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Practice paper

The value at risk of the mathematical provision: Critical issues

Rosa Cocozza, Emilia Di Lorenzo, Albina Orlando and Marilena Sibillo
Journal of Risk Management in Financial Institutions, 1 (3), 311-319 (2008)
https://doi.org/10.69554/OXFO1112

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.

Keywords: value at risk; life insurance; reserve; solvency; fair value

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Author's Biography

Rosa Cocozza is an associate professor of insurance and risk management at the University of Naples. Her research interests are in managerial quantitative modelling.

Emilia Di Lorenzo is a full professor of financial mathematics at the University of Naples. Her research interests are in actuarial mathematics and related fields.

Albina Orlando is a researcher at the Italian National Research Council. Her research interests are in numerical modelling for finance and insurance.

Marilena Sibillo is a full professor of financial mathematics at the University of Salerno. Her research interests are in actuarial mathematics and related fields.

Citation

Cocozza, Rosa, Di Lorenzo, Emilia, Orlando, Albina and Sibillo, Marilena (2008, June 1). The value at risk of the mathematical provision: Critical issues. In the Journal of Risk Management in Financial Institutions, Volume 1, Issue 3. https://doi.org/10.69554/OXFO1112.

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cover image, Journal of Risk Management in Financial Institutions
Journal of Risk Management in Financial Institutions
Volume 1 / Issue 3
© Henry Stewart
Publications LLP

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