Valuation and Hedging of the Ruin-Contingent Life Annuity (RCLA)

VALUATION AND HEDGING OF THE RUIN-CONTINGENT LIFE ANNUITY This paper analyzes a type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product is essentially a stand-alone version of the option embedded inside of a variable annuity, but without the buyer having to hand-over investment assets to the insurance company. The annuitant’s (i.e. long position) payoff from a generic RCLA is $1 of income per year for life but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA is two-fold. First, a numerous insurance companies (in the U.S.) are now offering ‘the option without the investments’ as an alternative to the variable annuity package. Practioners are calling them Contingent Deferred Annuities (CDAs), but to date they have not been proerly priced and analyzed in the scholarly literature. Second, the U.S. administration – both Treasury and Department of Labor – have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job.