Structured Monte Carlo 
Structured Monte Carlo
Like the historical simulation, the Monte Carlo simulation is a simulation method where the potential value changes of the risk factors are described by scenarios. In contrast to the historical simulation however, the scenarios are not determined using historical data but with the help of a random process. The random numbers required for this are created by a random number generator and can be transformed into the standard normal distribution by various methods.
In Monte Carlo simulation, it is assumed that there is a normal distribution of risk factor changes with an expected value of zero and a positive variance. The parameters required for the random process can be calculated from historical values (structured Monte Carlo).
Monte Carlo simulation comprises the following steps:
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 valuing every position anew using the simulated market data for each respective 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 (
delta positions).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 process used for both delta valuation and the delta-gamma approach is known as risk factor mapping.
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.
