Publication: Forecasting volatility: does continuous time do better than discrete time?
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2011-07
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Abstract
In this paper we compare the forecast performance of continuous and discrete-time
volatility models. In discrete time, we consider more than ten GARCH-type models and
an asymmetric autoregressive stochastic volatility model. In continuous-time, a
stochastic volatility model with mean reversion, volatility feedback and leverage. We
estimate each model by maximum likelihood and evaluate their ability to forecast the
two scales realized volatility, a nonparametric estimate of volatility based on highfrequency
data that minimizes the biases present in realized volatility caused by
microstructure errors. We find that volatility forecasts based on continuous-time models
may outperform those of GARCH-type discrete-time models so that, besides other
merits of continuous-time models, they may be used as a tool for generating reasonable
volatility forecasts. However, within the stochastic volatility family, we do not find such
evidence. We show that volatility feedback may have serious drawbacks in terms of
forecasting and that an asymmetric disturbance distribution (possibly with heavy tails)
might improve forecasting.
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Asymmetry, Continuous and discrete-time stochastic volatility models, GARCH-type models, Maximum likelihood via iterated filtering, Particle filter, Volatility forecasting