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.

Discrete-time volatility forecasting with persistent leverage effect and the link with continuous-time volatility modeling

Renò, Roberto
2012-01-01

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.
Fractional Brownian motion; Jumps; Leverage effect; Multifactor models; Volatility forecasting.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/927861
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