Multi-scaling of moments in stochastic volatility models

الأصل · EN

We introduce a class of stochastic volatility models (Xₜ)ₜ ≥ ₀ for which the absolute moments of the increments exhibit anomalous scaling: (|Xₜ₊ₕ - Xₜ|q) scales as hq/² for q < q*, but as hᵃ⁽q⁾ with A(q) < q/2 for q > q*, for some threshold q*. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driven by a Levy subordinator and the characteristic measure of the Levy process has power law tails, then multi-scaling occurs if and only if the mean reversion is superlinear.