Quantitative Risk Assessment Methods

Quantitative Risk Assessment

When to Use Quantitative Methods

• Financial risk measurement
• Capital allocation decisions
• Insurance and hedging analysis
• Regulatory requirements
• Investment decisions

Key Methodologies

Monte Carlo Simulation

Process:

1. Define input variables and distributions
2. Generate random samples
3. Calculate output for each scenario
4. Analyze distribution of results

Applications:

• Project cost and schedule estimation
• Credit portfolio losses
• Operational risk capital
• Cyber risk quantification

Key Outputs:

• Expected value (mean)
• Standard deviation
• Percentiles (5th, 50th, 95th)
• Loss exceedance curves

Value at Risk (VaR)

Definition: Maximum expected loss at a given confidence level over a specified time period.

Methods:

1. Historical Simulation

   • Use actual historical returns
   • No distributional assumptions
   • Limited by historical data

2. Parametric VaR

   • Assume normal distribution
   • Use mean and variance
   • Fast but less accurate for fat tails

3. Monte Carlo VaR

   • Simulate price paths
   • Flexible distributions
   • Computationally intensive

Expected Shortfall (ES)

Also called Conditional VaR (CVaR)

• Average loss beyond VaR
• Better captures tail risk
• Required by Basel III for market risk

Scenario Analysis

Sensitivity Analysis

• Vary one factor at a time
• Identify key risk drivers
• Create tornado diagrams

Stress Testing

• Extreme but plausible scenarios
• Multiple factors move together
• Historical or hypothetical

Reverse Stress Testing

• Start with failure outcome
• Work backward to causes
• Identify hidden vulnerabilities

Data Requirements

• Historical loss data
• Market data time series
• Expert judgment (calibrated)
• Industry benchmarks
• Scenario parameters

Validation and Backtesting

• Compare predictions to actuals
• Statistical tests for accuracy
• Model risk assessment
• Regular recalibration