Value At Risk Calculator

# Historical VaR configuration
historical_var_config = {
    "method": "historical_simulation",
    "data": {
        "returns": portfolio_returns,  # historical return series
        "period": "daily",
        "history_length": 252  # 1 year of trading days
    },
    "confidence_levels": [0.95, 0.99],
    "holding_period": 1,  # days
    "options": {
        "age_weighting": {
            "enabled": True,
            "decay_factor": 0.97
        }
    }
}

Parametric VaR

# Parametric (variance-covariance) VaR
parametric_var_config = {
    "method": "parametric",
    "portfolio": {
        "positions": {
            "Asset_A": {"value": 1000000, "weight": 0.4},
            "Asset_B": {"value": 750000, "weight": 0.3},
            "Asset_C": {"value": 750000, "weight": 0.3}
        }
    },
    "parameters": {
        "volatilities": {"Asset_A": 0.20, "Asset_B": 0.15, "Asset_C": 0.25},
        "correlation_matrix": [
            [1.0, 0.3, 0.2],
            [0.3, 1.0, 0.5],
            [0.2, 0.5, 1.0]
        ]
    },
    "confidence_level": 0.99,
    "holding_period": 10  # days
}

Monte Carlo VaR

# Monte Carlo VaR configuration
monte_carlo_var_config = {
    "method": "monte_carlo",
    "simulations": 100000,
    "model": {
        "type": "geometric_brownian_motion",
        "parameters": {
            "drift": "historical",
            "volatility": "garch"
        }
    },
    "portfolio_valuation": "full_revaluation",
    "confidence_levels": [0.95, 0.99],
    "holding_period": 10
}

Conditional VaR (Expected Shortfall)

CVaR represents the expected loss given that VaR is exceeded:

• CVaR at 95% = Average loss in worst 5% of scenarios
• Required by Basel III/IV for market risk capital
• More coherent risk measure than VaR

Stress Testing

# Stress test scenarios
stress_tests = {
    "scenarios": [
        {
            "name": "2008 Financial Crisis",
            "shocks": {"equity": -0.40, "credit_spreads": 0.03, "rates": -0.02}
        },
        {
            "name": "COVID-19 March 2020",
            "shocks": {"equity": -0.30, "volatility": 0.50, "credit_spreads": 0.02}
        },
        {
            "name": "Interest Rate Spike",
            "shocks": {"rates": 0.03, "equity": -0.15}
        }
    ],
    "output": ["portfolio_loss", "position_contributions"]
}

Input Schema

{
  "method": "historical|parametric|monte_carlo",
  "portfolio": {
    "positions": "object",
    "total_value": "number"
  },
  "data": {
    "returns": "array or path",
    "period": "string"
  },
  "parameters": {
    "confidence_levels": ["number"],
    "holding_period": "number",
    "volatility_model": "string"
  },
  "stress_testing": {
    "scenarios": ["object"]
  },
  "backtesting": {
    "enabled": "boolean",
    "test_period": "string"
  }
}

Output Schema

{
  "var_results": {
    "confidence_level": {
      "VaR": "number",
      "VaR_percent": "number",
      "CVaR": "number",
      "CVaR_percent": "number"
    }
  },
  "component_var": {
    "position": {
      "marginal_var": "number",
      "component_var": "number",
      "contribution_percent": "number"
    }
  },
  "stress_test_results": {
    "scenario_name": {
      "portfolio_loss": "number",
      "loss_percent": "number"
    }
  },
  "backtesting": {
    "exceptions": "number",
    "exception_rate": "number",
    "traffic_light": "green|yellow|red",
    "kupiec_test": "object",
    "christoffersen_test": "object"
  },
  "risk_attribution": "object"
}

Best Practices

1. Use multiple methods and compare results
2. Validate with backtesting regularly
3. Include fat tails (t-distribution or historical for parametric)
4. Update parameters (volatility, correlations) frequently
5. Complement VaR with stress testing
6. Report CVaR alongside VaR for tail risk
7. Document all assumptions and limitations

VaR Interpretation

Backtesting Standards

Integration Points

• Receives simulations from Monte Carlo Engine
• Connects with Risk Register Manager for risk assessment
• Supports Risk Analyst agent
• Integrates with Decision Visualization for risk charts