Valuation Perspectives and Decompositions for Variable Annuities with GMWB riders

TL;DR

This paper analyzes the valuation of GMWB riders in variable annuities, focusing on fair pricing from insurer and policyholder perspectives, and extends contract decomposition to include early surrender options.

Contribution

It introduces a novel decomposition approach for GMWB valuation that accounts for early surrender features, unifying insurer and policyholder viewpoints.

Findings

Extended valuation decomposition to include surrender options

Clarified the relationship between insurer and policyholder perspectives

Provided insights into fair pricing of GMWB riders with early lapse options

Abstract

The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of peri- odic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We consider fair pricing of the GMWB rider from a financial economic perspective. Particular focus is placed on the distinct perspectives of the insurer and policyholder and the unifying relationship. We extend a decomposition of the VA contract into components that reflect term-certain payments and embedded derivatives to the case where the policyholder has the option to surrender, or lapse, the contract early.