From Financial Economics to Fair Valuation

In this paper we address the issue of how to establish the fair value of an insurance-linked liability. This is done by considering the introduction into a simple, one-period market model of a new and quite general security (which, amongst other things, could be such a liability). We investigate the impact of this new security on the market and attempt to predict the price (the fair value) at which it will enter the market, assuming a liquid market. The model employed is very simple for two reasons. First, it allows us to derive analytical results for equilibrium prices (often impossible for more complex models). Second, its simplicity allows us without difficulty to identify specific effects, rather than muddy the water with more general, abstract or complex features. The model includes the following key features. First, investors have different levels of risk aversion. Second, investors are allowed to have different parameter estimates for the returns model. Third investors have different, risky future liabilities. A principal aim of the paper is to compare the equilibrium approach with the often-more-tractable risk-minimisation approach to pricing and reserving popular in financial mathematics. We find that there is a strong link between the two approaches. However, there are differences between the two prices derived. These are caused by: different investor liabilities; different parameter estimates between investors; difficulty in estimating investors’ levels of risk aversion. Of these we find that differences in estimates of the mean return on the new security causes the most significant differences.