  Starting from inhomogeneous time scaling and linear decorrelation between
successive price returns, Baldovin and Stella recently proposed a way to build
a model describing the time evolution of a financial index. We first make it
fully explicit by using Student distributions instead of power law-truncated
L\'evy distributions; we also show that the analytic tractability of the model
extends to the larger class of symmetric generalized hyperbolic distributions
and provide a full computation of their multivariate characteristic functions;
more generally, the stochastic processes arising in this framework are
representable as mixtures of Wiener processes. The Baldovin and Stella model,
while mimicking well volatility relaxation phenomena such as the Omori law,
fails to reproduce other stylized facts such as the leverage effect or some
time reversal asymmetries. We discuss how to modify the dynamics of this
process in order to reproduce real data more accurately.
