Estimation of the instantaneous volatility

  • Alexander Alvarez
  • Fabien Panloup
  • Monique Pontier
  • Nicolas Savy
Article

Abstract

This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: dXtatdt + σtdWt, where X denotes the log-price and σ is a càdlàg semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus on the instantaneous volatility for which we study estimators built as finite differences of the power variations of the log-price. We provide central limit theorems with an optimal rate depending on the local behavior of σ. In particular, these theorems yield some confidence intervals for σt.

Keywords

Central limit theorem Power variation Semimartingale 

Mathematics Subject Classification (2000)

Primary 60F05 Secondary 91B70 91B82 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Alexander Alvarez
    • 1
  • Fabien Panloup
    • 2
  • Monique Pontier
    • 3
  • Nicolas Savy
    • 3
  1. 1.La Habana UniversityHavanaCuba
  2. 2.Institut de Mathématiques de Toulouse et INSA ToulouseToulouseFrance
  3. 3.Institut de Mathétiques de Toulouse et Université de ToulouseToulouseFrance

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