The value at risk of the mathematical provision: Critical issues

The paper addresses the calculation of the value at risk of the mathematical provision applied in a fair valuation context. Following a balance-sheet approach, the classical definition of VaR may result in either a profit shrinkage or a proper loss. Therefore, the classical portfolio return distribution can be redesigned as a liability cost distribution, where critical values lie in the right-hand tail. In the case of the mathematical provision, the expected cost can be easily linked to the expected value of the reserve at the end of the risk horizon. After an overall view on the VaR problems from a managerial perspective, the paper presents, in addition to the choice of the VaR model and the number of risk factors to take into account, describing the calculation technique. The calculation, performed using a simulation approach, is developed as an application case of a life annuity portfolio and provides an estimate of the worst-case loss at a fixed confidence level after a fixed period of time.