The distribution of first-passage times and durations in FOREX and future markets
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag–Leffler survival function and the Weibull distribution. For the Mittag–Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter tmax, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag–Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag–Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag–Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail.
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Volume (Year): 388 (2009)
Issue (Month): 14 ()
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- J. Masoliver & M. Montero & J. Perello & G. H. Weiss, 2006.
"The continuous time random walk formalism in financial markets,"
- Masoliver, Jaume & Montero, Miquel & Perello, Josep & Weiss, George H., 2006. "The continuous time random walk formalism in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 577-598, December.
- Jaume Masoliver & Miquel Montero & Josep Perello, . "The continuous time random walk formalism in financial markets," Modeling, Computing, and Mastering Complexity 2003 24, Society for Computational Economics.
- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2000.
"Fractional calculus and continuous-time finance,"
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000.
"Fractional calculus and continuous-time finance II: the waiting-time distribution,"
cond-mat/0006454, arXiv.org, revised Nov 2000.
- Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
- N. Sazuka, 2006. "Analysis of binarized high frequency financial data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 129-131, 03.
- 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.
- Jaume Masoliver & Miquel Montero & George H. Weiss, 2002. "A continuous time random walk model for financial distributions," Papers cond-mat/0210513, arXiv.org.
- Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
- Sazuka, Naoya, 2007. "On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 500-506.
- Robert F. Engle, 2000.
"The Econometrics of Ultra-High Frequency Data,"
Econometric Society, vol. 68(1), pages 1-22, January.
- Sazuka, Naoya & Inoue, Jun-ichi, 2007. "Fluctuations in time intervals of financial data from the view point of the Gini index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 49-53.
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