Asymmetry and leverage in realized volatility

Manabu Asai, Michael McAleer and Marcelo Medeiros ()

No EI 2008-31, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

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.

Date: 2008-11-24
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Related works:
Working Paper: Asymmetry and Leverage in Realized Volatility (2009)
Working Paper: Asymmetry and Leverage in Realized Volatility (2009)
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