A model for multiscaling and clustering of volatility in financial indexes

We propose a stochastic model which matches some relevant stylized facts observed in time series of financial indexes, and that are not fully captured by the models most often used in this context. These stylized facts concern with the distribution of the log-returns (increments of the logarithm of the index). This distribution is not Gaussian, and its moments obey peculiar scaling relations (multiscaling). Moreover, absolute values of log-returns in disjoint (2) time intervals are positively correlated (clustering of volatility): their correlation has slow (sub-exponential) decay for moderate time distances (up to few months), and have a faster decay for larger distances. The simplicity of the model allows sharp analytic results, statistical estimation of its few parameters, and low computational effort in simulations, allowing its con- crete use in applications such as option pricing.