VaR. Value-at-Risk for Linear Loss  scenarios, i.e., α%  percentile of Linear Loss scenarios.  

 

Syntax

 

Parameters

matrix        is a Matrix of Scenarios:

       

where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.

is a confidence level.

Mathematical Definition

For continuous distributions, given and any specified probability level in  the -VAR Risk for Loss equals

 ,

 

where is probability distribution function of the loss .

 

For discrete distributions, considered in PSG, when models are based on scenarios and finite sampling, calculation of VaR Risk for Loss includes the following steps:

1. Calculate the values of Loss Function for all scenarios

.

2. Sort scenarios so that

.

3. If then

 

  If then: determine an index such that and .

4. If the index is such that the confidence level equals , then,  VaR Risk for Loss equals

 .

If    then

 

If then VaR Risk for Loss equals linear interpolation between VaR Risks for Loss with confidence levels                .

 

 

Example

 

Case Studies with VaR

 

See also

VaR for Gain,

VaR Normal Independent, VaR  Normal Dependent,

VaR Deviation, VaR Deviation Normal Independent, VaR Deviation Normal Dependent,

VaR for Mixture of Normal Independent, VaR Deviation for Mixture of Normal Independent