Extreme Events in Finance

Chapter 12Estimation Methods for Value at Risk

Saralees Nadarajah and Stephen Chan

School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

12.1 Introduction

12.1.1 History of VaR

In the last few decades, risk managers have truly experienced a revolution. The rapid increase in the usage of risk management techniques has spread well beyond derivatives and is totally changing the way institutions approach their financial risk. In response to the financial disasters of the early 1990s, a new method called Value at Risk (VaR) was developed as a simple method to quantify market risk (in recent years, VaR has been used in many other areas of risk including credit risk and operational risk). Some of the financial disasters of the early 1990s are the following:

• Figure 12.1 shows the effect of Black Monday, which occurred on October 19, 1987. In a single day, the Dow Jones stock index (DJIA) crashed down by 22.6% (by 508 points), causing a negative knock-on effect on other stock markets worldwide. Overall the stock market lost $0.5 trillion.
• The Japanese stock price bubble, creating a $2.7 trillion loss in capital; see Figure 12.2. According to this website, “the Nikkei Index after the Japanese bubble burst in the final days of 1989. Again, the market showed a substantial recovery for several months in mid-1990 before sliding to new lows.”
• Figure 12.3 describes the dot-com bubble. During 1999 and 2000, the NASDAQ rose at a dramatic rate with all technology stocks booming. ...