Article2004

Power and Bipower Variation with Stochastic Volatility and Jumps

2,033 citations0/0 files storedJournal of Financial Econometrics

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

Abstract

This article shows that realized power variation and its extension, realized bipower variation, which we introduce here, are somewhat robust to rare jumps. We demonstrate that in special cases, realized bipower variation estimates integrated variance in stochastic volatility models, thus providing a model-free and consistent alternative to realized variance. Its robustness property means that if we have a stochastic volatility plus infrequent jumps process, then the difference between realized variance and realized bipower variation estimates the quadratic variation of the jump component. This seems to be the first method that can separate quadratic variation into its continuous and jump components. Various extensions are given, together with proofs of special cases of these results. Detailed mathematical results are reported in Barndorff-Nielsen and Shephard (2003a).

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 1976Option pricing when underlying stock returns are discontinuous 2003Modeling and Forecasting Realized Volatility 1989Why Does Stock Market Volatility Change Over Time?1998Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts 1998Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models 2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models

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