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

We analyze an insurance instrument called a ruin‐contingent life annuity (RCLA), which is a stand‐alone version of the option embedded inside a variable annuity (VA) but without the buyer having to transfer investments to the insurance company. The annuitant's payoff from an RCLA is a dollar of income per year for life, deferred until a certain wealth process hits zero. We derive the partial differential equation (PDE) satisfied by the RCLA value assuming no arbitrage, describe efficient numerical techniques, and provide estimates for RCLA values. The practical motivation is twofold. First, numerous insurance companies are now offering similar contingent deferred annuities (CDAs). Second, the U.S. Treasury and Department of Labor have encouraged DC plans to offer longevity insurance to participants and the RCLA might be the ideal product.