Model Calibration and Validation

Model calibration fits parameters to market data; validation confirms the model performs adequately for its intended use. Both processes require systematic workflows, quantitative acceptance criteria, and documentation suitable for regulatory review.

Calibration Workflow

Step 1: Data Hygiene and Input Checks

Before calibration begins:

• Verify data timestamp (intraday staleness matters)
• Check for outliers (quotes >3 standard deviations from history)
• Exclude illiquid instruments (wide bid-ask, zero volume)
• Confirm data source consistency (same provider across tenors)

Data quality checklist:

• Quotes are from the same snapshot time
• Bid-ask spreads are within normal ranges
• All required tenors/strikes are present
• No corporate actions affect calibration instruments

Step 2: Define Objective Function

The objective function measures fit quality:

Sum of squared errors: Objective = Σ_i (Model_IV_i - Market_IV_i)²

Weighted by vega: Objective = Σ_i vega_i × (Model_IV_i - Market_IV_i)²

This weights ATM options (high vega) more heavily than wings.

Regularization: Objective = Σ_i (error_i)² + λ × (parameter_penalty)

Regularization prevents extreme parameters that overfit current data.

Step 3: Optimization

Common approaches:

• Gradient descent (for smooth objective)
• Levenberg-Marquardt (standard for least squares)
• Global optimization (simulated annealing, genetic algorithms)

Convergence criteria:

• Maximum iterations: 1,000
• Objective improvement threshold: < 0.01% change
• Parameter change threshold: < 0.1% change

Step 4: Overfitting Detection

Signs of overfitting:

• Parameters at boundary constraints
• Large parameter swings day-to-day
• Poor out-of-sample performance
• Unusual parameter values (e.g., vol of vol > 200%)

Out-of-sample test: Reserve 20% of instruments for validation. After calibrating to 80%, check error on held-out 20%. If held-out error >> in-sample error, overfitting is likely.

Step 5: Documentation and Audit Trail

Record for each calibration:

• Timestamp
• Data source and snapshot time
• Parameters before and after
• Objective function value
• Out-of-sample error
• Any manual overrides

Acceptance Thresholds

Volatility model (e.g., Heston, SABR):

• RMSE < 0.5 vols across calibration set
• Maximum error < 2.0 vols at any point
• Out-of-sample RMSE < 0.75 vols

Interest rate model (e.g., Hull-White, LMM):

• RMSE < 0.3 vols for swaption surface
• Yield curve repricing error < 0.1 bps

Failure action: If thresholds are not met:

1. Review input data for errors
2. Expand calibration set or adjust weights
3. Consider model limitations (may not fit this market)
4. Escalate to model governance if persistent

Governance Notes

Model calibration falls under SR 11-7 (Fed) and similar regulations:

Requirements:

• Independent validation of calibration methodology
• Regular backtesting against realized outcomes
• Change management for calibration logic updates
• Model inventory with tiering by materiality

Annual validation includes:

• Review of calibration accuracy over trailing year
• Benchmark comparison to alternative models
• Stress testing of calibrated parameters
• Documentation update for any methodology changes

Escalation timeline:

• Calibration failure >2 consecutive days: Notify risk management
• Threshold breach >5 days: Escalate to model governance committee
• Remediation required within 30 days of formal finding

Example Calibration Analysis

Heston model calibration to S&P 500 options:

Parameters:

Calibration results:

Validation conclusion: Model calibration meets all thresholds. Approved for production use.

RMSE Threshold Reference

Next Steps

For stress testing calibrated models, see Stress Testing Models for Extreme Moves.

To understand the models being calibrated, review Local vs. Stochastic Volatility Models.