Multiplicative Langevin Process for Volatilities Produces Observed Q-Variance Regularities
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910276371087360 |
|---|---|
| author | Press, William H. Dannenberg, Alex |
| author_facet | Press, William H. Dannenberg, Alex |
| contents | Q-variance (so-called) posits a statistical relationship $\mathbf{E}(σ^2 | z) = σ_0^2 + \tfrac{1}{2}z^2$ between an asset's volatility $σ^2$, as observed in a time interval $T$, and its (suitably scaled) return $z$ in the same interval. We here show that this relationship is {\em exactly equivalent} to to positing an Inverse Gamma probability distribution for $σ^2$ itself. We then show that such a distribution is exactly generated by a multiplicative Langevin process with an arbitrary, settable coherence time $τ_c$, so that very nearly the same Q-variance relationship will hold for all $T \ll τ_c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00800 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiplicative Langevin Process for Volatilities Produces Observed Q-Variance Regularities Press, William H. Dannenberg, Alex Pricing of Securities Statistical Finance Q-variance (so-called) posits a statistical relationship $\mathbf{E}(σ^2 | z) = σ_0^2 + \tfrac{1}{2}z^2$ between an asset's volatility $σ^2$, as observed in a time interval $T$, and its (suitably scaled) return $z$ in the same interval. We here show that this relationship is {\em exactly equivalent} to to positing an Inverse Gamma probability distribution for $σ^2$ itself. We then show that such a distribution is exactly generated by a multiplicative Langevin process with an arbitrary, settable coherence time $τ_c$, so that very nearly the same Q-variance relationship will hold for all $T \ll τ_c$. |
| title | Multiplicative Langevin Process for Volatilities Produces Observed Q-Variance Regularities |
| topic | Pricing of Securities Statistical Finance |
| url | https://arxiv.org/abs/2606.00800 |