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In this paper we focus on the initiation option featured in many Guaranteed Lifelong Withdrawal Benefit variable annuity contracts, granting their owner the right to decide the age at which lifetime withdrawals should begin. Such contracts have been successfully analysed using a PDE approach. The latter method is elegant, but becomes less viable when the valuation model is more involved and other guarantees are considered. As an alternative, we exploit the Least Squares Monte Carlo approach and model the interaction of the initiation option with lapses and other riders.

In this paper we propose a methodology for valuing future annuity contracts based on the Least-Squares Monte Carlo approach. We adopt, as first step, a simplified computational framework where just one risk factor is taken into account, and then we extend it introducing other sources of risk. We give a brief description of the valuation procedure and provide some numerical illustrations. Furthermore, to test the efficiency of the proposed methodology, we compare our results with those obtained by applying a straightforward and time-consuming approach based on nested simulations. Finally, we present some possible applications in the context of de-risking strategies for pension plans and in the valuation of guaranteed annuity options.

In this paper we study how policyholders and equityholders contribute to the formation of a life insurance company issuing participating contracts. The structure of these contracts is stylized and features a guaranteed rate of return and a terminal bonus, as in the pioneering model by Briys and de Varenne (1994, 1997). Policyholders aim at maximizing their preferences by choosing the leverage ratio and the guaranteed level, while being subject to regulatory constraints of fair valuation and solvency. We provide conditions under which non trivial contracts exist and analyze their properties.

In this paper we mirror the framework of generalized (non-)linear models to define the family of generalized age-period-cohort stochastic mortality models which encompasses the vast majority of stochastic mortality projection models proposed to date, including the well-known Lee-Carter and Cairns-Blake-Dowd models. We also introduce the R package StMoMo which exploits the unifying framework of the generalized age-period-cohort family to provide tools for fitting stochastic mortality models, assessing their goodness of fit and performing mortality projections. We illustrate some of the capabilities of the package by performing a comparison of several stochastic mortality models applied to the England and Wales population.

In this paper we assess the joint impact of biometric and financial risk on the market valuation of life insurance liabilities. We consider a stylized, contingent claim based model of a life insurance company issuing participating contracts and subject to default risk, as pioneered by Briys and de Varenne (1994, 1997), and build on their model by explicitly introducing biometric risk and its components, namely diversifiable and systematic risk. The contracts considered include pure endowments, deferred whole life annuities and guaranteed annuity options. Our results stress the predominance of systematic over diversifiable risk in determining fair participation rates. We investigate the interaction of contract design, market regimes and mortality scenarios, and show that, particularly for lifelong benefits, usually offered participation rates may not be sustainable even under moderate longevity improvements.

This paper summarises the work to date of Cass Business School and Hymans Robertson LLP in relation to assessing longevity basis risk. This work was commissioned by the Longevity Basis Risk Working Group (LBRWG) and funded by the Life and Longevity Markets Association (LLMA) and Institute and Faculty of Actuaries (IFoA). The LBRWG was formed by the LLMA and IFoA in December 2011 with a remit to investigate how to provide a market-friendly means of analysing longevity basis risk.

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 levels of rationality in the policyholder’s withdrawal behaviour 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.

Variable Annuities (VA) package living and death benefits, eventually aiming at constructing a post-retirement income, while offering a number of possible guarantees in respect of financial and mortality/longevity risks. In many circumstances, the policyholder keeps access to her fund, and can in particular cash money beyond the benefits already set. Apart from financial and mortality/longevity risks, the insurer is therefore exposed also to the risk of unexpected decisions of the policyholder. We suggest to adopt a comprehensive approach to these different risk sources, and we describe a unifying valuation framework of the guarantees under quite general assumptions.