# Michael Levine

*Written by: Andrea Rau, Ph.D. candidate in Statistics*

*Michael Levine*

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.

A huge number of volatility models have been proposed over the last 20-25 years; some of the better known ones are the classical AutoRegressive Conditional Heteroskedastic (ARCH) model, the generalized ARCH (GARCH), the exponential GARCH (EGARCH), and the threshold GARCH (TGARCH). All of these models assume a particular form of functional dependence of the volatility on past observations that often results in a lack of flexibility. This is equivalent to assuming that past observations influence the volatility of an asset in a specific way, whereas such an assumption is commonly unsupported by empirical evidence. As an example, in the case of ARCH and GARCH models, the functional form postulated precludes a researcher from modeling the leverage effect adequately; other models have different issues. To solve this problem, it is natural to try to move away from parametric assumptions underlying the classical volatility models and look at the modeling from the nonparametric viewpoint instead. This is a relatively new research area with wide implications for the future and many unsolved problems. Some of the most common challenges facing a researcher in this area are the overfitting of nonparametric models and the lack of data to estimate them adequately (commonly known as the "curse of dimensionality").

Professor Michael Levine, in collaboration with former Purdue doctoral student Dr. Jinguang (Tony) Li, has been working to develop a number of nonparametric volatility models that are more flexible than the traditional parametric ones. "Statistically speaking," said Levine, "most of this work lies at the crossroads of nonparametric statistics, especially nonparametric function estimation, and nonlinear time series." The nonparametric models being developed by Professor Levine allow a practitioner to estimate the influence of past information on the current volatility of the market, without making numerous assumptions that are difficult to verify in practice.

Professor Levine ultimately hopes to develop a number of asset price/return models that are "flexible, practically viable, and can be used by a financial analyst at an investment bank who is not likely to have a thorough knowledge of modern statistics." Ideally, this will enable practitioners to identify key sources of the current market volatility, predict the future volatility with few assumptions, and forecast other indicators (such as the VaR of a company) with high degree of precision.

In addition to his research, Professor Levine has taught several graduate courses on Advanced Statistical Methodology as well as Time Series Analysis at Purdue. "My philosophy of teaching is rather simple," said Professor Levine. "I think that good teaching requires significant amount of effort from both the instructor and the students. It is an absolute duty of an instructor to be well prepared for the class, be knowledgeable about the material and be ready for questioning, which can be challenging on occasion."

Professor Levine obtained his PhD in Statistics from the University of Pennsylvania in 2003. He joined the faculty of the Purdue Statistics department in August 2003, and is currently an Assistant Professor. "The Department of Statistics at Purdue is extremely friendly, and it provides a very good nurturing environment for junior faculty to grow professionally and to succeed in one's personal career goals," said Levine. "I think I am very lucky that I ended up at Purdue right after my graduation." His research interests include financial econometrics, nonlinear time series, and nonparametric function estimation. For more information about Professor Levine, please visit his homepage.

[1] "Analysis of Financial Time Series" by Ruey S. Tsay, 2005, Wiley, 2nd edition

Additional reading:

- Local Instrumental Variable (LIVE) Method For The Generalized Additive-Interactive Nonlinear Volatility Model
- Nonparametric estimation of volatility models with serially dependent innovations
- Joint Significance Testing of the Functional Components in the Nonlinear ARCH Model.

*September 2008*

*Last Updated*: Sep 11, 2017 11:45 AM