Estimation of integrated volatility of volatility with applications to goodness-of-fit testing

TL;DR

This paper develops nonparametric estimators for the integrated volatility of volatility in stochastic models, providing theoretical results and practical tools for model validation in high-frequency financial data.

Contribution

It introduces new bias-corrected and positive estimators for volatility of volatility with proven central limit theorems, enhancing model validation methods.

Findings

Estimators achieve the optimal convergence rate of n^{-1/4}.

Central limit theorems enable practical inference and goodness-of-fit testing.

Methodology applicable to high-frequency financial data analysis.

Abstract

In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on increments of spot volatility estimators. Some of those are positive by construction, others are bias corrected in order to attain the optimal rate $n^{-1/4}$. Associated central limit theorems are proven which can be widely used in practice, as they are the key to essentially all tools in model validation for stochastic volatility models. As an illustration we give a brief idea on a goodness-of-fit test in order to check for a certain parametric form of volatility of volatility.