A new Model for Stock Price Movements

Venier, Guido (2007): A new Model for Stock Price Movements. Published in: Journal of Applied Economic Sciences , Vol. 3, No. 3 (November 2008): pp. 327-347.

Abstract

This paper presents a new alternative diffusion model for asset price movements. In contrast to the popular approach of Brownian Motion it proposes Deterministic Diffusion for the modelling of stock price movements. These diffusion processes are a new area of physical research and can be created by the chaotic behaviour of rather simple piecewise linear maps, but can also occur in chaotic deterministic systems like the famous Lorenz system. The motivation for the investigation on Deterministic Diffusion processes as suitable model for the behaviour of stock prices is, that their time series can obey mostly observed stylized facts of real world stock market time series. They can show fat tails of empirical log returns in union with timevarying volatility i.e. heteroscedasticity as well as slowly decaying autocorrelations of squared log returns i.e. long range dependence. These phenomena cannot be explained by a geometric Brownian Motion and have been the largest criticism to the lognormal random walk. In this paper it will be shown that Deterministic Diffusion models can obey those empirical observed stylized facts and the implications of these alternative diffusion processes on economic theory with respect to market efficiency and option pricing are discussed.

• Item Type: MPRA Paper
• Language: English
• Keywords: Deterministic Diffusion, Stock Pricing, Fat Tails, Heteroscedasticity, Long Range Dependence, Option Pricing
• Subjects: G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D58 - Computable and Other Applied General Equilibrium Models; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D53 - Financial Markets; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; Z - Other Special Topics > Z0 - General; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D79 - Other

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