Change point detection in an Ornstein-Uhlenbeck process (a reflection of trading in financial markets)

Abstract: The financial market has become an area of increasing research interest for mathematicians and statisticians in recent years. Mathematical models and methods are increasingly being applied to study various parameters of the market. One of the parameters that have attracted lots of interest is `volatility'. It is the measure of variability of prices of instruments (e.g. stock, options etc.) traded in the market. It is used mainly to measure risk and to predict future prices of assets. In this paper, the volatility of financial price processes is studied using the Ornstein-Uhlenbeck process. The process is a mean reverting model which has good and well documented properties to serve as a model for financial price processes. At some random time point, a parameter change in the distribution of the price process occurs. In order to control the development of prices, it is important to detect this change as quickly as possible. The methods for detecting such changes are called `stopping rules'. In this work, stopping rules will be derived and analysed. Using simulations and analytical methods, the properties of these stopping rules will be evaluated.