A New Model For Stock Price Movements
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.
Volume (Year): 3 (2008)
Issue (Month): 3(5)_Fall2008 ()
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- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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.
- 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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"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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