Estimation of Integrated Volatility in Stochastic Volatility Models
AbstractIn 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, e.g. 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.
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Bibliographic InfoPaper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2003mf05.
Date of creation: 2003
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-08-17 (All new papers)
- NEP-ECM-2003-08-17 (Econometrics)
- NEP-ETS-2003-08-17 (Econometric Time Series)
- NEP-RMG-2003-08-17 (Risk Management)
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- Ole E. Barndorff-Nielsen & Neil Shephard, 2003.
"Econometrics of testing for jumps in financial economics using bipower variation,"
2003-W21, Economics Group, Nuffield College, University of Oxford.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
- Neil Shephard & Ole Barndorff-Nielsen, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Series Working Papers 2004-FE-01, University of Oxford, Department of Economics.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometrics of testing for jumps in financial economics using bipower variationÂ ," OFRC Working Papers Series 2004fe01, Oxford Financial Research Centre.
- Ole E. Barndorff-Nielsen & Svend Erik Graversen & Neil Shephard, 2003. "Power variation & stochastic volatility: a review and some new results," Economics Papers 2003-W19, Economics Group, Nuffield College, University of Oxford.
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