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The continuous time random walk formalism in financial markets

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Author Info
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)

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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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Publisher 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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Related research
Keywords: continuous time random walk volatility financial markets market microstructure

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Find related papers by JEL classification:
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
D4 - Microeconomics - - Market Structure and Pricing
L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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  1. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
  3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
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