The last 40 years have seen a dramatic increase in the complexity of markets. This is true in relation to the types of assets, securities, and commodities traded, as well as the mechanisms for trading and the linkages between markets. Recent decades have also witnessed a series of notable shocks and episodes of extreme volatility in a variety of markets.1 Consequently, while risk management has always been an essential function of market participants, its importance has reached unprecedented levels and is unlikely to abate.
Perhaps surprisingly, in light of recent attention on risk management, value at risk (VaR) remains the metric most popular in practice and often favored by regulators. Put simply, VaR is an estimate of the maximum loss that will occur over a given time period (τ) for a specified significance level (α). For example, if VaR is estimated to be $X with α = 5% and τ = 1 day, there is a 95% chance that losses over a 1-day period will not exceed $X. In practice, the choice of the significance level (α) and the time horizon (τ) will vary depending on the particular VaR application on hand and the risk manager's risk attitude.2