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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: [email protected]
Jochen Ruß
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraße 22, 89081 Ulm, Germany, Phone: +49 731 5031233 — Fax: +49 731 5031239, E-Mail: [email protected]
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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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References

Andersen, L.B.G. (2007) Efficient simulation of the Heston stochastic volatility model. Working paper, Bank of America.Google Scholar
Bacinello, A.R., Biffis, E. and Millossovich, P. (2009) Regression-Based Algorithms for Life Insurance Contracts with Surrender Guarantees. Quantitative Finance, First published on: 22 October 2009 (iFirst).Google Scholar
Bauer, D., Kling, A., and Ruß, J. (2008) A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities. ASTIN Bulletin, 38(2), November 2008, 621–651.CrossRefGoogle Scholar
Bingham, N.H. and Kiesel, R. (2004) Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives. Springer, Berlin.Google Scholar
Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637–654.Google Scholar
Coleman, T.F., Kim, Y., Li, Y. and Patron, M. (2006) Hedging Guarantees in Variable Annuities under Both Equity and Interest Rate Risks. Insurance: Mathematics and Economics, 38, 215–228.Google Scholar
Coleman, T.F., Kim, Y., Li, Y. and Patron, M. (2007) Robustly Hedging Variable Annuities with Guarantees under Jump and Volatility Risks. The Journal of Risk and Insurance, 74(2), 347–376.Google Scholar
Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A Theory of the Term Structure of Interest Rates. Econometrica, 53, 385–407.Google Scholar
Eraker, B. (2004) Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367–1403.CrossRefGoogle Scholar
Ewald, C.-O., Poulsen, R. and Schenk-Hoppe, K.R. (2009) Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance. Quantitative Finance, 9(6), September 2009, 693–704.Google Scholar
Glasserman, P. (2003) Monte Carlo Methods in Financial Engineering. Springer, Berlin.CrossRefGoogle Scholar
Heston, S. (1993) A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, 6(2), 327–344.CrossRefGoogle Scholar
Holz, D., Kling, A. and Ruß, J. (2008) GMWB For Life – An Analysis of Lifelong Withdrawal Guarantees. Working Paper, Ulm University, 2008.Google Scholar
Hull, J.C. (2008) Options, Futures and Other Derivatives. 7th edition. Prentice Hall, New Jersey.Google Scholar
Kahl, C. and Jäckel, P. (2006) Not-so-complex Logarithms in the Heston Model. Wilmott Magazine, September 2005, 94–103.Google Scholar
Mikhailov, S. and Nögel, U. (2003) Heston's Stochastic Volatility Model. Implementation, Calibration and Some Extensions. Wilmott Magazine, Juli 2003, 74–49.Google Scholar
Milevsky, M. and Posner, S.E. (2001) The Titanic Option: Valuation of the Guaranteed Minimum Death Benefit in Variable Annuities and Mutual Funds. The Journal of Risk and Insurance, 68(1), 91–126.Google Scholar
Milevsky, M. and Salisbury, T.S. (2006) Financial Valuation of Guaranteed Minimum Withdrawal Benefits. Insurance: Mathematics and Economics, 38, 21–38.Google Scholar
Taleb, N. (1997) Dynamic Hedging: Managing Vanilla and Exotic Options. Wiley Finance, New York.Google Scholar
Wilmott, P. (2006) Paul Wilmott on Quantitative Finance. John Wiley & Sons, Chichester.Google Scholar
Wong, B. and Heyde, C.C. (2006) On Changes of Measure in Stochastic Volatility Models. Journal of Applied Mathematics and Stochastic Analysis, Volume 2006, 1–13.Google Scholar