Monitoring volatility in Financial Market Trading Process

The financial market has been an area of increased research interest for mathematicians and statisticians. Some of the main research areas are on the log returns of assets (shares, bond, foreign exchange, option) and the volatility which is the variation in the log returns. The volatility is widely studied because of its applications in trading financial instruments which are, used for forecasting prices and measuring the risk of financial assets. In this work, a process of trading activities is considered. It is assumed that at a random time-point a parameter change in the trading process occurs, indicating changed trading behavior. It is important to be able to state that such a change has occurred quickly and accurately, which will help the investor to make a decision either to buy or sell financial assets. To effectively make this decision a financial model is developed using the family of Autoregressive Conditional Heteroskedastic (ARCH) and stopping rule is created which signal alarms as soon as return on financial asset goes beyond or below some threshold. The work ends with a model that can be applied to real data.