Modeling financial volatility is an important part of empirical finance. This paper provides a literature review of the most relevant volatility models, with a particular focus on forecasting models. We firstly discuss the empirical foundations of different kinds of volatility. The paper, then, analyses the non-parametric measure of volatility, named realized variance, and its empirical applications. A wide range of realized volatility models, both univariate and multivariate, is presented, such as time series models, MIDAS and GARCH-MIDAS models, Realized GARCH, and HEAVY models. We further discuss forecasting evaluation methods specifically suited for volatility models.
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