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ESTIMATING THE VOLATILITY OCCUPATION TIME VIA REGULARIZED LAPLACE INVERSION

Published online by Cambridge University Press:  25 May 2015

Jia Li ,
Viktor Todorov  and
George Tauchen
Jia Li*
Affiliation:
Duke University
Viktor Todorov
Affiliation:
Northwestern University
George Tauchen
Affiliation:
Duke University
*
*Address correspondence to Jia Li, Department of Economics, Duke University, Durham, NC 27708; e-mail: jl410@duke.edu.
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Abstract

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We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in the second step, we conduct a regularized Laplace inversion. Monte Carlo evidence suggests that the proposed estimator has good small-sample performance and in particular it is far better at estimating lower volatility quantiles and the volatility median than a direct estimator formed from the empirical cumulative distribution function of local spot volatility estimates. An empirical application shows the use of the developed techniques for nonparametric analysis of variation of volatility.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 5 , October 2016 , pp. 1253 - 1288
Copyright
Copyright © Cambridge University Press 2015 

References

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