Asymmetry and Leverage in Realized Volatility
AbstractA 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 that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and VaR thresholds are satisfactory.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-656.
Length: 32 pages
Date of creation: Aug 2009
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- Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2009. "Asymmetry and Leverage in Realized Volatility," CARF F-Series CARF-F-167, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
- Asai, M. & McAleer, M.J. & Medeiros, M.C., 2008. "Asymmetry and leverage in realized volatility," Econometric Institute Report EI 2008-31, Erasmus University Rotterdam, Econometric Institute.
- NEP-ALL-2009-09-19 (All new papers)
- NEP-ECM-2009-09-19 (Econometrics)
- NEP-FMK-2009-09-19 (Financial Markets)
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- Siem Jan Koopman & Marcel Scharth, 2011. "The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures," Tinbergen Institute Discussion Papers 11-132/4, Tinbergen Institute.
- Siem Jan Koopman & Marcel Scharth, 2011.
"The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures,"
Tinbergen Institute Discussion Papers
11-132/4, Tinbergen Institute.
- Siem Jan Koopman, 2012. "The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 76-115, December.
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