Functional diffusion driven stochastic volatility model

Kokoszka, P., Mohammadi, N., Wang, H. and Wang, S. ORCID: https://orcid.org/0000-0003-2113-5521 (2025) Functional diffusion driven stochastic volatility model. Bernoulli, 31 (2). pp. 922-947. ISSN 1573-9759 doi: 10.3150/24-BEJ1753

Abstract/Summary

We propose a stochastic volatility model for time series of curves. It is motivated by dynamics of intraday price curves that exhibit both between days dependence and intraday price evolution. The curves are suitably normalized to stationary in a function space and are functional analogs of point-to-point daily returns. The between curves dependence is modeled by a latent autoregression. The within curves behavior is modeled by a diffusion process. We establish the properties of the model and propose several approaches to its estimation. These approaches are justified by asymptotic arguments that involve an interplay between the latent autoregression and the intraday diffusions. The asymptotic framework combines the increasing number of daily curves and the refinement of the discrete grid on which each daily curve is observed. Consistency rates for the estimators of the intraday volatility curves are derived as well as the asymptotic normality of the estimators of the latent autoregression. The estimation approaches are further explored and compared by an application to intraday price curves of over seven thousand U.S. stocks and an informative simulation study.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/115802
Item Type	Article
Refereed	Yes
Divisions	Arts, Humanities and Social Science > School of Politics, Economics and International Relations > Economics
Publisher	Bernoulli Society for Mathematical Statistics & Probability
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