The Value at Risk of the Mathematical Provision: Critical Issues

Journal of Risk Management in Financial Institutions, Vol. 1, No. 3, pp. 311-319, 2008

Posted: 9 Jan 2011

See all articles by Rosa Cocozza

Rosa Cocozza

University of Naples Federico II - Faculty of Economics

Emilia Di Lorenzo

University of Naples Federico II - Faculty of Economics

Albina Orlando

Italian National Research Council (CNR)

Marilena Sibillo

Università degli Studi di Salerno

Date Written: 2008

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 identifying 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.

Keywords: Value at risk, life insurance, reserve, solvency, fair value

JEL Classification: G17, G22

Suggested Citation

Cocozza, Rosa and Di Lorenzo, Emilia and Orlando, Albina and Sibillo, Marilena, The Value at Risk of the Mathematical Provision: Critical Issues (2008). Journal of Risk Management in Financial Institutions, Vol. 1, No. 3, pp. 311-319, 2008, Available at SSRN: https://ssrn.com/abstract=1736963

Rosa Cocozza (Contact Author)

University of Naples Federico II - Faculty of Economics ( email )

Via Cintia Monte S. Angelo
Napoli, 80126
Italy
+39/81675083 (Phone)

HOME PAGE: http://www.docenti.unina.it/rosa.cocozza

Emilia Di Lorenzo

University of Naples Federico II - Faculty of Economics ( email )

Via Cintia, Monte S. Angelo
Napoli, 80126
Italy

Albina Orlando

Italian National Research Council (CNR) ( email )

Via San Martino della battaglia, 44
Roma, 00185
Italy

Marilena Sibillo

Università degli Studi di Salerno ( email )

Campus Universitario, 84084 Fisciano
Salerno, 80131
Italy

HOME PAGE: http://www.unisa.it//Facolta/Economia/docenti/Sibillo_/home.php?cms=yes

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