A simple model of volatility in financial data - An alternative to GARCH models
Abstract: Financial return series are often characterized by volatility clusters and a leptokurtic distribution. Many models that account for these properties exist, with the GARCH model proposed by Bollerslev (1986) being the most popular. This thesis explores an alternative model to capture the stochastic volatility in financial time series. The considered model is denoted the autoregressive gamma variance Gaussian mixture model and was proposed by Johannesson et al. (2016). The model consists of the product of two independent time series, namely an autoregressive Gaussian process and an autoregressive gamma process, where the gamma process modulates the variance of the Gaussian white noise. This thesis proposes and evaluates an alternative method to estimate the correlation coefficient of the gamma process. The proposed method outperforms the original method when the true correlation coefficient is exceedingly large, which is the case for almost all financial return series. In addition, this thesis develops basic unbiased methods to interpolate and predict the gamma process given the observed daily financial return. These partial results require further research to fully develop more advanced prediction methods.
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