A historical-parametric hybrid VAR

The calculation of value-at-risk by historical simulation suffers increasingly from the problem of missing market data as the number of time series being included grows. This problem therefore tends to be particularly severe when VAR is used for calculating specific risk. Robin Stuart shows how the familiar methods of historical simulation and parametric VAR can be combined to produce a new hybrid VAR possessing some of the best features of both and capable of addressing the problem of incomplete data analytically

In standard calculations of value-at-risk by historical simulation, some representation of the profit and loss (P&L) function is obtained for the portfolio of interest that permits it to be repriced under shocks to market variables observed in some specified historical time window. Often the P&L function is represented by a set of revaluations on a regular grid from which the P&L associated with any changes in market variables can be calculated by interpolation. Histories of market variable