# Scaling and Multiscaling in Financial Indexes: a simple model

## Giovedi 20 maggio - Dr. Francesco Caravenna

ARGOMENTI: Seminari

SEMINARI DI CALCOLO DELLE PROBABILITA'
Giovedi 20 maggio, alle 14:30 in aula 1A/150, il Dr. Francesco Caravenna del Dipartimento di Matematica Pura e Applicata dell'Universita' di Padova, terra' un seminario dal titolo "Scaling and Multiscaling in Financial Indexes: a simple model".

(joint work with A. Andreoli, P. Dai Pra and G. Posta)
We propose a simple stochastic model for time series, which captures some relevant stylized facts of financial indexes. Despite its simplicity, the model has several interesting properties, in particular for what concerns scaling. The empirical distribution of the log-returns (increments of the logarithm of the index) is non-Gaussian and may exhibit heavy tails. Log-returns corresponding to disjoint time intervals are uncorrelated but not independent: the correlation of their absolute values decays exponentially fast in the distance between the time intervals for large distances, while it has a slower decay for moderate distances. Finally, the distribution of the log-returns obeys scaling relations that are detected on real time series, but are not satisfied by most available models.

Rif. int. P. Dai Pra