Fractional calculus and continuous-time finance
AbstractIn this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predictions on the long-time behaviour of the waiting-time probability density are presented. Finally, a general scaling form is given, based on the solution of the fractional diffusion equation.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0411007.
Length: 11 pages
Date of creation: 05 Nov 2004
Date of revision:
Note: Type of Document - pdf; pages: 11. Preprint pdf version of a paper published in Physica A, vol.284, p.376-384, 2000.
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Stochastic processes; random walk; statistical finance; duration;
Other versions of this item:
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- G - Financial Economics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-11-22 (All new papers)
- NEP-ETS-2004-11-22 (Econometric Time Series)
- NEP-FIN-2004-11-22 (Finance)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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