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

Abstract

VALUATION AND HEDGING OF THE RUIN-CONTINGENT LIFE ANNUITYThis paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is $1 of income per year for life, akin to a defined benefit pension, 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 on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately $1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. 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.

Longevity-contingent deferred life annuities

“…A combination of demographic and financial indicators could nevertheless be used, provided the financial component reflects market performances in terms of stocks or interest-related instruments. This is in line with the innovative product studied by Huang et al (2013). A double-trigger mechanism, requiring that both the demographic component and the financial one reach specified target could be specified to decide when the payments start. In practice, the compilation of mortality statistics needed for the publication of demographic indicators by governmental agencies may require some time.…”

“…The type of annuity discussed in the present paper is similar to so-called contingent deferred annuities, including the ruin-contingent life annuity studied by Huang et al (2013). In such products, two distinct events must be triggered before the annuitant gets paid: the individual must obviously be alive but a second event related to the financial market has also to occur (for instance, a reference portfolio index reaches zero, as in the ruin-contingent life annuity case).…”

Workplace-Linked Pensions for an Aging Demographic

“…A second type of longevity protection product has been called a "Ruin-Contingent Life Annuity" (RCLA). These can be issued by insurers that protect policyholders against two separate and likely independent events: below-average investment returns, and above-average longevity (Huang et al 2012). The RCLA invests in a portfolio of assets agreed on by both insurers and annuitants, and the payouts depend on investment as well as survival outcomes.…”

The Only Spending Rule Article You Will Ever Need

“…25. RCLAs were proposed by Huang, Milevsky, and Salisbury (2014). To our knowledge, only one RCLA has been issued: ARIA from Transamerica.…”