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
Date Written: April 2, 2010
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: Suggested Citation