Economic capital is critical to a bank as it links a bank’s earnings and returns to risks that are specific to a business line or business opportunity. In addition, these economic capital measurements can be aggregated into a portfolio of holdings. Value at Risk or (VaR) is used in trying to understand how the entire organization is affected by the various risks of each holding as aggregated into a portfolio, after accounting for their cross-correlations among various holdings. VaR measures the maximum possible loss given some predefined probability level (e.g., 99.90%) over some holding period or time horizon (e.g., 10 days). The selected probability or confidence interval is typically a decision made by senior management at the bank and reflects the board’s risk appetite. Stated another way, we can define the probability level as the bank’s desired probability of surviving per year. In addition, the holding period is usually chosen such that it coincides with the time period it takes to liquidate a loss position.
VaR can be computed in several ways. Two main families of approaches exist: structural closed-form models and Monte Carlo risk simulation approaches. We will showcase both methods in this case, starting with the structural models.
The second and much more powerful approach is the use of Monte Carlo risk simulation. Instead of simply correlating individual business lines or assets in the structural models, entire probability distributions can be correlated using more advanced mathematical copulas and simulation algorithms in Monte Carlo simulation methods by using Risk Simulator. In addition, tens to hundreds of thousands of scenarios can be generated using simulation, providing a very powerful stress-testing mechanism for valuing VaR. In addition, distributional fitting methods are applied to reduce the thousands of data points into their appropriate probability distributions, allowing their modeling to be handled with greater ease.