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Modeling share price evolution as a continuous time random walk (CTRW) with non-independent price changes and waiting times

Author

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  • Repetowicz, Przemysław
  • Richmond, Peter

Abstract

A theory which describes the share price evolution at financial markets as a continuous time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function φX,T(x,t), which uses the concept of a Lévy stable distribution, is worked out. The evolution equation is formulated and it is shown that the process is non-Markovian. Finally, the theory is fitted to market data.

Suggested Citation

  • Repetowicz, Przemysław & Richmond, Peter, 2004. "Modeling share price evolution as a continuous time random walk (CTRW) with non-independent price changes and waiting times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 108-111.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:1:p:108-111
    DOI: 10.1016/j.physa.2004.06.097
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    Citations

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    Cited by:

    1. Jaros{l}aw Klamut & Tomasz Gubiec, 2018. "Directed Continuous-Time Random Walk with memory," Papers 1807.01934, arXiv.org.
    2. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.
    3. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    4. D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009. "European and American options: The semi-Markov case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194.

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