Longevity hedge effectiveness: A decomposition

We use a case study of a pension plan wishing to hedge the longevity risk in its pension liabilities at a future date. The plan has the choice of using either a customised hedge or an index hedge, with the degree of hedge effectiveness being closely related to the correlation between the value of the hedge and the value of the pension liability. The key contribution of this paper is to show how correlation and, therefore, hedge effectiveness can be broken down into contributions from a number of distinct types of risk factors. Our decomposition of the correlation indicates that population basis risk has a significant influence on the correlation. But recalibration risk as well as the length of the recalibration window are also important, as is cohort effect uncertainty. Having accounted for recalibration risk, additional parameter uncertainty has only a marginal impact on hedge effectiveness. Finally, the inclusion of Poisson risk only starts to become significant when the smaller population falls below about 10,000 members over age 50. Our case study shows that, at least for medium and large pension plans, longevity risk can be substantially hedged using index hedges as an alternative to customised longevity hedges. As a consequence, when the hedger's population involves more than about 10,000 members over age 50, index longevity hedges (in conjunction with the other components of an ALM strategy) can provide an effective and lower cost alternative to both a full buy-out of pension liabilities or even to a strategy using customised longevity hedges

Multiple mortality modeling in Poisson Lee-Carter framework

The academic literature in longevity field has recently focused on models for detecting multiple population trends (D'Amato et al., 2012b; Njenga and Sherris, 2011; Russolillo et al., 2011, etc.). In particular, increasing interest has been shown about "related" population dynamics or "parent" populations characterized by similar socioeconomic conditions and eventually also by geographical proximity. These studies suggest dependence across multiple populations and common long-run relationships between countries (for instance, see Lazar et al., 2009). In order to investigate cross-country longevity common trends, we adopt a multiple population approach. The algorithm we propose retains the parametric structure of the Lee-Carter model, extending the basic framework to include some cross-dependence in the error term. As far as time dependence is concerned, we allow for all idiosyncratic components (both in the common stochastic trend and in the error term) to follow a linear process, thus considering a highly flexible specification for the serial dependence structure of our data. We also relax the assumption of normality, which is typical of early studies on mortality (Lee and Carter, 1992) and on factor models (see e.g., the textbook by Anderson, 1984). The empirical results show that the multiple Lee-Carter approach works well in the presence of dependence

An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for $L_1$-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in $L_1$. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to get.Comment: Revised. 17 pages. To appear in Applied Mathematics & Optimizatio

Metropolis–Hastings Algorithms with acceptance ratios of nearly 1

Metropolis–Hastings algorithm, Polynomial ergodicity, Langevin diffusion, Metropolis adjusted Langevin algorithm,