Volatility Case

The international stock markets are constantly changing over time and the analysis and modelling of the volatility of these markets is one of the most important factors in option trading and risk management. Over the last thirty years there have been major changes in the financial markets. Examples include the US stock market collapse in October, 1987 and the Japanese stock market (Nikkei-225) crash towards the end of 1989 which resulted within three years that the stock index had lost more than 50% of its value. Other big financial crises include the collapse of Long Term Capital Management and the decline on the NASDAQ in early 2000 of internet, technology and new economy stocks. These changes make volatility modelling a difficult task for academicians and practitioners.

The correct volatility input in option pricing has an important influence in obtaining the correct option premium using the path breaking work of Black and Scholes (1973) and Merton (1973). Sundaresan (2000) provides a major review of continuous time models in finance and their many applications. The use of volatility analysis is also important in the computation in Value-at-Risk (VaR). VaR is mainly concerned with market risk. It is a single estimate of the amount by which an institution’s position in a risk category could decline due to general market movements during a holding period. General discussion on VaR is given in Duffie and Pan (1997) and Jorion (2006).

A number of models have been developed for modelling and forecasting volatility and a major review of econometric volatility models is given in Poon and Granger (2003). We will investigate the use of these models using the FTSE-100 stock market index for the UK, S&P 500 stock market index for the US and the Nikkei-225 for Japan.

This proposal is organized as follows: Section 2 provides a literature review of volatility models and Section 3 discusses the daily data to be used on the different