Mean Exit Time and Survival Probability within the Ctrw Formalism

11 Pages Posted: 9 Nov 2006

See all articles by Miquel Montero

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada

Jaume Masoliver

University of Barcelona - Department of Physics

Date Written: October 26, 2006

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.

Keywords: Continuous Time Random Walks, Markov Processes, Mean Exit Time, Risk Measures, Survival Probability

Suggested Citation

Montero, Miquel and Masoliver, Jaume, Mean Exit Time and Survival Probability within the Ctrw Formalism (October 26, 2006). Available at SSRN: https://ssrn.com/abstract=943054 or http://dx.doi.org/10.2139/ssrn.943054

Miquel Montero (Contact Author)

University of Barcelona - Departament de Física de la Matèria Condensada ( email )

Martí i Franquès, 1
Barcelona, Catalonia 08028
Spain
+34 93 403 92 53 (Phone)
+34 93 402 11 55 (Fax)

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

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