q-fin updates on arXiv.org
Wed, 26 Feb 2020 12:02:20 GMT language
We investigate relaxation and correlations in a class of mean-reverting
models for stochastic variances. We derive closed-form expressions for the
correlation functions and leverage for a general form of the stochastic term.
We also discuss correlation functions and leverage for three specific models --
multiplicative, Heston (Cox-Ingersoll-Ross) and combined multiplicative-Heston
-- whose steady-state probability density functions are Gamma, Inverse Gamma
and Beta Prime respectively, the latter two exhibiting "fat" tails. For the
Heston model, we apply the eigenvalue analysis of the Fokker-Planck equation to
derive the correlation function -- in agreement with the general analysis --
and to identify a series of time scales, which are observable in relaxation of
cumulants on approach to the steady state. We test our findings on a very large
set of historic financial markets data.