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The continuous time random walk formalism in financial markets

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  • Jaume Masoliver

    () (Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona, Spain)

  • Miquel Montero

    () (Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona, Spain)

  • Josep Perello

    () (Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona, Spain)

Abstract

We adapt the continuous time random walk (CTRW) formalism to describe the asset price evolution. We show some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price distribution from high-frequency data; and (ii) the inverse problem, that is, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to actual financial data and try to show that the CTRW offers alternative tools to deal with several complex issues of financial markets.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Modeling, Computing, and Mastering Complexity 2003 with number 24.

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Handle: RePEc:sce:cplx03:24

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Web page: http://zai.ini.unizh.ch/complexity2003/
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Keywords: continuous time random walk; volatility; financial markets; market microstructure;

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  1. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
  2. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
  3. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
  4. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA.
  5. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  6. Jaume Masoliver & Miquel Montero & George H. Weiss, 2002. "A continuous time random walk model for financial distributions," Papers cond-mat/0210513, arXiv.org.
  7. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  8. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
  9. R. Kutner & F. Switała, 2003. "Stochastic simulations of time series within Weierstrass-Mandelbrot walks," Quantitative Finance, Taylor and Francis Journals, vol. 3(3), pages 201-211.
  10. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  11. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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