Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts

Abstract

The authors offer a new perspective to the domain of guaranteed minimum death benefit contracts. These products have the particular feature to offer investors a guaranteed capital upon death. A complete methodology based on the generalized Fourier transform is proposed to investigate the impacts of jumps and stochastic interest rates. This paper thus extends Milevsky and Posner (2001). In contrast to their results, the fair costs of the guarantee feature are found to be substantially higher in this more general economy. Keywords Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts AbstractThe authors offer a new perspective to the domain of guaranteed minimum death benefit contracts. These products have the particular feature to offer investors a guaranteed capital upon death. A complete methodology based on the generalized Fourier transform is proposed to investigate the impacts of jumps and stochastic interest rates. This paper thus extends Milevsky and Posner (2001). In contrast to their results, the fair costs of the guarantee feature are found to be substantially higher in this more general economy.

Pricing and Hedging Variable Annuities in a Lévy Market: A Risk Management Perspective

“…For this last point, mortality tables or laws can be used. This determination of fair fees is a generalization of Milevsky and Posner, () and Quittard‐Pinon and Randrianarivony, ().…”

The Geneva Risk and Insurance Review 2011: A Catalyst for New Research Ideas

“…22 In their paper, Derman and Taleb (2005) have shown that dynamic hedging is neither strictly required nor strictly necessary for plausibly valuing options. 23 Quittard-Pinon and Randrianarivony (2011). 24 See Lai et al (2008).…”