Complete Market Valuation of the Ruin-Contingent Life Annuity (RCLA)
35 Pages Posted: 31 Jan 2009
Date Written: January 16, 2009
This paper values a type of exotic option in a complete market setting, called a ruin-contingent life annuity (RCLA). This product jointly hedges against financial market risk and personal longevity risk. 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 diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value assuming 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 that it is now embedded in approximately $800 billion worth of U.S. variable annuity (VA) policies which have recently attracted scrutiny from analysts and regulators.
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