Value-at-risk

Book excerpt: Value-at-risk (VaR) is a measure of market risk that has been widely adopted since the mid-1990s for use on trading floors. It describes how to design, implement, and use scalable production VaR measures on actual trading floors. Practical, detailed examples are drawn from markets around the world, including: Euro deposits, Pacific Basin equities, physical coffees, and North American natural gas. Real-world challenges relating to market data, portfolio mappings, multicollinearity, and intra-horizon events are addressed in detail. Exercises reinforce concepts and walk readers step-by-step through computations. Sophisticated techniques are fully disclosed, including: quadratic ("delta-gamma") methods for nonlinear portfolios, variance reduction (control variates and stratified sampling) for Monte Carlo VaR measures, principal component remappings, techniques to "fix" estimated covariance matrices that are not positive-definite, the Cornish-Fisher expansion, and orthogonal GARCH.