Value-at-risk (VaR) is the risk measure that estimates the maximum potential loss of risk exposure given confidence level and time period. For example, a one-day 99% value-at-risk of $10 million means that 99% of the time the potential loss over a one-day period is expected to be less than or equal to $10 million. In other words, there is 1% chance that the potential loss over a one-day period will be greater than $10 million.

Value-at-risk is popularly used not only in risk reporting, but also in multiple phases of the risk management life cycle, including:

• Setting risk limits and risk budgets
• Computing regulatory capital requirements (e.g., Basel III, Solvency II)
• Backtesting value-at-risk models
• Calculating conditional value-at-risk, stress testing, and sensitivity analysis

Depending on the asset classes and types of risk exposure, risk managers employ various mathematical techniques to calculate value-at-risk, including:

• Monte Carlo simulation
• Copula-based portfolio simulation
• Pricing and valuation of financial derivatives
• Econometrics models (e.g., interest rate models and GARCH models)

For more information, see Statistics and Machine Learning Toolbox™, Financial Toolbox™, Financial Instruments Toolbox™, and Risk Management Toolbox™.