Jennifer Alonso-García

Pricing and hedging guaranteed minimum withdrawal benefits under a general Lévy framework using the COS method

This paper extends the Fourier-cosine (COS) method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdrawal benefit (GMWB) riders. The COS method facilitates efficient computation of prices and hedge ratios of the GMWB riders when the underlying fund dynamics evolve under the influence of the general class of Lévy processes. Formulae are derived to value the contract at each withdrawal date using a backward recursive dynamic programming algorithm. Numerical comparisons are performed with results presented in Bacinello et al. [Scand. Actuar. J., 2014, 1–20], and Luo and Shevchenko [Int. J. Financ. Eng., 2014, 2, 1–24], to confirm the accuracy of the method. The efficiency of the proposed method is assessed by making comparisons with the approach presented in Bacinello et al. [op. cit.]. We find that the COS method presents highly accurate results with notably fast computational times. The valuation framework forms the basis for GMWB hedging. A local risk minimisation approach to hedging intra-withdrawal date risks is developed. A variety of risk measures are considered for minimisation in the general Lévy framework. While the second moment and variance have been considered in existing literature, we show that the Value-at-Risk (VaR) may also be of interest as a risk measure to minimise risk in variable annuities portfolios.

Guarantee Valuation in Notional Defined Contribution Pension Systems

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 systems 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.

Adequacy, Fairness and Sustainability of Pay-As-You-Go-Pension-Systems: Defined Benefit Versus Defined Contribution

There are three main challenges facing public pension systems. First, pension systems need to provide an adequate income for pensioners in the retirement phase. Second, participants wish a fair level of benefits in relation to the contributions paid. Last but no least, the pension system would need to be financially sustainable in the long run. In this paper, we analyse defined benefit versus defined contribution schemes in terms of adequacy, fairness and sustainability jointly. Also, risk sharing mechanisms, that involve changes in the key variables of the system, are designed to restore the financial sustainability at the same time that we study their consequences on the adequacy and fairness of the system.

NDC Schemes and Heterogeneity in Longevity: Proposals for Redesign

Strong and rising empirical evidence across countries finds that longevity is highly heterogeneous in key socioeconomic characteristics, including income. A positive relationship between lifetime income and life expectancy at retirement amounts to a straight tax/subsidy mechanism when the average cohort life expectancy is applied for annuity calculation, as done under nonfinancial defined contribution (NDC) schemes. Such a regressive redistribution and the ensuing labor market distortion put into doubt main features of the NDC scheme and call for alternative benefit designs to compensate for the heterogeneity. This paper explores five key mechanisms of compensation: individualized annuities; individualized contribution rates/account allocations; a two-tier contribution structure with socialized and individual rate structure; and two supplementary approaches under the two-tier approach to deal with the income distribution tails, and the distortions above a ceiling and below a floor. Using unique data from England and Wales and the United States, the analysis indicates that both individualized annuities and a two-tier contribution scheme are feasible and effective and thus promising policy options. To this end, however, a de-pooling of gender will be required.

Liquidity and Solvency in Pay-as-You-Go Defined Contribution Pension Schemes: A Continuous OLG Sustainability Framework

Notional Defined Contribution (NDC) pension schemes are defined contribution plans which are pay-as-you-go financed. From a design viewpoint, the countries where NDCs have been implemented cannot guarantee sustainability due to the choice of notional return paid to the contributions and the indexation rate paid to pensions. We study how the scheme should be designed to achieve liquidity and solvency with a limited set of assumptions in a continuous overlapping generations model that increases traceability of the results. The adequacy and actuarial fairness are also jointly studied in the numerical example for the population of Belgium. We find that the proposed indexation and notional rate act as automatic balancing mechanisms that ensure sustainability and actuarial fairness. However, the effect on pension adequacy depends on the generosity of the annuity scheme at retirement.