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Complete Market Valuation of the Ruin-Contingent Life Annuity (RCLA)

35 Pages Posted: 31 Jan 2009  

Huang Huaxiong

York University

Moshe A. Milevsky

York University - Schulich School of Business

T. S. Salisbury

York University

Date Written: January 16, 2009

Abstract

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.

Suggested Citation

Huaxiong, Huang and Milevsky, Moshe A. and Salisbury, T. S., Complete Market Valuation of the Ruin-Contingent Life Annuity (RCLA) (January 16, 2009). Available at SSRN: https://ssrn.com/abstract=1335454 or http://dx.doi.org/10.2139/ssrn.1335454

Huang Huaxiong

York University ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Tom S. Salisbury

York University ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

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