Grant: Discovery Grants Program - Individual

This research will continue my interest in financial econometric models and their statistical properties. In particular it will examine two broad classes of models: a)Threshold models for modeling volatility and bubbles in financial markets The threshold models to be examined could be as simple as an autoregressive process of order one, AR(1) or as complicated as GARCH and Stochastic Volatility (SV) with thresholds in both the return equation and the volatility equation. While these models are relatively straightforward to estimate, their statistical properties including stationarity conditions and the existence of a stationary distribution and moments are often unknown. This research aims to rectify this situation. Both applied time series statisticians and applied financial econometricians will benefit from the results. b)Financial market models which describe the workings of auctions and trading models for financial exchanges. For the financial market models the aim here is to develop the statistical properties of the models thereby leading to a better understanding of how trades occur and an equilibrium, between demand and supply, is reached. The models in question involve modeling the demand and supply processes as Poisson processes which may or may not have the same intensity of arrivals. The research will begin by analyzing the double-blind Dutch auction which is an important micro-structure model. A thorough understanding of this model will help considerably when we move on to examine more realistic models for high frequency machine trading on financial exchanges. The research from this section will aim to improve our understanding of how markets work and hopefully lead to better trading schemes in financial markets.