VaR is simplistically the loss quantile of the PL distribution. There are many ways to generate the distribution and to compute the quantile. By far the three most common methods used by banks are the parametric VaR, historical simulation VaR, and Monte Carlo VaR. Their popular use stems from the practical balance between simplicity and validity.
A VaR system must be simple enough to be intuitively understood by top management, regulators, and operators of the system. Abstract models that require specialized domain knowledge to comprehend seldom make it to conventional use. This is because risk management is a huge team effort—there are often hundreds of staff managing different aspects of the risk architecture and in different geographic locations. A simple model provides a common language in the chain of command.
The validity of a VaR model must be tested against the market. Until recently, VaR models have been generally accepted (for lack of a better alternative) on the grounds that the market behavior generally falls within the prediction of VaR. Statistically speaking, almost all (say 99%) of the time, the system is predictive. But the 2008 crisis has highlighted that this peacetime tool breaks down during times of crisis, just when it is needed most.
The best way to learn about VaR is to implement it on an Excel spreadsheet. We will illustrate all three VaR methods using the same test portfolio comprising a stock index, an option, and a ...