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The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours

Anna Rita Bacinello · Pietro Millossovich · Alvaro Montealegre

40 citations0/0 files storedScandinavian Actuarial Journal

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Stochastic processes and financial applications Insurance, Mortality, Demography, Risk Management Probability and Risk Models

Abstract

In this paper, we present a dynamic programming algorithm for pricing variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) under a general Lévy processes framework. The GMWB gives the policyholder the right to make periodical withdrawals from her policy account even when the value of this account is exhausted. Typically, the total amount guaranteed for withdrawals coincides with her initial investment, providing then a protection against downside market risk. At each withdrawal date, the policyholder has to decide whether, and how much, to withdraw, or to surrender the contract. We show how different policyholder’s withdrawal behaviours can be modelled. We perform a sensitivity analysis comparing the numerical results obtained for different contractual and market parameters, policyholder behaviours and different types of Lévy processes.

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References

1973The Pricing of Options and Corporate Liabilities 1976Option pricing when underlying stock returns are discontinuous 2003Financial Modelling with Jump Processes 1998Numerical Methods in Economics 1998The Variance Gamma Process and Option Pricing 2002The Fine Structure of Asset Returns: An Empirical Investigation 1990The Variance Gamma (V.G.) Model for Share Market Returns 2019Problems and Perspectives in Management

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