VaR and Other Risk Measures
1. Estimating Market Risk Measures
1.1 Parametric Approach
1.2 Expected Shortfall and Risk Measures
1.3 Quantile-quantile (QQ) plots
2. Non-parametric Approaches
2.1 Historical Simulation
2.2 Weighted Historical Simulation
3. Parametric Approaches: Extreme Value
3.1 Generalized Extreme Values (GEV)
3.2 Peaks over Threshold (POT)
4. Backtesting VaR
4.1 Basics of Backtesting VaR
4.2 Model Verification
4.3 Basel Rules
5. VaR Mapping
5.1 Basics of VaR Mapping
Mapping Principles
The portfolio generally involves a very large number of positions, including bonds, stocks, currencies, commodities, and their derivatives. It would be too complex and time-consuming to model all positions individually as risk factors. Mapping provides a shortcut, the positions can be simplified to a smaller number of positions on a set of elementary, or primitive, risk factors.
Mapping is also required as a solution to data problems in many common situations. Risk manager would have to replace these positions by exposures on similar risk factors already in the system.
Stale prices are not synchronously created, daily correlations across markets are too low, which will affect the measurement of portfolio risk.
Definition of VaR Mapping
A process by which the current values of the portfolio positions are replaced by exposures on the risk factors.
The Mapping Process
Step 1: marking all positions to market in current dollars or whatever reference currency is used.
Step 2: the market value for each instrument then is allocated to the risk factors.
Step 3: positions are summed for each risk factor.
Mapping can be of two kinds:
The first provides an exact allocation of exposures on the risk factors. The price is an exact function of the risk factors (such as derivatives).
The second exposures may have to be estimated. This occurs when a stock is replaced by a position in the stock index.
General and Specific Risk
The choice of the set of general (primitive) risk factors should reflect the tradeoff between better quality of the approximation and faster processing.
- Too many risk factors would be unnecessary, slow, and wasteful.
- Too few risk factors could create blind spots in the risk measurement system.
The choice of primitive risk factors also influences the size of specific risks. Specific risk is the risk due to issuer-specific price movements, after accounting for general market factors.
- The definition of specific risk depends on that of general market risk.
- A greater number of general risk factors should create less residual risk.
5.2 Methods of VaR Mapping
Methods of Mapping Fixed Income Portfolios
5.3 Applications of VaR Mapping
Mapping Linear Derivatives
Mapping Non-linear Derivatives