Market Risk VaR: The Historical Simulation Approach
In this chapter and the next, we cover the two main approaches to calculating VaR for market risk. The approach we consider in this chapter is known as historical simulation and is the one usually used by banks. It involves using the day-to-day changes in the values of market variables that have been observed in the past in a direct way to estimate the probability distribution of the change in the value of the current portfolio between today and tomorrow.
After describing the mechanics of the historical simulation approach, the chapter explains how to calculate the standard error of the VaR estimate, how the procedure can be modified so that recent data are given more weight, and how volatility data can be incorporated into the VaR estimates that are made. Finally, it covers extreme value theory. This is a tool that can be used to improve VaR estimates and deal with situations where the required VaR confidence level is very high.
All the models covered in this chapter are illustrated with a portfolio consisting of an investment in four different stock indices. Historical data on the indices and VaR calculations can be found at: www.rotman.utoronto.ca/∼hull/RMFI3e/VaRExample.
14.1 THE METHODOLOGY
Historical simulation involves using past data as a guide to what will happen in the future. Suppose that we want to calculate VaR for a portfolio using a one-day time horizon, a 99% confidence level, and 501 days of data. ...