Practical Partial Equilibrium Framework for Pricing of Mortality-Linked Instruments in Continuous Time

In this article we demonstrate the practical application of standard partial equilibrium, in backward stochastic differential equation (BSDE) framework, to pricing longevity bonds which are essential for functioning of the life market. The market for mortality linked instruments or so-called life market, is experiencing steady progress in its evolution (see Blake et al. (2018)), however, it is regretfully far from reaching its full potential estimated to be of tens of trillions of dollars (see Michaelson and Mulholland (2014)). 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 demonstrate an application of a partial equilibrium framework 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, by rooting ourselves in 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 on model parameters. As a theoretical contribution, we prove that our longevity bond completes the market.