Document Type masters report Author Name Volfson, Alexander URN etd-042910-153817 Title Exploring the optimal Transformation for Volatility Degree MS Department Mathematical Sciences Advisors Balgobin Nandram, Advisor Keywords Metropolis-Hastings algorithm Bayes Empirical Bayes stochastic volatility Box-Cox transformation Date of Presentation/Defense 2010-04-29 Availability unrestricted
This paper explores the fit of a stochastic volatility model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution, to the continuously compounded daily returns of the Australian stock index. Estimation was difficult, and over-fitting likely, because more variables are present than data. We developed a revised model that held a couple of these variables fixed and then, further, a model which reduced the number of variables significantly by grouping trading days. A Metropolis-Hastings algorithm was used to simulate the joint density and derive estimated volatilities. Though autocorrelations were higher with a smaller Box-Cox transformation parameter, the fit of the distribution was much better.
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