Abstract
Price dynamics of speculative markets is one of the most complex phenomena in economics. Already the statistical description turns out to be difficult. The most prominent characteristic of the distribution of logarithmic price differences (returns) Δy for a given time delay Δt is its lepto- kurtosis, i.e., the pronounced frequencies with which both small and large returns occur. Proper modelling of this effect is of practical relevance for risk management. The kurtosis of the return distribution is largest for Δt of the order of minutes and decreases monotonically with increasing Δt, accompanied by an according change in the form of the distribution [1, 2]. Simultaneously, the variance of the distribution increases: it depends on the time delay according to a power law ((Δy)2) ~ Δt ε2.
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Muller, U. A., Dacorogna, M. M., Olsen, R. B., Pictet, O. V., Schwarz, M., and Morgenegg, C.: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis, Journal of Banking and Finance 14 (1990), 1189–1208.
Baillie, R. T. and Bollerslev, T.: The message in daily exchange rates: a conditional variance tale, Journal of Business and Economic Statistics 7 (1989) 297–305; Intra-day and inter-market volatility in foreign exchange rates, Review of Economic Studies 58 (1990), 565–585.
Monin, A.S. and Yaglom, A.M.: Statistical Fluid Mechanics Vol. 1 & 2, MIT Press, Cambridge (MA),1971 & 1975
Kolmogorov, A. N.: The local structure of turbulence in a viscous incompressible fluid for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR 30 (1941), 301- 305
Kolmogorov, A. N.: Refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech. 13 (1962) 82–85.
Obukhov, A. M.:Some specific features of atmospheric turbulence, J.Fluid Mech. 13 (1962), 77–81
Castaing, B., Gagne, Y., and Hopfinger, E.: Velocity probability density functions of high Reynolds number turbulence, Physica D 46 (1990), 177–200.
Chabaud, B., Naert, A., Peinke, J., Chillä, F., Castaing, B., and Hebral, B.: Transition toward developed turbulence, Phys. Rev. Lett. 73 (1994) 3227–3230.
Peinke, J., Castaing, B., Chabaud, B., Chilla, F., Hébral, B., and Naert, A.: On a fractal and an experimental approach to turbulence, Fractals in the Natural and Applied Sciences A41 (1994), 295–304.
Naert, A., Puech, L., Chabaud, B., Peinke, J., Castaing, B., and Hebral, B.: Velocity intermittency in turbulence: how to objectively characterize it?, J. Phys. II France 4 (1984), 215–224.
Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P., and Dodge, Y.:Turbulent cascades in foreign exchange markets, submitted to Nature (1995).
Vassilicos, J. C.: Turbulence and intermittency, Nature 374 (1995), 408–409.
Mantegna, R. N. and Stanley, H. E.: Scaling behaviour in the dynamics of an economic index, Nature 376 (1995), 46–49
Muller, U. A., Dacorogna, M. M., Dave, R. D., Olsen, R. B., Pictet, O. V., and von Weizsacker, J. E.: Volatilities of different time resolutions — analyzing the dynamics of market components, Journal of Empirical Finance, in press.
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© 1996 Kluwer Academic Publishers
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Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P. (1996). Turbulence and Financial Markets. In: Gavrilakis, S., Machiels, L., Monkewitz, P.A. (eds) Advances in Turbulence VI. Fluid Mechanics and its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0297-8_46
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DOI: https://doi.org/10.1007/978-94-009-0297-8_46
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