Advanced Search
MyIDEAS: Login to save this paper or follow this series

The distribution of first-passage times and durations in FOREX and future markets

Contents:

Author Info

  • Naoya Sazuka
  • Jun-ichi Inoue
  • Enrico Scalas

Abstract

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 so-called Mittag-Leffler survival function and the Weibull distribution. For Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter t_ max, 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 one if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other side, 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 much more efficiently than a simple Weibull 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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://arxiv.org/pdf/0808.0372
File Function: Latest version
Download Restriction: no

Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0808.0372.

as in new window
Length:
Date of creation: Aug 2008
Date of revision:
Handle: RePEc:arx:papers:0808.0372

Contact details of provider:
Web page: http://arxiv.org/

Related research

Keywords:

Other versions of this item:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. 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, Elsevier, vol. 287(3), pages 468-481.
  2. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 387(8), pages 2025-2034.
  3. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance, EconWPA 0411007, EconWPA.
  4. 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, Elsevier, vol. 61(4), pages 577-598, December.
  5. N. Sazuka, 2006. "Analysis of binarized high frequency financial data," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 50(1), pages 129-131, 03.
  6. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, Econometric Society, vol. 68(1), pages 1-22, January.
  7. 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, Elsevier, vol. 376(C), pages 500-506.
  8. 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, Elsevier, vol. 383(1), pages 49-53.
  9. Jaume Masoliver & Miquel Montero & George H. Weiss, 2002. "A continuous time random walk model for financial distributions," Papers cond-mat/0210513, arXiv.org.
  10. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 362(2), pages 225-239.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Takero Ibuki & Jun-ichi Inoue, 2011. "Response of double-auction markets to instantaneous Selling–Buying signals with stochastic Bid–Ask spread," Journal of Economic Interaction and Coordination, Springer, vol. 6(2), pages 93-120, November.
  2. Aki-Hiro Sato & Takaki Hayashi & Janusz A. Ho{\l}yst, 2012. "Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix," Papers 1204.0426, arXiv.org.
  3. Aki-Hiro Sato & Takaki Hayashi & Janusz Hołyst, 2012. "Comprehensive analysis of market conditions in the foreign exchange market," Journal of Economic Interaction and Coordination, Springer, vol. 7(2), pages 167-179, October.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:arx:papers:0808.0372. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.