Modeling Structural Changes in Volatility Using Markov Switching GARH Models

Abstrakt

Knowing the risk associated with a financial investment is relevant for everyone in the financial world. Determining a way to estimate this risk accurately, has been a topic of discussion for decades. Knowledge regarding the behaviour of financial asset returns, has lead to a lot of interesting discoveries, such as the heavy tailed nature of the returns as well as the heteroscedastic behavior of the volatility. These findings have been accounted for in different ways throughout the years. A type of behaviour that is rarely accounted for in risk modeling is structural changes in the modeling, over time. These changes can be seen when the financial markets enter a crisis, where the volatility usually skyrocket. It is therefore interesting to model these periods differently, than periods where the financial markets are stable, and the volatility is generally low. This thesis applies the theory behind hidden Markov models to expand upon the GARCH model, such that it can account for periods of structurally different volatility. This model is called a Markov switching GARCH model, and it will be used to explain the volatility of the return process for a selected part of the S&P 500 index. In doing so the model parameters will be estimated based on a historical time period, that include times of financial crisis, as well as more stable times. When estimating the parameters of the MS-GARCH model based on this period, the variance of the financially stable periods converge to being constant, whereas the variance in the financial crises are modelled well by the GARCH model. Estimating the parameters in the MS-GARCH is made difficult since the structure of the model introduces a path dependence in the conditional variance. This is overcome by using a Bayesian estimation procedure, instead of maximum likelihood, to determine the parameter estimates. The method used for the estimation of the parameters is a Gibbs sampler, which is used due to its effectiveness when working with high dimensional estimation. The capabilities of the MS-GARCH model as a risk model are also examined. Here it is found to produce good risk estimates on historical observations, however the risk estimates generated from day to day, are not ideal.