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Asymmetry and leverage in realized volatility

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  • Asai, M.
  • McAleer, M.J.
  • Medeiros, M.C.

Abstract

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In both the conditional and stochastic volatility literature, there has been some confusion between the definitions of asymmetry and leverage. In this paper, we first show the relationship among conditional, stochastic, integrated and realized volatilities. Then we develop a new asymmetric volatility model, which takes account of small and large, and positive and negative, shocks. Using the new specification, we examine alternative volatility models that have recently been developed and estimated in order to understand the differences and similarities in the definitions of asymmetry and leverage. We extend the new specification to realized volatility by taking account of measurement errors. As an empirical example, we apply the new model to the realized volatility of Standard and Poor’s 500 Composite Index using Efficient Importance Sampling to show the new specification of asymmetry significantly improves the goodness of fit.

Suggested Citation

  • Asai, M. & McAleer, M.J. & Medeiros, M.C., 2008. "Asymmetry and leverage in realized volatility," Econometric Institute Research Papers EI 2008-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:13904
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    Cited by:

    1. Siem Jan Koopman & Marcel Scharth, 2012. "The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 76-115, December.

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