Research Profile: Michael Levine - Developing nonparametric volatility models in financial econometrics

In financial econometrics, modeling the behavior of the prices and returns of financial assets, such as stocks, stock market indices and different derivative securities, is a central problem.  It is known from many years of empirical observation that most of these data are almost uncorrelated. However, a more subtle form of dependence is almost always present; usually, the variance of the data is strongly dependent on past observations. In practice, this means that the conditional variance of such data should be modelled as function of the past in order to explain it. This conditional variance is commonly called the volatility of financial asset in financial and econometric literature. Financial volatility modeling has been a subject of continuing research by both time series statisticians and financial econometricians for more than two decades.

One of the reasons volatility modeling is important is because it allows researchers to estimate the Value at Risk (VaR) for anybody holding a particular financial asset.  VaR is an estimate of the amount by which the value of the holding in a given financial asset could decline due to general market movements during a given holding period [1]. Clearly, this measure can be used to assess the market risk of an asset portfolio.

Modelling of financial volatility must take into account some commonly observed empirical facts. The most important of them are the volatility clustering and the leverage effect. The volatility clustering means that the volatility of an asset usually alternates between periods of high oscillation and periods of relative calm; both of these periods tend to have a noticeable time length. In other words, it is almost unheard of to see sudden jumps of volatility that subside very quickly – highly volatile markets usually last for an extended period of time. The leverage means that the volatility changes more appreciably in response to "bad news" (large negative movements in the price of an asset) than to "good news" (large positive movements in the price of an asset). Every attempt to model the volatility of financial data should try to produce a model that is capable of explaining these two important empirical facts.

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