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CALCULATING VARIABLE ANNUITY LIABILITY “GREEKS” USING MONTE CARLO SIMULATION

Published online by Cambridge University Press:  05 January 2015

Mark J. Cathcart ,
Hsiao Yen Lok ,
Alexander J. McNeil  and
Steven Morrison
Mark J. Cathcart
Affiliation:
Standard Life Group, Edinburgh EH1 2DH, UK E-mail: mark.j.cathcart@gmail.com
Hsiao Yen Lok
Affiliation:
Heriot-Watt University, Edinburgh, Maxwell Institute for Mathematical Sciences, Edinburgh EH14 4AS, UK E-mail: yhl30@hw.ac.uk
Alexander J. McNeil*
Affiliation:
Heriot-Watt University, Edinburgh, Maxwell Institute for Mathematical SciencesEdinburgh EH14 4AS, UK
Steven Morrison
Affiliation:
Moody's Analytics, Edinburgh EH3 8RD, UK E-mail: steven.morrison@moodys.com
*
E-mail: a.j.mcneil@hw.ac.uk
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Abstract

The implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or “Greeks”). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a “bump and revalue” method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.

Keywords

Stochastic simulationMonte Carlo estimationvariable annuityGreekssensitivitiesHeston stochastic volatility modelpathwise methodlikelihood-ratio methodstochastic interest rates
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 2 , May 2015 , pp. 239 - 266
Copyright
Copyright © ASTIN Bulletin 2015 

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