Pricing Variable Annuity Guarantees in a Local Volatility framework
In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatility, while interest rates follow a Hull-White one-factor Gaussian model. Notwithstanding the fact that in this framework, the local volatility depends on a particularly complicated expectation where no closed-form expression exists and it is neither directly related to European call prices or other liquid products, we present in this contribution different methods to calibrate the local volatility model. We further compare Variable Annuity Guarantee prices obtained in three different settings, namely the local volatility, the stochastic volatility and the constant volatility models all combined with stochastic interest rates and show that an appropriate volatility modelling is important for these long-dated derivatives. More precisely, we compare prices of GAO, GMIB Rider and barrier types GAO obtained by using local volatility, stochastic volatility and constant volatility models.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- van Haastrecht, Alexander & Plat, Richard & Pelsser, Antoon, 2010. "Valuation of guaranteed annuity options using a stochastic volatility model for equity prices," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 266-277, December.
- Marc Atlan, 2006. "Localizing Volatilities," Papers math/0604316, arXiv.org.
- Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
- repec:sol:wpaper:2013/59526 is not listed on IDEAS
- Pelsser, Antoon, 2003.
"Pricing and hedging guaranteed annuity options via static option replication,"
Insurance: Mathematics and Economics,
Elsevier, vol. 33(2), pages 283-296, October.
- Antoon Pelsser, 2002. "Pricing and Hedging Guaranteed Annuity Options via Static Option Replication," Tinbergen Institute Discussion Papers 02-037/2, Tinbergen Institute.
- Schrager, David F. & Pelsser, Antoon A.J., 2004. "Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 369-398, October.
- Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
- Griselda Deelstra & Grégory Rayée, 2013.
"Local Volatility Pricing Models for Long-Dated FX Derivatives,"
Applied Mathematical Finance,
Taylor & Francis Journals, vol. 20(4), pages 380-402, September.
- Griselda Deelstra & Gr\'egory Ray\'ee, 2012. "Local Volatility Pricing Models for Long-dated FX Derivatives," Papers 1204.0633, arXiv.org.
- Chi Chiu Chu & Yue Kuen Kwok, 2007. "Valuation Of Guaranteed Annuity Options In Affine Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 363-387.
- Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
- Boyle, Phelim & Hardy, Mary, 2003. "Guaranteed Annuity Options," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(02), pages 125-152, November.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1204.0453. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.