title: Scaling and data collapse for the mean exit time of asset prices.
abstract: We study theoretical and empirical aspects of the mean exit time (MET) 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 prefactor 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 two-state and 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.
authors.affiliation: Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain. miquel.montero@ub.edu
authors.forename: Miquel
authors.initials: M
authors.lastname: Montero
authors.forename: Josep
authors.initials: J
authors.lastname: Perelló
authors.forename: Jaume
authors.initials: J
authors.lastname: Masoliver
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Lillo
authors.forename: Salvatore
authors.initials: S
authors.lastname: Miccichè
authors.forename: Rosario N
authors.initials: RN
authors.lastname: Mantegna