Introduction

As financial trading systems have become more sophisticated, there has been increased awareness of the dangers of very large losses. This awareness has been heightened by a number of highly publicised catastrophic incidents:

• Barings. In February 1995, the Singapore subsidiary of this long-established British bank lost about $1.3 billion because of the illegal activity of a single trader, Nick Leeson. As a result the bank collapsed, and was subsequently sold for one pound.

• Orange County. Bob Citron, the Treasurer of Orange County, had invested much of the county's assets in a series of derivative instruments tied to interest rates. In 1994, interest rates rose, and Orange County went bankrupt, losing $1.7 billion.

• Daiwa Bank. A single trader, Toshihide Iguchi, lost $1.1 billion of the bank's money over a period of 11 years, the losses only coming to light when Iguchi confessed to his managers in July 1995.

• Long Term Capital Management. In the most spectacular example to date, this highly-regarded hedge fund nearly collaped in September 1998. LTCM was trading a complex mixture of derivatives which, according to some estimates, gave it an exposure to market risk as high as $200 billion. Things started to go wrong after the collapse of the Russian economy in the summer of 1998, and to avoid a total collapse of the company, 15 major banks contributed to a $3.75 billion rescue package.

These and other examples have increased awareness of the need to quantify probabilities of large losses, and for risk management systems to control such events. The most widely used tool is Value at Risk (henceforth, VaR).