Optimal surrender strategies for equity-indexed annuity investors

Abstract

An equity-indexed annuity (EIA) is a hybrid between a variable and a fixed annuity that allows the investor to participate in the stock market and earn at least a minimum interest rate. The investor sacrifices some of the upside potential for the downside protection of the minimum guarantee. Because EIAs allow investors to participate in equity growth without the downside risk, their popularity has grown rapidly.An optimistic EIA owner might consider surrendering an EIA contract, paying a surrender charge, and investing the proceeds directly in the index to earn the full (versus reduced) index growth, while using a risk-free account for downside protection. Because of the popularity of these products, it is important for individuals and insurers to understand the optimal policyholder behavior.We consider an EIA investor who seeks the surrender strategy and post-surrender asset allocation strategy that maximize the expected discounted utility of bequest. We formulate a variational inequality and a Hamilton-Jacobi-Bellman equation that govern the optimal surrender strategy and post-surrender asset allocation strategy, respectively. We examine the optimal strategies and how they are affected by the product features, model parameters, and mortality assumptions. We observe that in many cases, the "no-surrender" region is an interval (w l , w u ); i.e., that there are two free boundaries. In these cases, the investor surrenders the EIA contract if the fund value becomes too high or too low. In other cases, there is only one free boundary; the lower (or upper) surrender threshold vanishes. In these cases, the investor holds the EIA, regardless of how low (or high) the fund value goes. For a special case, we prove a succinct and intuitive condition on the model parameters that dictates whether one or two free boundaries exist.

Stochastic modeling and fair valuation of drawdown insurance

“…This early cancellation feature is similar to the surrender right that arises in many common insurance products such as equityindexed annuities (see e.g. [8], [21], [22]). Due to the timing flexibility, the investor may stop the premium payment if he/she finds that a drawdown is unlikely to occur (e.g.…”

Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs

“…Finally, we use the definitions of h 1 (β l , D, t i ) and h 2 (α l , β l , D, t i ) in (19) to derive (20). (18) and properly split the indicator sets.…”

“…These authors interpret the surrender option as an American option and provide numerical solutions for optimal stopping problems to determine its price. The second group of papers assumes optimal dynamic lapsation for rational and risk-averse investors [20,21]. The authors assume that policyholders maximize their expected utility, which is modeled via a constant relative risk 1 Source: White Mountain Insurance Group Report 2010.…”

Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model

“…Original works on this aspect can be found in Tiong [2]. Stepped works can be found in Boyle and Tian [3], Gerber and Shiu [4], Hardy [5], Jaimungal [6], Kijima and Wong [7], Lee [8], Lin and Tan [9], and Moore [10]. These authors studied the pricing, hedging, and risk management of various features of EIA.…”