoint PPT Presentation
Destabilizes Speculative Markets Klaus Pawelzik with Felix Patzelt - - PowerPoint PPT Presentation
Annihilation of Information Destabilizes Speculative Markets Klaus Pawelzik with Felix Patzelt Institute for Theoretical Physics University Bremen Markets are dynamical systems Markets are in some equilibrium !? Markets are close to a
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Markets are in some equilibrium !? Markets are close to a critical state ?!
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A new mechanism: self-organized critical control
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t T t t t
M T T T
) (
1
Continuous closed loop control in humans
Mouse Balancing Dynamics:
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Power laws of human control
Y Y P ) (
- F. Patzelt & K. P., Phys. Rev. Lett. 2011.
Line: Adaptive control with reaction delay
The Principle of Information Annihilation
- F. Patzelt & K. P., Frontiers Comp. Neurosci. 2008.
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... also in financial markets?
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A Minimal Realistic Market Model as Adaptive Control System
- Markets are systems of interacting agents
- Agents' actions are orders (puts and calls)
- Prices are generated deterministically
Dynamics? Adaptation? Control?
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Ingredients 1
The Price:
t t t
p
- ffer
demand ) ( ) (
t t t t t
p p p
- ffer
demand
t t t
p
- ffer
demand
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Ingredients 2
The (Log-)Return:
1
ln
t t t
p p r
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Ingredients 3
N i t i i N i t i i t
S M p
1 ) ( 1 ) (
) 1 (
P S M i N
i i
,..., 1 ns' informatio '
- n
depend 1,0 decisions s Agent' stocks and money with agents random
i
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Ingredients 4
Trading at price p (conservation of assets):
i i i i i i i i i i i i
p S M S S p M S M M 1 ) 1 ( 1 ) 1 ( 1
- free risk parameter
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Ingredients 5
- Intrinsic information = signs of past m returns
'Endogenous Information'
m
P P t r t t 2 ) ) ( ( ) ( 2 ( ) 1 ( , mod
- Extrinsic information = random
'Exogenous Information'
P
t
,..., 1
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Exogenous Information becomes annihilated! Trading is an efficient learning algorithm!
1 . , 5 , 27 m N
Results 1:
Dynamics from extrinsic information
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Results 2:
A critical point for exogenous information
Trading is an optimal learning algorithm!
N
m
2
2 / 1
c
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Results 3:
Dynamics from intrinsic information
5 . , 12 , 212 m N
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What causes the large price jumps? (part one)
01 . , 12 , 2 , 2
6 12
m N N
P
, endogenous information
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Results 4:
High kurtosis fluctuations beyond critical line! Phase diagrams: reduction of return magnitude: kurtosis of return distribution:
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Results 5: Homogenous exogenous information
Phase diagrams: reduction of return magnitude: kurtosis of return distribution:
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What causes the large price jumps? (part two) Correlations of returns with surprise:
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Results 6:
Self-referential dynamics can reproduce stylized facts!
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Efficient adaptive control in financial markets can explain extreme return fluctuations
- Redistribution of assets via trading is equivalent to an efficient learning
rule with the objective of minimizing predictable price fluctuations.
- 'Rationality' of a market as a whole can rely on simple agents (idiots)
as long as they are sufficiently diverse. Non-negativity:
- Removement of predictable fluctuations from endogenous information
(e.g. when speculation is dominant) destabilizes the dynamics and results in large return fluctuations. 2 / 1
c
The 'Information Annihilation Instability' (IAI) is a general principle that dominates many systems involving rapid adptive control.
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See our poster #49
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Thank you!
Thanks to Josephine Mielke
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