1 Probability Distributions & Random Variables 1.1 Random Variables A random variable is a numerical description of the outcome of a statistical experiment. A random variable that may assume only a finite number or an infinite sequence of values is said to be discrete; one that may assume any value in some interval on the real number line is said to be continuous. 1.2 Probability Distributions of Random Variables A probability distribution is a mathematical function that gives the probability of occurrence of different possible outcomes for an experiment.

1 What is linear regression? In statistics, linear regression is a linear approach for modelling the relationships between a scalar dependent variable and one (or more) independent variables. The relationships are modelled using linear predictor functions whose unknown model parameters are estimated from the data - known as linear models. Linear regression has many practical uses which broadly fall into one of the following two categories: Prediction and forecasting which uses linear regression to fit a predictive model to an observed data set of values of the dependent and independent variables using a training data set before using the fitted model to make predictions using a testing data set.

Quick Summary In this project we shall investigate the use of GARCH models for calculating Value at Risk (VaR). Specifically we will fit a GARCH(1,1) model to a time-series data set of FTSE100 closing prices between 7 November 2002 and 6 October 2010 before comparing our results with previous results attained using other methods for calculating VaR. We will discuss the appropriateness of the GARCH model assumptions for our data setand look at fitting other GARCH models to attain improved VaR predictions.