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The continuous time random walk formalism in financial markets

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Author Info
J. Masoliver
M. Montero
J. Perello
G. H. Weiss

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Abstract

We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss 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, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to financial data to show that the CTRW offers alternative tools to deal with several complex issues of financial markets.

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File URL: http://arxiv.org/abs/physics/0611138
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File URL: http://arxiv.org/pdf/physics/0611138
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number physics/0611138.

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Date of creation: Nov 2006
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Publication status: Published in Journal of Economic Behaviour and Organization 61 (2006) 577-598.
Handle: RePEc:arx:papers:physics/0611138

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  1. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Quantitative Finance Papers cond-mat/9907161, arXiv.org. [Downloadable!]
  2. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA. [Downloadable!]
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  3. M. Raberto & E. Scalas & F. Mainardi, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Quantitative Finance Papers cond-mat/0203596, arXiv.org. [Downloadable!]
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  4. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Quantitative Finance Papers cond-mat/9905305, arXiv.org. [Downloadable!]
  5. 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)
  6. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Quantitative Finance Papers cond-mat/0006454, arXiv.org, revised Nov 2000. [Downloadable!]
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  7. 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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  8. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  9. מחקר - ביטוח לאומי, 1900. "קרן מנוף," Working Papers 35, National Insurance Institute of Israel. [Downloadable!]
  10. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," Journal of Business, University of Chicago Press, vol. 36, pages 420. [Downloadable!]
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