Scaling and Data Collapse for the Mean Exit Time of Asset Prices

11 Pages Posted: 18 Jul 2005

See all articles by Miquel Montero

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada

Josep Perelló

University of Barcelona - Department of Physics

Jaume Masoliver

University of Barcelona - Department of Physics

Fabrizio Lillo

Università di Bologna

Salvatore Miccichè

University of Palermo - Department of Physics and Chemistry

Rosario N. Mantegna

University of Palermo

Date Written: 2005

Abstract

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

Keywords: Continuous time random walk, mean exit time, Markov process

JEL Classification: C22

Suggested Citation

Montero, Miquel and Perello, Josep and Masoliver, Jaume and Lillo, Fabrizio and Miccichè, Salvatore and Mantegna, Rosario Nunzio, Scaling and Data Collapse for the Mean Exit Time of Asset Prices (2005). Available at SSRN: https://ssrn.com/abstract=757766 or http://dx.doi.org/10.2139/ssrn.757766

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)

Josep Perello

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (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)

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

Salvatore Miccichè

University of Palermo - Department of Physics and Chemistry ( email )

Viale delle Scienze, Ed. 17
Palermo, PA 90128
Italy
+3909123899145 (Phone)

HOME PAGE: http://www.unipa.it/~salvatore.micciche

Rosario Nunzio Mantegna

University of Palermo ( email )

Dipartimento di Fisica e Chimica
Viale delle Scienze, Edificio 18
Palermo, PA I-90128
Italy
+3909123899074 (Phone)
+3909123860815 (Fax)

HOME PAGE: http://www.unipa.it/persone/docenti/m/rosario.mantegna

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