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

Origin of the hot gas in low-mass protostars, Herschel-PACS spectroscopy of HH 46

Aims. “Water In Star-forming regions with Herschel” (WISH) is a Herschel key programme aimed at understanding the physical and chemical structure of young stellar objects (YSOs) with a focus on water and related species. Methods. The low-mass protostar HH 46 was observed with the Photodetector Array Camera and Spectrometer (PACS) on the Herschel Space Observatory to measure emission in H2O, CO, OH, [O i], and [C ii] lines located between 63 and 186 μm. The excitation and spatial distribution of emission can disentangle the different heating mechanisms of YSOs, with better spatial resolution and sensitivity than previously possible. Results. Far-IR line emission is detected at the position of the protostar and along the outflow axis. The OH emission is concentrated at the central position, CO emission is bright at the central position and along the outflow, and H2O emission is concentrated in the outflow. In addition, [O i] emission is seen in low-velocity gas, assumed to be related to the envelope, and is also seen shifted up to 170 km s−1 in both the red- and blue-shifted jets. Envelope models are constructed based on previous observational constraints. They indicate that passive heating of a spherical envelope by the protostellar luminosity cannot explain the high-excitation molecular gas detected with PACS, including CO lines with upper levels at >2500 K above the ground state. Instead, warm CO and H2O emission is probably produced in the walls of an outflow-carved cavity in the envelope, which are heated by UV photons and non-dissociative C-type shocks. The bright OH and [Oi] emission is attributed to J-type shocks in dense gas close to the protostar. In the scenario described here, the combined cooling by far-IR lines within the central spatial pixel is estimated to be 2 × 10−2 L, with 60–80% attributed to J- and C-type shocks produced by interactions between the jet and the envelope