Validation of a GMM Approach to Estimate Parameters in a Rough Volatility Setting in the Presence of Microstructure Noise
Authors
Andreassen, Asbjørn Bach ; Dam, Rasmus
Term
4. term
Education
Publication year
2022
Abstract
Dette speciale undersøger, om Generalized Method of Moments (GMM) kan bruges pålideligt til at estimere parametre i en rough-volatilitetsmodel, hvor volatiliteten drives af en fraktionel Ornstein–Uhlenbeck-proces, når højfrekvente prisdata er forurenet af mikrostrukturstøj. Vi gennemfører en simulationsundersøgelse, der sammenligner estimering baseret på tre estimatorer af integreret volatilitet: klassisk realiseret volatilitet, realiseret volatilitet med 5-minutters sampling (RV5) og moduleret realiseret kovarians (MRC), som er robust over for mikrostrukturstøj. Simulationerne vurderer både nøjagtigheden af parameterestimatet og om den teoretiske parameterfordeling påvirkes af støj. Resultaterne indikerer, at den teoretiske fordeling af parametre forbliver uændret, når der anvendes en støjrobust estimator (MRC) for integreret volatilitet. Til sidst anvendes GMM-metoden på højfrekvente priser for S&P 500 ETF’en SPY i perioden 1999–2009, hvor vi finder, at volatiliteten er rough, i overensstemmelse med tidligere studier.
This thesis evaluates whether the Generalized Method of Moments (GMM) can reliably estimate parameters in a rough-volatility framework, where volatility is driven by a fractional Ornstein–Uhlenbeck process, when high-frequency price data are affected by microstructure noise. We conduct a simulation study comparing three estimators of integrated volatility: classic realized volatility, realized volatility with 5-minute sampling (RV5), and modulated realized covariance (MRC), which is robust to microstructure noise. The simulations assess both estimation accuracy and whether the theoretical distribution of parameters is altered by noise. The results suggest that the theoretical parameter distribution is unaffected when a noise-robust estimator (MRC) of integrated volatility is used. Finally, we apply the GMM procedure to high-frequency prices of the S&P 500 ETF SPY from 1999 to 2009 and find that the volatility process is indeed rough, consistent with related work.
[This summary has been generated with the help of AI directly from the project (PDF)]
Documents