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“Market Value Of Insurance Liabilities: Reconciling the Actuarial Appraisal and Option Pricing Methods”, Luke N. Girard, January 2000

This paper makes a significant contribution to actuarial science. Much of recent research has been devoted to the use of actuarial appraisal method (AAM) and option pricing method (OPM) in determining the market value of liabilities. Robert Reitano (1997) presented a clear explanation of these approaches, together with a discussion of their strengths and weaknesses. Girard continues this discussion, showing that these two approaches are in fact consistent with each other and can provide the same value to the liability when the assumptions used for OPM and AAM are correctly specified. Girard proposed a model that relates the OPM and AAM approaches in Section IV, where eight definitions (or assumptions) are presented. This framework of analysis is general and comprehensive. For clarity of exposition, I think readers would benefit from a presentation that identifies more clearly the main results of the paper and the salient features of the model. Further, a discussion of the practical implications for the actuarial profession is important. For example, how should these results affect our pricing methodology? How are liability cash flows and discount rates specified? How is the cost of capital related to the level of required surplus determined? The Girard model can be used as a tool to provide answers to these questions, and I will extend Girard’s paper in these areas in this discussion. Specifically, the purpose of my discussion is to identify four results of the Girard model and discuss the insights that the model can provide. The results can be stated as follows: 1. Assumptions of OPM and AAM can be specified to ensure that they provide the same liability valuation 2. Financial reporting analytics are related to the total return (market valuation analysis) framework 3. A treatment of taxes is provided in the valuation analysis 4. The cost of capital is related to the leverage in product pricing. The implications of these results for the actuarial profession in product pricing, profitability analysis,