Discrete-time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous-time Volatility Modeling

34 Pages Posted: 17 Dec 2008 Last revised: 6 Apr 2010

See all articles by Fulvio Corsi

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Roberto Renò

University of Verona - Department of Economics

Date Written: April 2, 2010

Abstract

We first propose a reduced-form model in discrete time for S&P500 volatility showing that the forecasting performance of a volatility model 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 which are able to reproduce the statistical features captured by the reduced-form 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 multi-factor Markovian model is able to reproduce the persistence of both volatility and leverage effect.

The impact of jumps can instead be associated with a common jump component in price and volatility. These findings cast serious doubts on the need of modeling volatility with a genuine long memory component, while reinforcing the view of volatility being generated by the superposition of multiple factors.

Keywords: Volatility Forecasting, High Frequency Data, Leverage Effect, Jumps, Fractional Brownian Motion, Multifactor Models

JEL Classification: C13, C22, C51, C53

Suggested Citation

Corsi, Fulvio and Renò, Roberto, Discrete-time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous-time Volatility Modeling (April 2, 2010). Available at SSRN: https://ssrn.com/abstract=1316953 or http://dx.doi.org/10.2139/ssrn.1316953

Fulvio Corsi (Contact Author)

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Roberto Renò

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

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