Baldovin-Stella stochastic volatility process and Wiener process mixtures

Pier Paolo Peirano (1) , Damien Challet (2)

1 CFM - Capital Fund Management
2 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a powerful and consistent 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 Lévy distributions and 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, we show that the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The basic 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.

Mots clés: Stochastic volatility model; long memory; stylized fact; fat tails

Domaines: Finance quantitative [q-fin.CP]

Pier Paolo Peirano, Damien Challet. Baldovin-Stella stochastic volatility process and Wiener process mixtures. The European Physical Journal B: Condensed Matter and Complex Systems, 2012, 85 (8), pp.276. ⟨10.1140/epjb/e2012-30134-y⟩. ⟨hal-00734355⟩