The paper addresses the calculation of the value at risk (VaR) of the mathematical provision applied in a fair valuation context. Following a balance-sheet approach, the classical definition of VaR needs some clarifications. For indentifying worst cases it is opportune to observe that an increase in the value of the liability corresponds to expenses or, better, additional costs, which 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, the choice of the VaR model and the number of risk factors to take into account, in addition to 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.

### The value at risk for the mathematical provision. Critical issue.

#### Abstract

The paper addresses the calculation of the value at risk (VaR) of the mathematical provision applied in a fair valuation context. Following a balance-sheet approach, the classical definition of VaR needs some clarifications. For indentifying worst cases it is opportune to observe that an increase in the value of the liability corresponds to expenses or, better, additional costs, which 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, the choice of the VaR model and the number of risk factors to take into account, in addition to 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11386/1847142`
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