Article2009

INFERENCE FOR THE JUMP PART OF QUADRATIC VARIATION OF ITÔ SEMIMARTINGALES

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

Abstract

Recent research has focused on modeling asset prices by Itô semimartingales. In such a modeling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference of realized variance and realized multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realized variance and realized multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump part of the asymptotic variance of the estimation bias. Eventually, this leads to a feasible asymptotic theory that is applicable in practice. Finally, Monte Carlo studies reveal a good finite sample performance of the proposed feasible limit theory.

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References

1998Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts 2003Limit Theorems for Stochastic Processes 2001The distribution of realized stock return volatility 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 2007Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility 2005Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation

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2009Stochastic Volatility and Stochastic Leverage 2011Estimation of the instantaneous volatility 2015ESTIMATION OF INTEGRATED COVARIANCES IN THE SIMULTANEOUS PRESENCE OF NONSYNCHRONICITY, MICROSTRUCTURE NOISE AND JUMPS 2012Efficient and Feasible Inference for the Components of Financial Variation Using Blocked Multipower Variation

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