Estimation of integrated volatility in stochastic volatility models
Author(s) -
Woerner Jeannette H. C.
Publication year - 2005
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.548
Subject(s) - stochastic volatility , econometrics , estimator , volatility (finance) , realized variance , economics , sabr volatility model , geometric brownian motion , implied volatility , mathematics , statistics , diffusion process , economy , service (business)
Abstract In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the p th power variation (i.e. the sum of p th absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.