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LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS

Ole Eiler Barndorff-Nielsen · Jean Jacod · Neil Shephard

54 citations0/0 files storedEconometric Theory

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

In this paper we provide an asymptotic analysis of generalized bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation, and bipower variations that have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.Ole E. Barndorff-Nielsen's work is supported by the Centre for Analytical Finance (CAF), which is funded by the Danish Social Science Research Council. Neil Shephard's research is supported by the UK's ESRC through the grant “High frequency financial econometrics based upon power variation.” We thank the editor, Peter Phillips, and the referees for their stimulating comments on an earlier version.

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References

1999Continuous Martingales and Brownian Motion 1987Expected stock returns and volatility 2003Modeling and Forecasting Realized Volatility 1989Why Does Stock Market Volatility Change Over Time?1980On estimating the expected return on the market 2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models 2001The Distribution of Realized Exchange Rate Volatility 2004Power and Bipower Variation with Stochastic Volatility and Jumps

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