Pricing of Ratchet equity-indexed annuities under stochastic interest rates
AbstractWe consider the valuation of simple and compound Ratchet equity-indexed annuities (EIAs) in the presence of stochastic interest rates. We assume that the equity index follows a geometric Brownian motion and the short rate follows the extended Vasicek model. Under a given forward measure, we obtain an explicit multivariate normal characterization for multiple log-returns on the equity index. Using such a characterization, closed-form price formulas are derived for both simple and compound Ratchet EIAs. An efficient Monte Carlo simulation scheme is also established to overcome the computational difficulties resulting from the evaluation of high-dimensional multivariate normal cumulative distribution functions (CDFs) embedded in the price formulas as well as the consideration of additional complex contract features. Finally, numerical results are provided to illustrate the computational efficiency of our simulation scheme and the effects of various model and contract parameters on pricing.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 41 (2007)
Issue (Month): 3 (November)
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Web page: http://www.elsevier.com/locate/inca/505554
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- Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
- Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002.
"The concept of comonotonicity in actuarial science and finance: applications,"
Insurance: Mathematics and Economics,
Elsevier, vol. 31(2), pages 133-161, October.
- Dhaene, Jan & Denuit, Michel & Goovaerts, Marc & Kaas, R & Vyncke, D, 2002. "The concept of comonotonicity in actuarial science and finance : applications," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/224321, Katholieke Universiteit Leuven.
- Nielsen, J. A. & K. Sandmann, 1995.
"The Pricing of Asian Options under Stochastic Interest Rates,"
Discussion Paper Serie B
323, University of Bonn, Germany, revised Dec 1995.
- J. A. Nielsen & K. Sandmann, 1996. "The pricing of Asian options under stochastic interest rates," Applied Mathematical Finance, Taylor and Francis Journals, vol. 3(3), pages 209-236.
- Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
- Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor and Francis Journals, vol. 4(3), pages 301-314.
- Alan Brace & Dariusz G�atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
- Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
- Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
- repec:ner:louvai:info:hdl:2078.1/105440 is not listed on IDEAS
- Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
- Vanduffel, Steven & Chen, X & Dhaene, Jan & Goovaerts, Marc & Kaas, R & Valdez, E, 2006. "A note on optimal lower bound approximations for risk measures of sums of lognormals," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/121182, Katholieke Universiteit Leuven.
- Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
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