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We support three current methods used for calculating Value at Risk (VaR):
All methods have a common base but then diverge in how they actually calculate Value at Risk. They also have a common problem in assuming that the future will follow the past. This shortcoming is normally addressed by supplementing any VAR figures with appropriate sensitivity analysis and/or stress testing.
Our VaR calculation follows five steps:
• Identification of positions
• Identification of risk factors affecting valuation of positions.
• Assignment of probabilities (or statistical distribution) to possible risk factors values.
• Creation of pricing functions for positions as a function of values of risk factors.
• Calculation of VaR
The Variance-Covariance method makes a number of assumptions. The accuracy of the results depends on how valid these assumptions are. The method gets its name from the variance-covariance matrix of securities that is used to calculate VaR.
The method starts by calculating the standard deviation and correlation for the risk factor and then uses these values to calculate the standard deviations and correlation for the changes in the value of the individual securities that form the position. If price, variance and correlation data is available for individual securities then this information is used directly. The values are then used to calculate the standard deviation of the portfolio.
VaR for a specific confidence interval is then calculated by multiplying the standard deviation by the appropriate normal distribution factor.
In some cases a method equivalent to the variance covariance approach is used to calculate VaR. This method does not generate the variance covariance matrix. The modified approach can be used where, due to the nature of the institutions strategies, a number of positions would net close to zero on a portfolio basis and also where the set of securities employed is so large that a variance - covariance approach would have significant resource/time requirements.
Historical Simulation Method
This approach requires fewer statistical assumptions for underlying market factors. It applies the historical (100 days) changes in price levels to current market prices in order to generate a hypothetical data set. The data set is then ordered by the size of gains/losses. VAR is the value that is equaled or exceeded the required percentage of times (1, 5, 10).
Monte Carlo Simulation
The approach is similar to the Historical simulation method described above except for one big difference. The hypothetical data set used is generated by a statistical distribution rather than historical price levels. The assumption is that the selected distribution captures or reasonably approximates price behavior of the modeled securities.