Financial Risk Forecasting

The focus of this chapter is on the statistical techniques used for analyzing prices andreturns in financial markets. The concept of a stock market index is defined followed bya discussion of prices, returns and volatilities. Volatility clusters, the fat-tailed propertyof financial returns and observed sharp increases in correlations between assets duringperiods of financial turmoil (i.e., nonlinear dependence) will also be explored.Various statistical techniques are introduced and used in this chapter for the analysisof financial returns. While readers may have seen these techniques before, Appendix Acontains an introduction to basic statistics and time series methods for financial applications.The most common statistical methods presented in this chapter are implementedin the two programming languages discussed in this book: R and Matlab. Theselanguages are discussed in more detail in Appendix B for R and Appendix C for Matlab.We illustrate the application of statistical methods by using observed stock marketdata, the S&P 500 for univariate methods and a portfolio of US stocks for multivariatemethods. The data can be downloaded from sources such as finance.yahoo.comdirectly within R and Matlab, as demonstrated by the source code in this chapter.A key conclusion from this chapter is that we are likely to measure risk incorrectly byusing volatility because of the presence of volatility clusters, fat tails and nonlineardependence. This impacts on many financial applications, such as portfolio management,asset allocation, derivatives pricing, risk management, economic capital andfinancial stability