Date of Award

Summer 5-7-2012

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Risk Management and Insurance

First Advisor

Daniel Bauer

Second Advisor

Glenn Harrison

Third Advisor

Ajay Subramanian

Fourth Advisor

Eric Ulm

Fifth Advisor

Yongsheng Xu

Abstract

Policyholder exercise behavior presents an important risk factor for life insurance companies. Yet, most approaches presented in the academic literature – building on value maximizing strategies akin to the valuation of American options – do not square well with observed prices and exercise patterns.

Following a recent strand of literature, in order to gain insights on what drives policyholder behavior, I first develop a life-cycle model for variable annuities (VA) with withdrawal guarantees. However, I explicitly allow for outside savings and investments, which considerably affects the results. Specifically, I find that withdrawal patterns after all are primarily motivated by value maximization – but with the important asterisk that the value maximization should be taken out from the policyholders’ perspective accounting for individual tax benefits.

To this effect, I develop a risk-neutral valuation methodology that takes these different tax structures into consideration, and apply it to our example contract as well as a representative empirical VA. The results are in line with corresponding outcomes from the life cycle model, and I find that the withdrawal guarantee fee from the empirical product roughly accords with its marginal price to the insurer.

I further consider the implications of policyholder behavior on product design. In particular – due to differential tax treatments and contrary to option pricing theory – the marginal value of such guarantees can become negative, even when the holder is a value maximizer. For instance, as I illustrate with both a simple two-period model and an empirical VA, a common death benefit guarantee may indeed yield a negative marginal value to the insurer.

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