Historical Simulation 

Use

Using historical simulation, you can calculate the VaR on the basis of full or delta valuations.

Historical market price changes are stored in simulation scenarios. A simulation scenario is created for every risk consolidation level for every day in the time series. In this scenario, the system only changes the market prices for which the risk is to be calculated in the particular risk consolidation level.

To determine the interest rate risk, for example, scenarios are created in which only the zero coupon yields are changed.

The system uses these simulation scenarios to value the position and calculates the value at risk on the basis of the resulting gains and losses.

By generating simulation scenarios, the system is able to consider all price changes and the probability of their common, simultaneous occurrence. As a result, the historical simulation takes all the price changes for a given day into account at the same time. This means that the correlations between the individual risk factors are already included.

This procedure enables you to map complex price changes that cannot be modeled using the variance/covariance approach.

Integration

VaR values are displayed on the basis of the risk hierarchy.

With the full valuation approach, each position on each risk hierarchy is revalued using the historical market data for the respective risk factor. The positions are not aggregated for the risk hierarchy.

With the delta approach, it is assumed that the NPV differences can be added (taking the respective +/- signs into account) to aggregate the positions for the risk hierarchy.

Scope of functions

Fictitious profits and losses from the full and delta valuations form the basis for VaR. VaR can be calculated by the R/3 system in the following ways using the distribution of profits and losses:

The simulated profits and losses calculated for each day in the historical period are sorted by size taking into account the +/- sign.

The value at risk (VaRconfidence) for a confidence level is k-the nth smallest profit/loss, where:

k = ((1 - confidence level) * No. of simulation days) + 1

The value at risk is displayed as a positive or negative value.

For 200 days the VaR95% is the 11 th smallest profit/loss value, since

k = ((1-0.95) * 200) + 1 = 10 + 1

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 (VaRconfidence) for a confidence level is the 2k-largest profit/loss, where:

k = ((1 - confidence level) * No. of simulation days) + 1

The value at risk is always displayed as a negative value. If k is larger than the number of simulation values (where the confidence level is very low), the value at risk is displayed as zero.

For 200 days the VaR95% is the 22 nd largest profit/loss value, since

k = [(1-0.95) * 200 ] +1 = 11

and therefore 2k = 22

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, twice the number of sample values are used.

The value at risk (VaRconfidence) for a confidence level is the k-largest profit/loss, where:

k = ((1 - confidence level) * 2 * No. of simulation days) +1

The value at risk is always displayed as a negative value. If k is larger than the number of simulation values (where the confidence level is very low), the value at risk is displayed as zero.

For 200 days the VaR95% is the 21 st largest profit/loss value, since

k = [(1-0.95) * 400 ] +1 = 21

The simulated profits and losses are assumed to be values in a sample which has an expected value of zero with normal distribution. The standard deviation is calculated using a statistical estimation procedure. The value at risk is then determined by multiplying the variance by the confidence level.

The value at risk is always displayed as a negative value.