On the Hedging of Variable Annuities with Ratchet in Jump Models

Abstract

This paper suggests a unified methodology for assessing the risk embedded in ratchet guarantees offered in life insurance Variable Annuity contracts. Using a non-Gaussian setting in line with most stylized features observed in the market, we address these questions from an operational risk management perspective. Since the well-known and widely used delta-hedging ratio is not optimal, one of the most important problem raised is the hedging issue. The research suggests many theoretical solutions whose efficiency from a computational point of view is controversial and rarely studied. This paper tries to fill this gap by suggesting a unified method for fast pricing and hedging the market risk embedded in ratchet guarantees offered in VA. The authors also present a model-free recursive formula that facilitates the pricing and the hedging of Guaranteed Minimum Accumulation Benefits known as GMAB.