Volatility Estimation of General Gaussian Ornstein-Uhlenbeck Process

2019/09/15 by Salwa Bajja, Bajja, Salwa, Qian Yu +1
Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1909.06715

openalex publication_date 2019/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study the asymptotic behaviour of the realized quadratic variation of a process ∫₀^tu_sdG^H_s, where u is a β-Hölder continuous process with β>1-H and G^H is a self-similar Gaussian process with parameters H∈(0,3/4). We prove almost sure convergence uniformly in time, and a stable weak convergence for the realized quadratic variation. As an application, we construct strongly consistent estimator for the integrated volatility parameter in a model driven by G^H.

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