An elementary model of price dynamics in a financial market: Distribution, Multiscaling & Entropy
| dc.creator | Reimann, Stefan | |
| dc.date | 2006-02-14 | |
| dc.date.accessioned | 2026-07-07T12:07:43Z | |
| dc.date.available | 2026-07-07T12:07:43Z | |
| dc.description | Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $τ(β)$. Empirical data considered are daily prices of 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 model implies that the distribution of log-returns is Laplacian $f_Z(z) \sim \exp(-\frac{|z|}α)$, whose single parameter $α$ 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 daily log returns are close to being Laplacian distributed. The spectra of Hurst exponents of both, empirical data $τ_{emp}$ and simulated data due to our model $τ_{theor}$, are compared. Due to the finding of non-linear Hurst spectra, the Renyi entropy (RE) $R_β(f_Z)$is considered. An explicit functional form of the RE for an exponential distribution is derived. Theoretical REs of simulated asset return trails are in good agreement with the RE estimated from empirical returns. | |
| dc.description | 13 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/physics/0602097 | |
| dc.identifier | http://arxiv.org/abs/physics/0602097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209068 | |
| dc.subject | Physics and Society | |
| dc.subject | Statistical Finance | |
| dc.title | An elementary model of price dynamics in a financial market: Distribution, Multiscaling & Entropy | |
| dc.type | text |