Library of Methods and Models > Other Models > Value-At-Risk > Historical Method of Calculation
The method is used to calculate the VaR model.
Portfolio value at the current date for each organization included into calculation is calculated as follows:
Where:
pl,j. The quantity of the j-th financial instrument in the portfolio of the l-th organization.
ν1,j. Price of the j-th financial instrument at the calculation date.
E = ǁelǁ. The vector that contains values of portfolios for all financial instruments involved in calculation and for all organizations.
Create a matrix of financial instrument prices taking into account yield type. If logarithmic yield is used, the calculations are based by the following formula:
If logarithmic yield is not used:
Where:
F = ǁfi,jǁ. Price matrix.
ν1,j. Price of the j-th financial instrument on the calculation date.
i = 1, 2, … N. The number of selected elements in the date dimension (matrix of financial instruments). i = 1 corresponds to the youngest date of the period, while N corresponds to the calculation date.
Portfolio value is calculated for all financial instruments, for each organization involved in calculation, and for each date contained in the yield matrix (starting from h + 1):
Where:
pl,j. The quantity of the j-th financial instrument in the portfolio of the l-th organization.
fi,j. Price of the j-th financial instrument at the i-th date. i = h+1, … , N.
The PDiff matrix is used to create a vector of values sorted in ascending order for each organization. PDiffl - price vector sorted ascending for the l-th organization.PDiffl - price vector sorted ascending for the l-th organization.
Calculate the coefficient to get the value of the PDiffl vector by the formula:
Where
α. Value of significance level (available values lie within the range from 0 to 1).
MinDim. Value of minimum limit in the vector.
MaxDim - value of maximum limit in the vector.
Formula to calculate VaR portfolio:
Where el - the portfolio's value for all financial instruments included into calculations, for the l-th organization.
The output parameter is the matrix VaR = ǁVaRlǁ, that contains VaR of portfolio of each organization included into calculations.
See also:
