Historical Simulation 
Use
Here the historical market price changes are stored in simulation scenarios. A simulation scenario is created for each day in the time series for every risk consolidation level. In this scenario, only those market prices for which the risk is to be determined at that particular risk consolidation level are changed.
To determine the interest rate risk, scenarios are created in which only the zero bond yields are changed.
The position is valued using these simulation scenarios, and the value at risk is determined on the basis of the resulting gains and losses.
When simulation scenarios are created, all price changes are taken into account with the probability of their common, simultaneous occurrence. In the historical simulation therefore, all price changes for a day flow into the historical simulation at the same time. As a consequence, the correlations between the individual risk factors are already taken into account.
With this procedure you can also display complex price changes which cannot be modeled using the variance/covariance approach.
Integration
The value at risk amounts are displayed using the risk and portfolio hierarchies.
With the full valuation approach, the profit and loss is calculated for every position on every risk hierarchy level by revaluing every position using the historical market data for each respective relevant risk factor.
In the delta approach, the aggregation across the risk hierarchy is based on the assumption that you can add together the NPV differences according to the +/- sign. For each portfolio on a risk factor level, the system calculates the reactivity of the NPV to the risk factors, independent of the historical market prices.
In the delta-gamma approach, non-linear terms of the second order (gamma positions) are additionally taken into account at the risk factor level. This gamma position can be used as a key figure in drilldown reporting.
The three methods can also be combined with one another (combination procedure). In this case the selection of the respective method takes place depending on the value in the differentiation rule stored in the evaluation type and specific to the valuation rule. These settings specific to the valuation rule are only interpreted, however, once the combination procedure has been stored in the Customizing for the value at risk type.
Scope of Functions
The fictitious profits and losses resulting from the valuations form the basis for determining the value at risk. In the SAP system, value at risk can be calculated in the following ways based on the distribution of profits and losses:
· From simulated profits and losses
The simulated profits and losses determined for each day in the historical period are sorted by size taking into account the +/- sign.
The value at risk for a confidence level is the nth smallest profit/loss, where:
n = ((1 - confidence level) x No. of simulation days) +1.
The value at risk is displayed as a positive or negative value.
With 200 days, VaR95% is the 11th smallest profit/loss, since
n = ((1-0.95) x 200) + 1 = 11
· From absolute profits and losses
The simulated profits and losses determined for each day in the historical period are transformed into absolute amounts and sorted by size without taking into account the +/- sign.
The value at risk for a confidence level is the nth largest profit/loss, where:
n = ((1 - confidence level) x No. of simulation days) *2+ 1
The value at risk is always displayed as a negative value. If n is larger than the number of simulation values (with a very low confidence level), the value at risk is displayed as zero.
With 200 days, VaR95% is the 21st largest profit/loss, since
n = [(1-0.95)*200*2] +1 = 21
This method only provides odd values for the sample evaluation and the value-at-risk is overestimated. You can calculate more exact values with the same CPU time using the following methods:
· From absolute profits and losses (double the number of values)
The simulated profits and losses determined for each day in the historical period are transformed into absolute amounts and sorted by size without taking into account the +/- sign. However, double the number of sample values is used.
The value at risk for a confidence level is the nth largest profit/loss, where:
n = ((1 - confidence level) x 2 x No. of simulation days) +1.
The value at risk is always displayed as a negative value. If n is larger than the number of simulation values (with a very low confidence level), the value at risk is displayed as zero.
With 200 days, VaR95% is the 21st largest profit/loss, since
n = [(1-0.95)x400] +1 = 21
· Assuming normal distribution
The simulated profits and losses are assumed to be values in a sample having an expected value of zero with normal distribution. The standard deviation is determined using a statistical estimation. The value at risk then results from the multiplication of the standard deviation by the confidence level.
The value at risk is always displayed as a negative value.