Value at Risk 
Value at Risk
Definition
Value at risk (VaR) represents the potential loss in value of a position (expressed as NPV) which could (with a certain probability) be realized before the position is hedged or liquidated. VaR is thus an extension of NPV analysis, leading to uniform risk quantification. The difference being, that VaR takes into account the uncertainty of future market developments.
Use
Uniform application of the NPV approach within VaR allows for a consolidation of VaR over every part of a company. You can aggregate risks arising from products, currencies and organizational units in any way you like and aggregate the results to represent the total risk. Value at risk analysis therefore plays an important role in controlling global risk for the entire company.
Within the framework of Risk Management, value at risk is a key value for controlling. VaR also provides the basis for the internal risk controlling models proposed by the Basel Committee on Banking Supervision. Keep in mind that the final decision about which operative controlling measures are appropriate has to be made by the risk controlling department of your company. As a key figure, VaR only has a warning function.
Risk/return control represents a further use of VaR analysis. Within modern portfolio management, expected yields are viewed in relation to committed risks.
Structure
The value at risk is determined by the value of the committed position and the volatility of market prices. It is also influenced by the average retention period of the position, until the position is hedged or liquidated. The following calculation methods are used for VaR:
In the historical simulation, n comparative NPV calculations are carried out. This involves calculating n net present values resulting from the current market data modified by n historical market data changes. The changes to the historical market data are included in the NPV simulation as relative changes. These simulated NPVs are compared with the NPV calculated from current market data. This produces n potential gains/losses.
The correlations of the individual market prices and the dependencies between the positions are implicitly taken into account.
The historical simulation can be carried out using one of the following approaches:
If you use the full approach, n NPV calculations are carried out for all market data records valid in the past and compared with the NPV of the current market data. This produces n potential gains/losses.
If you use the delta approach, the system estimates the elasticity of the price function to the various parameters that affect the price. The NPV differences result from weighting the sensitivity with the price differences from the historical market data. As for the full valuation, this produces n potential gains/losses.
In the variance/covariance approach, potential loss is calculated from the volatility of the risk factors. The volatility of the risk factors can be estimated from historical market data from each of the respective risk factors (standard deviation), or imported from external sources (datafeed, market data file).
The resulting risks are aggregated via correlation matrices, taking any interdependencies into account.