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Risks 2016, 4(3), 22; doi:10.3390/risks4030022

A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

The Commonwealth Scientific and Industrial Research Organisation, PO BOX 52, North Ryde, NSW 1670, Australia
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Academic Editor: Nadine Gatzert
Received: 4 February 2016 / Revised: 25 May 2016 / Accepted: 25 June 2016 / Published: 5 July 2016
(This article belongs to the Special Issue Life Insurance and Pensions)
View Full-Text   |   Download PDF [735 KB, uploaded 5 July 2016]   |  

Abstract

In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework and review the existing numerical methods. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is easier to implement and faster when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation. View Full-Text
Keywords: variable annuity; guaranteed living and death benefits; guaranteed minimum accumulation benefit; optimal stochastic control; direct integration method variable annuity; guaranteed living and death benefits; guaranteed minimum accumulation benefit; optimal stochastic control; direct integration method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Shevchenko, P.V.; Luo, X. A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework. Risks 2016, 4, 22.

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