Planeamento
Aulas
1. Introduction to Value at Risk (VaR)
- Definition and attractive features
1. Introduction to Value at Risk (VaR) (continued)
- Total vs. Risk Factor VaR
- Decomposition: Systematic and Specific VaR, Stand-alone VaR, Marginal and Incremental VaR
- Associated risk metrics and coherence
- Introduction to VaR models: Normal Linear VaR, Historical Simulation and Monte Carlo Simulation
2. Parametric Linear VaR models
- Foundations of Normal Linear VaR: Normal Linear VaR formula, Static vs. Dynamic VaR, scaling for different risk horizons, adjusting for autocorrelation, Stand-alone, Marginal and Incremental VaR
2. Parametric Linear VaR models (continued)
- Normal Linear VaR for stock portfolios: Systematic and Specific VaR, estimation of Specific VaR, Systematic VaR decomposition
2. Parametric Linear VaR models (continued)
- Portfolio mapping: risk factors and risk factor sensitivities and cash-flow mapping
2. Parametric Linear VaR models (continued)
- Portfolio mapping: risk factors and risk factor sensitivities and cash-flow mapping
2. Parametric Linear VaR models (continued)
- Portfolio mapping: risk factors and risk factor sensitivities and cash-flow mapping
- Normal Linear VaR for cash-flow maps
- Exponentially Weighted Moving Average estimation of covariance matrices
2. Parametric Linear VaR models (continued)
- Exercises
2. Parametric Linear VaR models (continued)
- Non-Normal Linear VaR: student t and mixture distributions
3. Historical Simulation
- Standard historical VaR: definition, choice of sample size and data frequency, scaling historical VaR assuming stable distributions
3. Historical Simulation (continued)
- Improving the sensitivity of historical VaR to changing market conditions: volatility adjustment of returns and filtered historical simulation
3. Historical Simulation (continued)
- Improving the precision of historical VaR at extreme quantiles
- Historical VaR for linear portfolios: volatility adjustment and estimation of specific VaR for a stock portfolio, marginal historical VaR
4. Monte Carlo VaR
- Introduction and random number generation
- Modeling dynamic properties in risk factor returns: multi-step vs. one-step Monte Carlo VaR, volatility clustering and mean reversion
4. Monte Carlo VaR (continued)
- Modeling risk factor dependence: multivariate normal, multivariate normal mixture
- Exercises
5. Quantile Regression VaR Estimation
- Introduction to quantile regressions
- Estimation of VaR by quantile regression
6. Risk model risk
- Backtesting: exceedance rates, unconditional and conditional coverage tests, independence tests, regression based tests, bias statistics for normal linear VaR, distribution forecasts
6. Risk model risk
- Backtesting: exceedance rates, unconditional and conditional coverage tests, independence tests, regression based tests, bias statistics for normal linear VaR, distribution forecasts
7. Scenario analysis and stress testing
- Scenarios on financial risk factors: single case vs. distribution scenarios, historical vs. hypothetical scenarios
- Stress testing: stressed covariance matrices, generating hypothetical covariance matrices, stress tests based on principal components analysis
8. Capital allocation
- Minimum market risk capital requirements for banks: Basel accords, internal models, standardized rules
8. Capital allocation
- Economic capital allocation: measurement of economic capital, RORAC, RAROC