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 critical state ?!

A new mechanism: self-organized critical control

Continuous closed loop control in humans Mouse Balancing Dynamics:       0 T T ( T M )  t 1 t t T t

Power laws of human control    Y ( ) P Y Line: Adaptive control with reaction delay F. Patzelt & K. P., Frontiers Comp. Neurosci. 2008. F. Patzelt & K. P., Phys. Rev. Lett. 2011. The Principle of Information Annihilation

... also in financial markets?

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?

Ingredients 1 The Price: demand demand demand ( p )    t t t t p p p offer offer offer t t t ( ) p t t t t

Ingredients 2 The (Log-)Return:   p    t ln r   t   p  1 t

Ingredients 3 random agents with money and stocks N i M S i i   Agent' s decisions 1,0 depend on ' informatio ns'      1 ,..., P i N     ( t ) M i i   i 1 p t N      ( t ) ( 1 ) S i i  i 1

Ingredients 4 Trading at price p (conservation of assets):   S               i   1 ( 1 ) M M p i i i i   M i   M 1                 i  S S 1 ( 1 ) i i i i   S p i  - free risk parameter

Ingredients 5     • Extrinsic information = random 1 ,..., P t ' Exogenous Information ' • Intrinsic information = signs of past m returns ' Endogenous Information ' mod ,          m ( 1 ) ( 2 ( ) ( ( ) 0 ) 2 t t r t P P

Results 1: Dynamics from extrinsic information     2 7 N , m 5 , 0 . 1 Exogenous Information becomes annihilated! Trading is an efficient learning algorithm!

Results 2: A critical point for exogenous information   1 / 2 c m 2   N Trading is an optimal learning algorithm!

Results 3: Dynamics from intrinsic information     2 12 , 12 , 0 . 5 N m

What causes the large price jumps? (part one)      12 6 , endogenous information 2 , 2 , 12 , 0 . 01 N N m P

Results 4: High kurtosis fluctuations beyond critical line! Phase diagrams: reduction of return magnitude: kurtosis of return distribution:

Results 5: Homogenous exogenous information Phase diagrams: reduction of return magnitude: kurtosis of return distribution:

What causes the large price jumps? (part two) Correlations of returns with surprise:

Results 6: Self-referential dynamics can reproduce stylized facts!

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)   1 / 2 as long as they are sufficiently diverse. Non-negativity: c • Removement of predictable fluctuations from endogenous information (e.g. when speculation is dominant) destabilizes the dynamics and results in large return fluctuations. The 'Information Annihilation Instability' (IAI) is a general principle that dominates many systems involving rapid adptive control.

See our poster #49

Thanks to Josephine Mielke Thank you!

see also our paper at http://arxiv.org/abs/1211.6695