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A New Model For Stock Price Movements

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  • Guido VENIER

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.

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Bibliographic Info

Article provided by Spiru Haret University, Faculty of Financial Management and Accounting Craiova in its journal Journal of Applied Economic Sciences.

Volume (Year): 3 (2008)
Issue (Month): 3(5)_Fall2008 ()
Pages: 329-350

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Handle: RePEc:ush:jaessh:v:3:y:2008:i:3(5)_fall2008:p:329-350

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Web page: http://www2.spiruharet.ro/facultati/facultate.php?id=14
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Related research

Keywords: Deterministic Diffusion; Stock Pricing; Fat Tails; Heteroscedasticity; Long Range Dependence; Option Pricing;

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  1. repec:att:wimass:9520 is not listed on IDEAS
  2. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
  3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  4. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
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Cited by:
  1. Huang, Weihong & Zheng, Huanhuan & Chia, Wai-Mun, 2010. "Financial crises and interacting heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1105-1122, June.
  2. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2012. "The bull and bear market model of Huang and Day : Some extensions and new results," BERG Working Paper Series 89, Bamberg University, Bamberg Economic Research Group.
  3. Venier, Guido, 2008. "A Simple Hypothesis Test for Heteroscedasticity," MPRA Paper 11591, University Library of Munich, Germany.

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