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Estimation of Integrated Volatility in Stochastic Volatility Models

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Author Info
Jeannette H.C. Woerner
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, 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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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2003mf05.

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Date of creation: 2003
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Handle: RePEc:sbs:wpsefe:2003mf05

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  2. repec:att:wimass:199317r is not listed on IDEAS
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  5. Sam Howison & Avraam Rafailidis & Henrik Rasmussen, 2003. "On the Pricing and Hedging of Volatility Derivatives," OFRC Working Papers Series 2003mf06, Oxford Financial Research Centre. [Downloadable!]
  6. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
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  13. 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. [Downloadable!]
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  21. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
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  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
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