Equilibrium Pricing Approach for Longevity Bonds

Though it is experiencing steady progress in its evolution (see Blake et al. (2018)), the market for mortality linked instruments or so-called life market, is far from reaching its full potential estimated to be of tens of trillions of dollars (see Michaelson and Mulholland (2014)). Currently highly illiquid and compared to equity markets with a relatively very low number of transactions, the life market is comprised of series of negotiated, high monetary value, over-the-counter transactions between few agents that have different risk preferences. To accommodate these realities we consider a partial equilibrium model for pricing longevity bonds. We do this under the assumption of stochastic mortality intensity that affects the income of economic agents who trade in risky financial security and longevity bond to maximize their monetary utilities. Thus, our pricing methodology is based on a foundational economic principle. As a practical contribution, we find the endogenous equilibrium bond price which is numerically computed. In a realistic setting of two agents in a transaction, numerical experiments confirm the expected intuition of price dependence of model parameters.