Derivatives

CHAPTER 44Value at Risk

Aims

• To explain the concept of value at risk (VaR).
• To measure VaR using the variance-covariance (VCV) approach.
• To outline methods used in forecasting volatility.
• To use backtesting to assess the accuracy of VaR forecasts.
• To outline the ‘Basel internal models’ approach in setting regulatory standards.

44.1 INTRODUCTION

Financial institutions, particularly large investment banks, hold positions in a wide variety of assets such as stocks, bonds, foreign exchange, as well as futures and options contracts. Because prices of these assets can move quickly and by large amounts, investment banks want to know what risk they are holding over the next 24 hours as well as over the next week or month. Once they know what their risk position is then they can either decide to maintain or reduce it or alternatively to hedge the risk – usually by using derivatives. Risk due to price changes is known as ‘market risk’ and measuring and monitoring changing market risk is the subject of this chapter.

For their own prudential reasons financial intermediaries need to measure the overall ‘dollar’ market risk of their portfolio, which is usually referred to as value at risk (VaR). In addition, the regulatory authorities use VaR to set minimum capital adequacy requirements for financial institutions. If a bank has a high VaR then the regulator may limit the amount of dividends paid to stockholders, so that the bank can increase its ‘capital’ via an increase in its retained ...