Optimal Policyholder Behavior in Personal Savings Products and its Impact on Valuation

Guaranteed Minimum Withdrawal Benefits (GMWBs) provide the right but not the obligation to withdraw a certain amount every year free of charge and independent of the investment performance. My dissertation studies optimal policyholder behavior in personal savings products and the resulting financial risks for the issuer by analyzing in detail these guarantees. In particular, I provide novel insights on the following two important research questions: What drives optimal policyholder behavior in life insurance? And what are the implications of optimal exercise behavior for product design?;Insurers' attempts to estimate and correctly anticipate policyholder withdrawal behavior vary tremendously and are typically driven by intuition and past behavior rather than economic insights. This is problematic due to the scarcity of data for these relatively new products, and the inability to extrapolate the observed behavior to different market conditions. In contrast, the actuarial literature has approached the problem from an arbitrage pricing perspective, where policyholders are assumed to exercise their options in a way that maximizes the risk-neutral market-consistent value of the resulting cash flows. The implied policyholder behavior, however, does not square well with observed prices and empirical exercise patterns.;I address this discrepancy in my first essay, Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities. Since the market for personal savings products exhibits frictions -- typically, investors cannot sell their policies, or parts thereof, at their risk-neutral value -- and is incomplete, key assumptions underlying standard arbitrage pricing are violated. Therefore, (optimal) exercise behavior might be affected by the policyholders' preferences.;To analyze this in more detail, I develop a life-cycle model for a Variable Annuity with a withdrawal guarantee as well as outside investment opportunities. I find that while the valuation results are rather insensitive to preference characteristics, they are strongly affected by the consideration of appropriate tax treatments: The tax-deferred growth property of Variable Annuities (in the U.S.) not only makes them a popular long-term investment vehicle, but also shapes the investors' optimal withdrawal behavior.;Based on these insights, I then develop a risk-neutral valuation approach that incorporates the proper tax treatments, and -- as expected given my earlier findings -- valuation results closely resemble those from the life-cycle model. I also find that they are substantially different from the case analyzed in the literature, that is without considering taxation. In particular, my analysis of an empirical Variable Annuity product suggests that the GMWB fees are sufficient to cover the costs of the guarantee, contrary to findings from the literature. Hence, one key result from this essay is that the consideration of taxes alone appears sufficient to explain policyholder exercise behavior within Variable Annuities including a GMWB.;My second essay, On Negative Option Values in Personal Savings Products, concerns the design of personal savings products. In particular, I demonstrate that it is possible for financial options to have negative marginal value for the issuer. The key insight is that when the financial market exhibits frictions and is incomplete, market participants deviate from traditional arbitrage pricing and their value functions no longer are direct opposites. If subjective valuation is affected by individual preferences, the idea of risk-sharing comes to mind. However, negative option values can arise even when policyholder and insurer both are value maximizers: The consideration of taxes introduces a third (inactive) party -- the government -- to the transaction.;For instance, in the context of Variable Annuities, adding a standard guarantee may incentivize the policyholder to reduce her withdrawals and the likelihood of surrender, and thus also her tax obligations (as tax payments are deferred). Since the government collects fewer taxes, there is more money to be distributed between the two main parties. If, in addition, the policyholder holds other (implicit or explicit) options from the same issuer, and the presence of the additional option makes exercising them less optimal, it is conceivable that both investor and issuer gain from the addition of the option -- at the expense of the third party.;In Sections 2 and 3 of Essay 2, I demonstrate with a two-period model and by implementing an empirical product, respectively, that a death benefit guarantee (GMDB) written on a Variable Annuity with a GMWB may result in exactly such an effect: The death benefit guarantee has a negative value to its issuer, so that both insurer and policyholder benefit from the product (at the expense of the government). It may thus come as no surprise that death benefit guarantees have become a standard feature in Variable Annuity policies, and most withdrawal guarantees (including the one that I use as an empirical example) now also promise to return the remaining benefits base in case of the policyholder's death. (Abstract shortened by UMI.)...