Market Risk: VaR Approaches, Backtesting, and Stress Testing
Parametric, historical, and Monte Carlo VaR applied to market risk — plus regulatory backtesting requirements and stress testing methodologies.
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Concept visual
Backtesting Exception Pattern
Clusters of exceptions are more informative than isolated misses when you evaluate a VaR model.
Why it matters
Backtesting is not just exception counting. You are also checking stability, clustering, and whether the model breaks in stress.
Market Risk: VaR Approaches, Backtesting, and Stress Testing
Market Risk Categories
Market risk is the risk of loss from adverse movements in market prices. The FRM categorizes market risk into:
- Interest rate risk — Changes in yield curves affect bond prices, swap values, and interest rate derivatives
- Equity risk — Stock price movements impact equity portfolios and equity derivatives
- Currency risk — Exchange rate fluctuations affect positions denominated in foreign currencies
- Commodity risk — Price changes in oil, gold, agricultural products, etc.
Each category requires specific risk factor identification and modeling.
Risk Factor Mapping
Before computing VaR, complex instruments must be mapped to standard risk factors.
Cash Flow Mapping for Bonds
A 7-year bond is mapped to cash flows at standard vertices (e.g., 5-year and 10-year), weighted by present value and duration sensitivity. This allows the use of a standard covariance matrix.
Delta-Normal for Options
Options are mapped using their Greeks:
- Delta-equivalent position: Δ × S × Quantity
- For portfolios with significant gamma: use delta-gamma-normal approac
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