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EnglishWe introduce a class of stochastic volatility models (Xt)t≥0 for which the absolute moments of the increments exhibit anomalous scaling: double-struck E (| 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.
| Titolo: | Multi-scaling of moments in stochastic volatility models |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Abstract: | We introduce a class of stochastic volatility models (Xt)t≥0 for which the absolute moments of the increments exhibit anomalous scaling: double-struck E (| 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. |
| Handle: | http://hdl.handle.net/11562/1009573 |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| SPA15.pdf | Documento in Pre-print |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11562/1009573
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