Generalized Volatility Model And Calculating VaR Using A New Semiparametric Model

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The first part of the dissertation concerns financial volatility models. Financial volatility has some stylized facts, such as excess kurtosis, volatility clustering and leverage effects. A good volatility model should be able to capture all these stylized facts. Among the volatility models, ARCH, GARCH, EGARCH and stochastic volatility models are the most important. We propose a generalized volatility model or GVM in this part, which is a generalization of all the ARCH family and stochastic volatility models. The GVM adopts the structure of the generalized linear model (GLM). GLM was originally intended for independent data. However, using partial likelihood, GLM can be extended to time series, and can then be applied to predict financial volatility. Interestingly, the family of ARCH models are special cases of GVM. Also, any covariates can be added easily to a GVM model. As an example, we use GVM to predict the realized volatility. Because of the availability of high frequency data in today's market, we can calculate realized volatility directly. We compare the prediction results of GVM with that of other classical models. By the measure of mean square error, GVM is the best among these the models.

The second part of this dissertation is about value at risk (VaR). The most common methods to compute VaR are GARCH, historical simulation, and extreme value theory. A new semiparametric model based on density ratio is developed in Chapter three. By assuming that the density of the return series is an exponential function times the density of another reference return series, we can derive the density function of the portfolio's distribution. Then, we can compute the corresponding quantile or the VaR. We ran a monte carlo simulation to compare the semiparametric model and the traditional VaR models under many different scenarios. In several cases, the semiparametric model performs quite satisfactorily. Furthermore, when applied to real data, the semiparametric model performs best among all the considered models using the metric of failure rate.