We present and discuss a stochastic model of financial assets dynamics based
on the idea of an inverse renormalization group strategy. With this strategy we
construct the multivariate distributions of elementary returns based on the
scaling with time of the probability density of their aggregates. In its
simplest version the model is the product of an endogenous auto-regressive
component and a random rescaling factor designed to embody also exogenous
influences. Mathematical properties like increments' stationarity and
ergodicity can be proven. Thanks to the relatively low number of parameters,
model calibration can be conveniently based on a method of moments, as
exemplified in the case of historical data of the S&P500 index. The calibrated
model accounts very well for many stylized facts, like volatility clustering,
power law decay of the volatility autocorrelation function, and multiscaling
with time of the aggregated return distribution. In agreement with empirical
evidence in finance, the dynamics is not invariant under time reversal and,
with suitable generalizations, skewness of the return distribution and leverage
effects can be included. The analytical tractability of the model opens
interesting perspectives for applications, for instance in terms of obtaining
closed formulas for derivative pricing. Further important features are: The
possibility of making contact, in certain limits, with auto-regressive models
widely used in finance; The possibility of partially resolving the long-memory
and short-memory components of the volatility, with consistent results when
applied to historical series.Comment: Main text (17 pages, 13 figures) plus Supplementary Material (16
pages, 5 figures