Value at Risk Calculator Skill

Value at Risk Calculator

Overview

The Value at Risk Calculator skill provides comprehensive capabilities for calculating VaR and related risk metrics using multiple methodologies. It supports financial risk assessment, operational risk quantification, and regulatory compliance through parametric, historical, and simulation-based approaches.

Capabilities

Historical simulation VaR
Parametric VaR (variance-covariance)
Monte Carlo VaR
Conditional VaR (CVaR/Expected Shortfall)
Incremental and component VaR
Stress testing
Backtesting and validation
Regulatory reporting support

Used By Processes

Monte Carlo Simulation for Decision Support
Risk Assessment
Decision Quality Assessment

Usage

Historical Simulation VaR

# 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

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

VaR Interpretation

| Metric | Meaning | |--------|---------| | VaR 95% = $1M | 95% confident loss won't exceed $1M | | CVaR 95% = $1.5M | If loss exceeds VaR, average loss is $1.5M | | Incremental VaR | Change in portfolio VaR from adding position | | Component VaR | Position's contribution to total VaR |

Backtesting Standards

| Exceptions (250 days) | Zone | Interpretation | |----------------------|------|----------------| | 0-4 | Green | Model is acceptable | | 5-9 | Yellow | Model may have issues | | 10+ | Red | Model needs review |

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

Agent Skills: Value at Risk Calculator

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