Modelling net carrying amount of shares for market consistent valuation of life insurance liabilities

The attractiveness of insurance saving products is driven, among others, by dividends payments to policyholders and participation in profits. These are mainly constrained by regulatory measures on profit-sharing on the basis of statutory accounts. Moreover, since both prudential and financial reporting regulation require market consistent best estimate measurement of insurance liabilities, cash-flows projection models have to be used for such a purpose in order to derive the underlying financial incomes. Such models are based on Monte-Carlo techniques. The latter should simulate future accounting profit and losses needed for profit-sharing mechanisms. In this paper we deal with impairment losses on equity securities for financial portfolios which rely on instrument-by-instrument assessment (when projection models consider groups of shares). Our motivation is to describe the joint distribution of market value and impairment provision of a book of equity securities, with regard to the French accounting rules for depreciation. The results we obtain enable to improve the ability of projection models to represent such an asymmetric mechanism. Formally, an impairment loss is recognized for an equity instrument if there has been a significant and prolonged decline in its market value below the carrying cost (acquisition value). Such constraints are formalized using an assumption on the dynamics of the equity, and leads to a complex option-like pay-off. Using this formulation, we propose analytical formulas for some quantitative measurements related the impairments losses of a book of financial equities. These are derived on a general framework and some tractable example are illustrated. We also investigate the operational implementation of these formulas and compare their computational time to a basic simulation approach.