Guarantee Valuation in Notional Defined Contribution Pension Systems
ASTIN Bulletin, vol. 46, pp. 677-707, DOI: org/10.1017/asb.2016.21
30 Pages Posted: 10 Dec 2015 Last revised: 10 Feb 2017
Date Written: August 5, 2016
The notional defined contribution pension scheme combines pay-as-you-go financing and a defined contribution pension formula. The return on contributions is based on an index set by law, such as the growth rate of GDP, average wages or contribution payments. The volatility of this return compromises the system's pension adequacy and therefore guarantees may be needed. Here, we provide a minimum return guarantee to the pension contributions. The price is calculated in a utility indifference framework. We obtain a closed-form solution for a general dependence structure with exponential preferences and in presence of stochastic short interest rates.
Keywords: Public pension, pay-as-you-go, option pricing, incomplete markets, exponential utility
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