An Analysis of the Guaranteed Withdrawal Benefits for Life Option

Abstract

In this paper, we present an analysis of the "Guaranteed Withdrawal Benefits" (GWB) for life option, a recent and popular product that many insurance companies are offering as a retirement planning solution.Under the GWB for life plan, the investor is promised increasing withdrawals during retirement for her lifetime, while still being invested in the markets. GWB for life thus transfers financial and longevity related risks from an individual investor to the insurance company underwriting the guarantee. We first analyze a continuous time version of this product in a Black Scholes economy with simplifying assumptions on population mortality and obtain an analytical solution for the product value. This analysis reveals the high sensitivity the product bears to several risk factors. We then price the GWB in a realistic setting using different asset pricing models, including those that allow the interest rates and the volatility of returns to be stochastic. Our analysis reveals that 1) GWB has insufficient price discrimination and is susceptible to adverse selection and 2) valuations can vary substantially depending on which class of models is used. We believe the ambiguity in value and the presence of significant risks, which can be challenging to hedge, should create concerns to the insurance companies offering the GWB, their investors and clients as well as the regulators.

Pricing and hedging GLWB in the Heston and in the Black–Scholes with stochastic interest rate models

“…This effectively reduces the problem dimension. The similarity reduction (2.3) was also exploited from Shah and Bertsimas in Shah and Bertsimas (2008). We can observe how the reduction similarity works both in the case of a contract that does not contain mechanisms for increasing the base benefits (ratchet), both for contracts with these properties.…”

The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours

“…Rider PH behaviour Fund process [12] GMWB static * GBM [32] GMWB static/dynamic GBM [8] GMWB static * /dynamic GBM [14] GMWB dynamic GBM [17] GMWB dynamic GBM [15] GMWB dynamic GBM/Merton [40] GLW static SIR+SV [34] GMWB static SIR [9] GMWB dynamic RS [35] GLW static GBM [3,4] In this paper, we show how an approach based on dynamic programming can accomodate any fund return distribution within the class of Lévy processes, allowing therefore a great variety of statistical features such as kurtosis and skewness.…”

Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees

“…Shah and Bertsimas (2008) analyze the impact of various risk factors, like market risks and mortality risks, in the fair value of GLWB using the continuous time models. Under the assumption of static withdrawal strategy, Piscopo and Haberman (2011) analyze the impact of mortality risk using a flexible model of mortality dynamics on the fair value of GLWB.…”