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An Elementary Model of Price Dynamics in a Financial Market: Distribution, Multiscaling & Entropy


Reimann, Stefan (2006). An Elementary Model of Price Dynamics in a Financial Market: Distribution, Multiscaling & Entropy. Working paper series / Institute for Empirical Research in Economics No. 271, University of Zurich.

Abstract

Stylized facts of empirical assets log-returns include the existence of semi heavy tailedndistributions and a non-linear spectrum of Hurst exponents. Empirical datanconsidered are daily prices from 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is driven by expectations. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics. This 0-order modelnimplies that the distribution of log-returns is Laplacian, whose single parameter can be regarded as a measure for the long-time averaged liquidity in the respective market. A comparison with the (more general) Weibull distribution shows that empirical log returns are close to being Laplacian distributed. The spectra of Hurst exponents of both, empirical data and simulated data due to our model, are compared. Due to the finding of non-linear Hurst spectra, the Renyi entropy is considered. An explicit functional form of the RE for an exponential distribution is derived. Theoretical of simulated asset return trails are in good agreement with the estimated from empirical returns.n

Abstract

Stylized facts of empirical assets log-returns include the existence of semi heavy tailedndistributions and a non-linear spectrum of Hurst exponents. Empirical datanconsidered are daily prices from 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is driven by expectations. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics. This 0-order modelnimplies that the distribution of log-returns is Laplacian, whose single parameter can be regarded as a measure for the long-time averaged liquidity in the respective market. A comparison with the (more general) Weibull distribution shows that empirical log returns are close to being Laplacian distributed. The spectra of Hurst exponents of both, empirical data and simulated data due to our model, are compared. Due to the finding of non-linear Hurst spectra, the Renyi entropy is considered. An explicit functional form of the RE for an exponential distribution is derived. Theoretical of simulated asset return trails are in good agreement with the estimated from empirical returns.n

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Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Institute for Empirical Research in Economics (former)
Dewey Decimal Classification:330 Economics
Language:English
Date:February 2006
Deposited On:29 Nov 2011 22:47
Last Modified:12 Aug 2017 13:01
Series Name:Working paper series / Institute for Empirical Research in Economics
ISSN:1424-0459
Official URL:http://www.econ.uzh.ch/wp.html

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