Statistical Analysis of Financial Markets

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This research will continue my interest in financial econometrics. In particular it will examine via statistical analysis several broad aspects of financial markets: a) Poisson driven market models b) The properties of threshold models for modeling volatility. c) Assessment of financial forecasting ability. d) Ex-post utility in relation to portfolio optimization. a) The availability of more and more high frequency financial data, in recent years, has resulted in a large number of empirical studies. However, there are very few papers developing theoretical models explaining the evolution of the observed data. My proposed research aims to develop alternative theoretical models, based on Poisson processes, to explain the workings of double blind Dutch auctions and limit order financial markets. b) Threshold models are very useful for modeling regime changes and hence financial volatility.This research aims to examine statistical aspects of threshold models for financial volatility such as GARCH and Stochastic Volatility. c) The assessment of financial forecasting ability is a very real practical and relevant task. Practitioners often use what is known as the Hit Rate, defined as the probability that the forecaster correctly forecasts the sign of the future asset return. In realistic non-normal situations this research aims to examine the statistical properties of the hit rate and its relationship to the correlation between the forecast and the observed. d) Ex-post utility is much discussed in economics but its econometric properties are rarely investigated. The aim of this research is to pursue such an investigation in relation to portfolio optimization.