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Abstract
The calculation of value-at-risk (VAR) 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. The author 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. It draws on the spirit of the CAPM and treats the probability distribution associated with missing data analytically, thereby providing an efficient alternative to Monte Carlo methods. The characteristics of the profit and loss (P&L) distributions for daily observations are carried through the calculation by means of their cumulants and then combined to form an overall P&L distribution.