Mortality Derivatives and the Option to Annuitize

York University Finance Working Paper No. MM08-1

31 Pages Posted: 8 Nov 2001  

Moshe A. Milevsky

York University - Schulich School of Business

David Promislow

York University - Department of Mathematics & Statistics

Multiple version iconThere are 2 versions of this paper

Date Written: August 2001

Abstract

Most U.S.-based insurance companies offer holders of their tax-sheltered savings plans (VAs), the long-term option to annuitize their policy at a pre-determined rate over a pre-specified period of time. Currently, there is approximately one trillion dollars invested in such policies, with guaranteed annuitization rates, in addition to any guaranteed minimum death benefit. The insurance company has essentially granted the policyholder an option on two underlying stochastic variables; future interest rates and future mortality rates. Although the (put) option on interest rates is obvious, the (put) option on mortality rates is not. Motivated by this product, this paper attempts to value (options on) mortality-contingent claims, by stochastically modelling the future hazard-plus-interest rate.

Heuristically, we treat the underlying life annuity as a defaultable coupon-bearing bond, where the default occurs at the exogenous time of death. From an actuarial perspective, rather than considering the force of mortality (hazard rate) at time-t for a person now age-x, as a number, we view it as a random variable forward rate,whose expectation is the force of mortality in the classical sense.

Our main qualitative observation is that both mortality and interest rate risk can be hedged, and the option to annuitize can be priced by locating a replicating portfolio involving insurance, annuities and default-free bonds. We provide both a discrete and continuous-time pricing framework.

Keywords: insurance, risk management, longevity

JEL Classification: J26, G11

Suggested Citation

Milevsky, Moshe A. and Promislow, David, Mortality Derivatives and the Option to Annuitize (August 2001). York University Finance Working Paper No. MM08-1. Available at SSRN: https://ssrn.com/abstract=289551 or http://dx.doi.org/10.2139/ssrn.289551

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

David Promislow

York University - Department of Mathematics & Statistics ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

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