Stress Testing Models for Extreme Moves
Stress Testing Models for Extreme Moves
The March 2020 COVID crash and the 2018 volatility spike (Volmageddon) demonstrated that models calibrated to normal conditions can fail spectacularly during stress. Systematic stress testing identifies model vulnerabilities before markets reveal them at the worst possible time.
Scenario Library Design
Stress Scenario Workflow:
- Define scenario library: Collect historical and hypothetical extreme events
- Apply shocks to inputs: Shift spot, volatility, rates, correlations
- Price positions under stress: Recalculate valuations and Greeks
- Attribute P/L: Decompose changes into risk factors
- Report and escalate: Communicate results to risk committees
- Remediate if needed: Adjust limits, hedges, or model parameters
Scenario Categories
Historical scenarios:
| Event | Date | Spot Shock | Vol Shock | Rate Shock |
|---|---|---|---|---|
| Black Monday | Oct 1987 | -20% | +400 bps | -50 bps |
| Asian Crisis | Aug 1997 | -15% | +300 bps | +100 bps |
| GFC | Oct 2008 | -25% | +500 bps | -200 bps |
| Volmageddon | Feb 2018 | -10% | +400 bps | +25 bps |
| COVID Crash | Mar 2020 | -30% | +600 bps | -150 bps |
Hypothetical scenarios:
| Scenario | Spot Shock | Vol Shock | Rate Shock | Correlation |
|---|---|---|---|---|
| Equity crash | -25% | +500 bps | -100 bps | +0.3 |
| Rate spike | -10% | +200 bps | +300 bps | +0.2 |
| Vol explosion | -5% | +800 bps | 0 | +0.1 |
| Liquidity squeeze | -15% | +300 bps | +50 bps | +0.4 |
Shock Magnitudes
Standard stress shock calibration:
| Risk Factor | Moderate Stress | Severe Stress | Extreme |
|---|---|---|---|
| Equity spot | -15% | -25% | -40% |
| Implied vol | +200 bps | +400 bps | +800 bps |
| Interest rates | +100 bps | +300 bps | +500 bps |
| Credit spreads | +100 bps | +300 bps | +600 bps |
| FX | +/- 10% | +/- 20% | +/- 30% |
Execution and Cadence
Reporting cadence:
- Daily: Key position P/L under 2-3 core scenarios
- Weekly: Full scenario library review
- Monthly: Model performance vs. stress outcomes
- Quarterly: Governance committee presentation
Run checklist:
- Data preparation: Collect current positions, valuations, and Greeks
- Scenario application: Apply shocks to market data and recalculate
- Quality control: Verify calculations against prior runs; investigate outliers
- Report generation: Produce P/L by desk, product, and scenario
P/L Attribution
Attribute stress P/L to risk factors:
First-order (linear): ΔP/L_delta = Delta × ΔSpot ΔP/L_vega = Vega × ΔVol ΔP/L_rho = Rho × ΔRate
Second-order (convexity): ΔP/L_gamma = ½ × Gamma × (ΔSpot)² ΔP/L_vanna = Vanna × ΔSpot × ΔVol ΔP/L_volga = Volga × (ΔVol)²
Attribution waterfall example:
| Factor | Contribution | % of Total |
|---|---|---|
| Delta | -$15.2M | 52% |
| Gamma | +$3.1M | -11% |
| Vega | -$8.5M | 29% |
| Other Greeks | -$2.4M | 8% |
| Unexplained | -$0.5M | 2% |
| Total | -$23.5M | 100% |
Unexplained residual: If unexplained exceeds 5% of total, investigate model limitations or data issues.
Remediation Triggers and Governance
Trigger levels:
| Metric | Amber | Red |
|---|---|---|
| Stress P/L vs. limit | >75% | >100% |
| Unexplained residual | >5% | >10% |
| Model error vs. threshold | >2× RMSE | >5× RMSE |
| Greeks breach | Any | Multiple |
Escalation path:
- Amber trigger: Desk head notification, increased monitoring
- Red trigger: Risk committee notification within 24 hours
- Persistent red: Model governance review, potential trading restrictions
Remediation actions:
- Reduce position size
- Add hedges for specific risk factors
- Increase margin/capital reserves
- Adjust model calibration
- Request model re-validation
Stress Test Documentation
Each stress test run should document:
- Scenario name and parameters
- Date and time of run
- Positions included
- P/L results by desk and product
- Attribution breakdown
- Comparison to limits
- Any anomalies or exceptions
- Approval signature for quarterly reports
Audit trail enables regulatory examination and internal review.
Example Stress Report Summary
Date: 2025-01-15 Scenario: COVID-style crash (-30% spot, +600 bps vol)
| Desk | Current P/L | Stress P/L | Limit | Utilization |
|---|---|---|---|---|
| Equity Options | +$12.5M | -$45.2M | $75M | 60% |
| Index Vol | -$2.1M | -$18.7M | $25M | 75% |
| Exotic Derivatives | +$5.3M | -$22.4M | $30M | 75% |
| Firm Total | +$15.7M | -$86.3M | $100M | 86% |
Observations:
- Firm within limits but at 86% utilization
- Equity Options desk has concentration risk in short gamma
- Exotic Derivatives stress driven by barrier knock-out
Recommendation: Monitor closely; consider reducing short gamma exposure if market vol rises.
Next Steps
For governance framework around models, see Model Risk Governance Practices.
For calibration procedures, review Model Calibration and Validation.