Functional diffusion driven stochastic volatility model

TL;DR

This paper introduces a novel stochastic volatility model for intraday price curves, capturing both between-day dependence and intraday dynamics, with proven properties and practical estimation methods validated on real stock data.

Contribution

It develops a functional stochastic volatility model incorporating latent autoregression and diffusion processes, with asymptotic estimation theory and empirical validation.

Findings

Consistent estimators for intraday volatility curves.

Asymptotic normality of latent autoregression estimators.

Effective modeling of intraday price dynamics across thousands of stocks.

Abstract

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 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.