Two Paradigms for the Market Value of Liabilities

Asset/liability management (ALM) theory and practices of insurers have matured and developed from early applications to guaranteed investment contracts (GICs) to all annuity and insurance products today. An important and logical next step of inquiry is the definition of, and calculation procedures for, the market value of an insurance liability. Because all ALM strategies have as their goal the management of some value of assets in relation to some value of liabilities, this inquiry will provide at last a canonical basis for ALM: the management of relative market values. To set the stage for this exploration, the theory and application of pricing in a complete market are reviewed, as are the practical limitations of this theory in the real, and far from complete, financial markets. The notion of an ad hoc pricing model is developed, and examples are reviewed and critiqued. These models, though imperfect compared with pricing in a complete market, bridge the gap between pricing theory and practice. The current state of the liabilities market is also discussed, and this market is seen to naturally split into a ‘‘long’’ and a ‘‘short’’ submarket. Of particular interest is the theoretical possibility of these markets becoming broad-based, deep and active, and the conclusions are relevant to the issue of long/short price equalization. Two paradigms are then explored for defining and subsequently calculating an insurance liability market value. A ‘‘paradigm’’ is a generalized model or framework for accomplishing the task at hand. Each paradigm reflects observable market trading activity, however infrequent, and each is based on methods of valuation consistent with finance-theoretic approaches that are routinely used for the market valuation of assets. In addition, each paradigm allows for a sequence of ad hoc valuation methodologies, which differ in the extent to which various risks are explicitly modeled versus judgmentally reflected in a risk spread. These paradigms are discussed and contrasted, and arguments made for the potential evolution of the respective values if a ‘‘liability’’ market began trading actively. Practical constraints on the realization of this evolution are also noted. The last section of this paper discusses a host of considerations related to the application of option-pricing theory to insurance company liabilities.