Valuing guaranteed minimum accumulation benefits by a change of numéraire approach

Yiming Huang, Rogemar Mamon and Heng Xiong

Insurance: Mathematics and Economics, 2022, vol. 103, issue C, 1-26

Abstract: Three correlated risk factors, namely, financial, mortality and lapse risks, are modelled in an integrated way to support the valuation of guaranteed minimum accumulation benefits (GMAB). The dynamics of such risk factors under the risk-adjusted measure needed for valuation are derived. A sequence of reference probability measure changes is employed to obtain a compact and implementable price representations. We demonstrate how a change of numéraire approach facilitates the valuation of a GMAB rider in a variable annuity. A numerical illustration is presented to confirm the computational efficiency and accuracy of our proposed valuation methodology. In particular, our proposed approach on average takes only 0.07% of the computing time for the Monte-Carlo (MC) simulation technique to complete the valuation calculation. Furthermore, the standard errors of our approach's results are lower than those obtained from the MC-based computations. A sensitivity analysis is also performed with respect to various parameters. When there are no renewal options in a GMAB contract, we get the special case of a guaranteed minimum maturity benefit for which a closed-form valuation solution is established.

Keywords: Variable annuities; Investment guarantee; Stochastic model; Change of numéraire; Lapse risk (search for similar items in EconPapers)
JEL-codes: C02 C32 G13 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:103:y:2022:i:c:p:1-26

DOI: 10.1016/j.insmatheco.2021.11.002

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