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Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling

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  • Fulvio Corsi
  • Roberto Renò

Abstract

We first propose a reduced-form model in discrete time for S&P 500 volatility showing that the forecasting performance can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models that are able to reproduce the statistical features captured by the discrete-time model. We show that a single-factor model driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multifactor Markovian model fully replicates the persistence of both volatility and leverage effect. The impact of jumps can be associated with a common jump component in price and volatility. This article has online supplementary materials.

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  • Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    • Handle: RePEc:taf:jnlbes:v:30:y:2012:i:3:p:368-380
    DOI: 10.1080/07350015.2012.663261
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