Artificial market model based on deterministic agents and derivation of limit of GARCH type process
Aki-Hiro Sato, Hideki Takayasu
Abstract
We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability density function of market price changes has power law tails. Autocorrelation coefficient of the changes has an anti-correlation, and autocorrelation coefficient of squared changes (volatility correlation function) has a long time correlation. A probability density function of intervals between successive trading follows a geometric distribution. GARCH type stochastic process is theoretically derived from this market model in a limit case. We discuss factors of the market price fluctuations and a relation between the volatility of the market prices and a demand-supply curve. We conclude that the power law tails and the long time volatility result from mechanism of the GARCH type stochastic process.
Create a lesson
Related papers
Dynamically Reentrant Skyrmion Phase in Oscillating Magnetic Fields
Z. Demir Vatansever, E. Vatansever, A. Vasilopoulos et al.
Mutual linearity in semi-Markov networks
Julian B. Voits, Ulrich S. Schwarz
Steady states in asymmetric exclusion processes with reactions: Fluctuations and non-mean field behaviour
Rohn Chatterjee, Atri Goswami, Sudip Mukherjee
Marginal Operator Deformations and Pseudocriticality in Baxter--Wu Models
Hyun-Yong Lee, Naoki Kawashima, Nikolaos G. Fytas et al.
Kardar--Parisi--Zhang density hydrodynamics in a coherent XXZ--ASEP Lindbladian
Yansheng Liu, Daoguang Li, Kaixiang Lu et al.
Brownian gyrator model with stochastic resetting
Satya N. Majumdar, Gregory Schehr, Pascal Viot et al.