dorsal/arxiv
View SchemaMean Exit Time and Survival Probability within the CTRW Formalism
| Authors | Miquel Montero, Jaume Masoliver |
|---|---|
| Categories | |
| ArXiv ID | physics/0607268 |
| URL | https://arxiv.org/abs/physics/0607268 |
| DOI | 10.1140/epjb/e2007-00128-1 |
| Journal | Eur. Phys. J. B 57, 181-185 (2007) |
Abstract
An intense research on financial market microstructure is presently in progress. Continuous time random walks (CTRWs) are general models capable to capture the small-scale properties that high frequency data series show. The use of CTRW models in the analysis of financial problems is quite recent and their potentials have not been fully developed. Here we present two (closely related) applications of great interest in risk control. In the first place, we will review the problem of modelling the behaviour of the mean exit time (MET) of a process out of a given region of fixed size. The surveyed stochastic processes are the cumulative returns of asset prices. The link between the value of the MET and the timescale of the market fluctuations of a certain degree is crystal clear. In this sense, MET value may help, for instance, in deciding the optimal time horizon for the investment. The MET is, however, one among the statistics of a distribution of bigger interest: the survival probability (SP), the likelihood that after some lapse of time a process remains inside the given region without having crossed its boundaries. The final part of the article is devoted to the study of this quantity. Note that the use of SPs may outperform the standard "Value at Risk" (VaR) method for two reasons: we can consider other market dynamics than the limited Wiener process and, even in this case, a risk level derived from the SP will ensure (within the desired quintile) that the quoted value of the portfolio will not leave the safety zone. We present some preliminary theoretical and applied results concerning this topic.
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"abstract": "An intense research on financial market microstructure is presently in\nprogress. Continuous time random walks (CTRWs) are general models capable to\ncapture the small-scale properties that high frequency data series show. The\nuse of CTRW models in the analysis of financial problems is quite recent and\ntheir potentials have not been fully developed. Here we present two (closely\nrelated) applications of great interest in risk control. In the first place, we\nwill review the problem of modelling the behaviour of the mean exit time (MET)\nof a process out of a given region of fixed size. The surveyed stochastic\nprocesses are the cumulative returns of asset prices. The link between the\nvalue of the MET and the timescale of the market fluctuations of a certain\ndegree is crystal clear. In this sense, MET value may help, for instance, in\ndeciding the optimal time horizon for the investment. The MET is, however, one\namong the statistics of a distribution of bigger interest: the survival\nprobability (SP), the likelihood that after some lapse of time a process\nremains inside the given region without having crossed its boundaries. The\nfinal part of the article is devoted to the study of this quantity. Note that\nthe use of SPs may outperform the standard \"Value at Risk\" (VaR) method for two\nreasons: we can consider other market dynamics than the limited Wiener process\nand, even in this case, a risk level derived from the SP will ensure (within\nthe desired quintile) that the quoted value of the portfolio will not leave the\nsafety zone. We present some preliminary theoretical and applied results\nconcerning this topic.",
"arxiv_id": "physics/0607268",
"authors": [
"Miquel Montero",
"Jaume Masoliver"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1140/epjb/e2007-00128-1",
"journal_ref": "Eur. Phys. J. B 57, 181-185 (2007)",
"title": "Mean Exit Time and Survival Probability within the CTRW Formalism",
"url": "https://arxiv.org/abs/physics/0607268"
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