Multi-scaling of moments in stochastic volatility models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Pra, P. Dai¹  Pigato, P.^1,2 

[1] Univ Padua, Dipartimento Matemat Pura & Appl, I-35121 Padua, Italy

[2] Univ Paris Est Marne la Vallee, Lab Anal & Math Appl, F-77454 Marne La Vallee 2, France

关键词: Multi-scaling;    Stochastic volatility;    Heavy Tails;   

DOI  :  10.1016/j.spa.2015.04.007

来源: Elsevier

【 摘 要 】

We introduce a class of stochastic volatility models (X-t)(t >= 0) for which the absolute moments of the increments exhibit anomalous scaling: E (|Xt+h - X-t|(q)) scales as h(q/2) for q < q*, but as h(A(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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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