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A new Model for Stock Price Movements

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  • Venier, Guido

Abstract

A new alternative diffusion model for asset price movements is presented. 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 reason for the investigation on deterministic diffusion processes as suitable model for the behaviour of stock prices is, that their time series can obey certain stylized facts of real world stock market time series. For example they can show fat tails of empirical log returns in union with varying volatility i.e. heteroscedacity as well as slowly decaying autocorrelations of squared log returns. These phenomena could not be explained by a simple Brownian motion and have been the most criticism to the lognormal random walk. The scope is to show that deterministic diffusion models can explain the occurrence of those empirical observed stylized facts and to discuss the implications for economic theory with respect to market efficiency and option pricing.

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File URL: http://mpra.ub.uni-muenchen.de/11593/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9146.

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Date of creation: 10 Aug 2007
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Handle: RePEc:pra:mprapa:9146

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Keywords: stock pricing; chaos theory; deterministic diffusion; heteroscedasticity; fat tails; long range dependence; stylized facts of economic time series; fractional brownian motion; levy stable distributions; brownian motion; black scholes; option pricing; CAPM; market efficiency;

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  1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  2. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  3. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
  4. 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.
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Cited by:
  1. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2013. "The bull and bear market model of Huang and Day: Some extensions and new results," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2351-2370.
  2. Venier, Guido, 2008. "A Simple Hypothesis Test for Heteroscedasticity," MPRA Paper 11591, University Library of Munich, Germany.
  3. 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.

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