A semi-Markov model with memory for price changes
We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov which depends also on a memory index. The index is introduced to take into account periods of high and low volatility in the market. First of all we derive the equations governing the process and then theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010.
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.:
- Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
- 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, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
- Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004.
"Waiting-times and returns in high-frequency financial data: an empirical study,"
- Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
- M. Raberto & E. Scalas & F. Mainardi, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Papers cond-mat/0203596, arXiv.org.
- 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.
- F. Petroni & M. Serva, 2003. "Spot foreign exchange market and time series," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(4), pages 495-500, August.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1109.4259. 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.