Modelling Net Carrying Amount of Shares for Market Consistent Valuation of Life Insurance Liabilities

Abstract

The attractiveness of insurance saving products is driven by dividend payments to policyholders and participation in profits. These are mainly constrained by regulatory disposals on profit-sharing on the basis of statutory accounts. Moreover, since both prudential (Solvency II) and financial reporting (IFRS 17) regulations require market consistent best estimate measurement of insurance liabilities, cash-flow projection models have to be used in order to derive the underlying financial incomes. In most cases, such models are based on Monte-Carlo techniques, which simulate future accounting profit and losses needed for profit-sharing mechanisms. In this paper, we deal with modelling future impairment losses on equity securities for financial portfolios. As a matter of fact, if impairment losses are determined on an instrument-by-instrument basis, projection models deal with model points of financial instruments (e.g. groups of shares). Since individual depreciation mechanisms are non-linear, projecting is quite a challenge for model designers. 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 derived results can more effectively represent such an asymmetric mechanism by using our results. 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 about the dynamics of the equity, and lead to a complex option-like pay-off. Using this formulation, we propose analytical formulas for some quantitative measurements related to the impairment losses of a financial equities book. These are derived from a general framework and some tractable examples are illustrated. We also investigate the operational implementation of these formulas and compare theircomputational time to a basic simulation approach.