Volatility occupation times

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estim...

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Bibliographic Details
Main Authors: LI, Jia, TODOROV, Viktor, TAUCHEN, George
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2013
Subjects:
Online Access:https://ink.library.smu.edu.sg/soe_research/2569
https://ink.library.smu.edu.sg/context/soe_research/article/3568/viewcontent/Volatility_Occupation_Times.pdf
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Institution: Singapore Management University
Language: English
Description
Summary:We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estimator of its density. We prove the consistency of our estimators and further derive bounds for their rates of convergence. We use these results to estimate nonparametrically the quantiles associated with the volatility occupation measure.