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Fractional calculus and continuous-time finance

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Author Info
Enrico Scalas (Universita' del Piemonte Orientale, Alessandria, Italy)
Rudolf Gorenflo (Freie Universitaet Berlin, Berlin, Germany)
Francesco Mainardi (Universita' di Bologna, Bologna, Italy)

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Abstract

In 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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File URL: http://129.3.20.41/eps/fin/papers/0411/0411007.pdf
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Publisher Info
Paper provided by EconWPA in its series Finance with number 0411007.

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Length: 11 pages
Date of creation: 05 Nov 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0411007

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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Web page: http://129.3.20.41

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Related research
Keywords: Stochastic processes; random walk; statistical finance; duration;

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Find related papers by JEL classification:
G - Financial Economics

This paper has been announced in the following NEP Reports:

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  1. Alvaro Cartea & Diego del-Castillo-Negrete, 2006. "Fractional Diffusion Models of Option Prices in Markets with Jumps," Birkbeck Working Papers in Economics and Finance 0604, Birkbeck, Department of Economics, Mathematics & Statistics. [Downloadable!]
  2. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA. [Downloadable!]
    Other versions:
  3. B. Düring & G. Toscani, 2007. "Hydrodynamics from kinetic models of conservative economies," CoFE Discussion Paper 07-06, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  4. Enrico Scalas, 2005. "Five Years of Continuous-time Random Walks in Econophysics," Finance 0501005, EconWPA. [Downloadable!]
    Other versions:
  5. Alvaro Cartea & Thilo Meyer-Brandis, 2007. "How Does Duration Between Trades of Underlying Securities Affect Option Prices," Birkbeck Working Papers in Economics and Finance 0721, Birkbeck, Department of Economics, Mathematics & Statistics. [Downloadable!]
  6. J. Masoliver & M. Montero & J. Perello & G. H. Weiss, 2006. "The continuous time random walk formalism in financial markets," Quantitative Finance Papers physics/0611138, arXiv.org. [Downloadable!]
    Other versions:
  7. Cartea, Álvaro & Meyer-Brandis, Thilo, 2009. "How Duration Between Trades of Underlying Securities Affects Option Prices," MPRA Paper 16179, University Library of Munich, Germany. [Downloadable!]
  8. Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004. "Waiting-times and returns in high-frequency financial data: an empirical study," Finance 0411014, EconWPA. [Downloadable!]
    Other versions:
  9. Enrico Scalas & Mauro Gallegati & Eric Guerci & David Mas & Alessandra Tedeschi, 2006. "Growth and Allocation of Resources in Economics: The Agent-Based Approach," Quantitative Finance Papers physics/0608221, arXiv.org. [Downloadable!]
  10. Fei Ren & Gao-Feng Gu & Wei-Xing Zhou, 2009. "Scaling and memory in the return intervals of realized volatility," Quantitative Finance Papers 0904.1107, arXiv.org, revised Aug 2009. [Downloadable!]
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