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The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities

Published online by Cambridge University Press:  09 August 2013

Alexander Kling ,
Frederik Ruez  and
Jochen Ruß
Alexander Kling
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraße 22, 89081 Ulm, Germany, Phone: +49 731 5031242 — Fax: +49 731 5031239, E-Mail: a.kling@ifa-ulm.de
Jochen Ruß
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraße 22, 89081 Ulm, Germany, Phone: +49 731 5031233 — Fax: +49 731 5031239, E-Mail: j.russ@ifa-ulm.de
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Abstract

We analyze different types of guaranteed withdrawal benefits for life, the latest guarantee feature within variable annuities. Besides an analysis of the impact of different product features on the clients' payoff profile, we focus on pricing and hedging of the guarantees. In particular, we investigate the impact of stochastic equity volatility on pricing and hedging. We consider different dynamic hedging strategies for delta and vega risks and compare their performance. We also examine the effects if the hedging model (with deterministic volatility) differs from the data-generating model (with stochastic volatility). This is an indication for the model risk an insurer takes by assuming constant equity volatilities for risk management purposes, whereas in the real world volatilities are stochastic.

Keywords

Variable AnnuitiesGuaranteed Minimum BenefitsPricingHedgingHedge PerformanceStochastic VolatilityModel Risk
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 41 , Issue 2 , November 2011 , pp. 511 - 545
Copyright
Copyright © International Actuarial Association 2011

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