A Univariate Volatility Modelling combining the GARCH model with the Volatility Index VIX

Abstract

In this thesis I shall examine the characteristics of the volatility in the financial markets. In particular, the volatility is extrapolated both from the historical volatility by time series of past market prices and from derivative instruments providing an implied volatility. The first part explores the causes of volatility, especially volatility clustering, and explain the behavioural reactions of the stockholders. It is a well-known fact that there are GARCH models and many others that are accurate and useful to estimate the conditional variance. Anyway, looking the historical returns could be not be enough to fit the model on the data. Our purpose is to create a non-linear Univariate model to evaluate the financial markets using the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model with the CBOE Volatility Index (VIX) as a exogenous variable. The exogenous variable VIX is independent of the GARCH model but is included in the new model we want to realize. Using the daily rates of return of 10 major indices, we want to determine if the new model created, adding an exogenous variable, is better than the single GARCH model. Therefore, the empirical analysis analyse the volatility implementing the GARCH with the exogenous implied volatility, determined look forward in time, being derived from the market price of a market-traded derivative. It is using the Variance Swaps, based on the S&P 500 Index, the core index for U.S. equities, and estimates expected volatility by aggregating the weighted prices of S&P 500 puts and call over a wide range of strike prices. By empirically examining the time series of different world indices we hope to produce a more complete understanding of the utility of the VIX into the GARCH models.