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Scaling and data collapse for the mean exit time of asset prices

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  • Miquel Montero
  • Josep Perello
  • Jaume Masoliver
  • Fabrizio Lillo
  • Salvatore Micciche
  • Rosario N. Mantegna

Abstract

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

Suggested Citation

  • Miquel Montero & Josep Perello & Jaume Masoliver & Fabrizio Lillo & Salvatore Micciche & Rosario N. Mantegna, 2005. "Scaling and data collapse for the mean exit time of asset prices," Papers physics/0507054, arXiv.org.
    • Handle: RePEc:arx:papers:physics/0507054
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    Cited by:

    1. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo & Rosario Mantegna, 2009. "Diffusive behavior and the modeling of characteristic times in limit order executions," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 547-563.
    2. Miquel Montero, 2021. "Predator–prey model for stock market fluctuations," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(1), pages 29-57, January.
    3. Villarroel, Javier & Montero, Miquel, 2009. "On properties of continuous-time random walks with non-Poissonian jump-times," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 128-137.
    4. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.

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