Berlin 2015 – wissenschaftliches Programm
SOE 4.2: Vortrag
Montag, 16. März 2015, 11:00–11:15, MA 001
Stylized Dynamics from Efficient Pricing — •Felix Patzelt and Klaus Pawelzik — Institute for Theoretical Physics, University of Bremen, Germany
Mainstream economic theories describe financial markets as systems that transform available information into prices. This view is consistent with the finding that price changes are hard to predict. It has, however, proven difficult to reconcile with the excessive movements of real prices.
The origins of empirical ``stylized facts'' of price time series, on the other hand, are often investigated using multi-agent models. Difficulties to coordinate the agent's strategies can lead to slowly shifting market imbalances that modulate the market's volatility due to non-linearities.
Here we combine these seemingly opposing views in a minimal and analytically fully tractable model. We first show that simple efficient bidding processes where prices follow a martingale inevitably form ``bubbles''. We furthermore consider a simple non-linearity for the generation of prices that arises naturally from the imbalance of supply and demand. It amplifies the modulation the price volatility similar to much more complicated models. This model quantitatively reproduces the empirical scaling laws of the distributions and temporal correlations of (logarithmic) price-change magnitudes independent of parameters. It can be mapped to an equivalent diffusion process which might be used to estimate market imbalances underlying real price time series and more complex models.