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Fractional calculus and continuous-time finance

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Author Info
Enrico Scalas
Rudolf Gorenflo
Francesco Mainardi

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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 L\'evy 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://arxiv.org/abs/cond-mat/0001120
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File URL: http://arxiv.org/pdf/cond-mat/0001120
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number cond-mat/0001120.

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Date of creation: Jan 2000
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Handle: RePEc:arx:papers:cond-mat/0001120

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  1. Jaume Masoliver & Miquel Montero & Josep Perello, . "The continuous time random walk formalism in financial markets," Modeling, Computing, and Mastering Complexity 2003 24, Society for Computational Economics.
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  2. 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!]
  3. 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!]
  4. 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!]
  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. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA. [Downloadable!]
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  7. Enrico Scalas, 2005. "Five Years of Continuous-time Random Walks in Econophysics," Finance 0501005, EconWPA. [Downloadable!]
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  8. 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!]
  9. 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!]
  10. Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004. "Waiting-times and returns in high-frequency financial data: an empirical study," Finance 0411014, EconWPA. [Downloadable!]
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