Valuation of guaranteed annuity options using a stochastic volatility model for equity prices
AbstractGuaranteed annuity options are options providing the right to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970's and 1980's when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990's. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 47 (2010)
Issue (Month): 3 (December)
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Web page: http://www.elsevier.com/locate/inca/505554
Guaranteed annuity option (GAO) Guaranteed Minimum Income Benefit (GMIB) Stochastic volatility Stochastic interest rates Variable annuities;
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- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
Econometric Society, vol. 68(6), pages 1343-1376, November.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
- Dirk G. Baur, 2007.
"Stock-bond co-movements and cross-country linkages,"
The Institute for International Integration Studies Discussion Paper Series
- Dirk G. Baur, 2010. "Stock-bond co-movements and cross-country linkages," International Journal of Banking, Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 111-129.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
- 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.
- Antoon Pelsser, 2002.
"Pricing and Hedging Guaranteed Annuity Options via Static Option Replication,"
Tinbergen Institute Discussion Papers
02-037/2, Tinbergen Institute.
- 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.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- 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.
- Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
- Deelstra, Griselda & Rayée, Grégory, 2013.
"Pricing Variable Annuity Guarantees in a local volatility framework,"
Insurance: Mathematics and Economics,
Elsevier, vol. 53(3), pages 650-663.
- Griselda Deelstra & Gr\'egory Ray\'ee, 2012. "Pricing Variable Annuity Guarantees in a Local Volatility framework," Papers 1204.0453, arXiv.org, revised Apr 2012.
- Feng, Runhuan & Volkmer, Hans W., 2012. "Analytical calculation of risk measures for variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 636-648.
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