Volatility Models for Stylized Facts of High-Frequency Financial Data

TL;DR

This paper develops new volatility models for high-frequency financial data that capture key stylized facts like volatility clustering and leverage effects, and introduces a robust Huber regression estimator with optimal convergence properties.

Contribution

The paper proposes novel volatility diffusion models tailored for high-frequency data and introduces a Huber regression estimator with proven asymptotic efficiency.

Findings

The models effectively capture stylized facts such as volatility clustering and leverage effects.

The Huber regression estimator achieves an optimal convergence rate of n^{(1-b)/b}.

Bias adjustment methods improve estimator accuracy.

Abstract

This paper introduces novel volatility diffusion models to account for the stylized facts of high-frequency financial data such as volatility clustering, intra-day U-shape, and leverage effect. For example, the daily integrated volatility of the proposed volatility process has a realized GARCH structure with an asymmetric effect on log-returns. To further explain the heavy-tailedness of the financial data, we assume that the log-returns have a finite $2b$-th moment for $b \in (1,2]$. Then, we propose a Huber regression estimator which has an optimal convergence rate of $n^{(1-b)/b}$. We also discuss how to adjust bias coming from Huber loss and show its asymptotic properties.