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FAST COMPUTATION OF RISK MEASURES FOR VARIABLE ANNUITIES WITH ADDITIONAL EARNINGS BY CONDITIONAL MOMENT MATCHING

Published online by Cambridge University Press:  02 November 2017

Nicolas Privault  and
Xiao Wei
Nicolas Privault
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link Singapore 637371
Xiao Wei*
Affiliation:
China Institute for Actuarial Science & School of Insurance, Central University of Finance and Economics, 39 South College Road, Haidian District, Beijing 100081, P.R. China
*
E-Mail: [email protected]
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Abstract

We propose an approximation scheme for the computation of the risk measures of guaranteed minimum maturity benefits (GMMBs) and guaranteed minimum death benefits (GMDBs), based on the evaluation of single integrals under conditional moment matching. This procedure is computationally efficient in comparison with standard analytical methods while retaining a high degree of accuracy, and it allows one to deal with the case of additional earnings and the computation of related sensitivities.

Keywords

Variable annuity guaranteed benefitsrisk measuresvalue at riskconditional tail expectationconditional moment matchingadditional earnings91B3097M3065C30
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 171 - 196
Copyright
Copyright © Astin Bulletin 2017 

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References

Bauer, D., Kling, A. and Russ, J. (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. ASTIN Bulletin, 38 (2), 621–651.CrossRefGoogle Scholar
Carr, P. and Schröder, M. (2004) Bessel processes, the integral of geometric Brownian motion, and Asian options. Theory of Probability and Its Applications, 48 (3), 400–425.Google Scholar
Curran, M. (1994) Valuing Asian and portfolio options by conditioning on the geometric mean price. Management Science, 40 (12), 1705–1711.Google Scholar
Deelstra, G., Diallo, I. and Vanmaele, M. (2010) Moment matching approximation of Asian basket option prices. Journal of Computational and Applied Mathematics, 234, 1006–1016.Google Scholar
Deelstra, G., Liinev, J. and Vanmaele, M. (2004) Pricing of arithmetic basket options by conditioning. Insurance Mathematics and Economics, 34, 55–57.CrossRefGoogle Scholar
Dai, T.-S., Yang, S.S. and Liu, L.-C. (2015) Pricing guaranteed minimum/lifetime withdrawal benefits with various provisions under investment, interest rate and mortality risks. Insurance Mathematics and Economics, 64, 364–379.Google Scholar
Feng, R. and Volkmer, H.W. (2012) Analytical calculation of risk measures for variable annuity guaranteed benefits. Insurance Mathematics and Economics, 51, 636–648.Google Scholar
Feng, R. and Volkmer, H.W. (2014) Spectral methods for the calculation of risk measures for variable annuity guaranteed benefits. ASTIN Bulletin, 44 (3), 653–681.Google Scholar
Goudenège, L., Molent, A. and Zanette, A. (2016) Pricing and hedging GLWB in the Heston and in the Black–Scholes with stochastic interest rate models. Insurance Mathematics and Economics, 70, 38–57.Google Scholar
Levy, E. (1992) Pricing European average rate currency options. Journal of International Money and Finance, 11, 474–491.Google Scholar
Moening, T. and Zhu, N. (2016) Lapse-and-reentry in variable annuities. Journal of Risk and Insurance. DOI: 10.1111/jori.12171.Google Scholar
Privault, N. and Yu, J.D. (2016) Stratified approximations for the pricing of options on average. Journal of Computational Finance, 19 (4), 95–113.CrossRefGoogle Scholar
Turnbull, S. and Wakeman, L. (1992) A quick algorithm for pricing European average options. Journal of Financial and Quantitative Analysis, 26, 377–389.Google Scholar
Yor, M. (1992) On some exponential functionals of Brownian motion. Advances in Applied Probability, 24 (3), 509–531.Google Scholar