Modelling Volatility using GARCH Processes

Abstract

Following the initial work on portfolio theory in the 1950s, volatility has become an extremely important concept in finance, appearing regularly in models of, for example, asset pricing and risk management. Much of the interest in volatility has to do with it not being directly observable, and several alternative measures have been developed to approximate it empirically. The most common measure of volatility has been the unconditional standard deviation of historical returns. The use of this measure, however, is severely limited by it not necessarily being an appropriate representation of financial risk and by the fact that returns tend not to be independent and identically distributed, so making the standard deviation a potentially poor estimate of underlying volatility.