Pricing Longevity-Linked Securities in the Presence of Mortality Trend Changes

Abstract

Even though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.

On the economics of the longevity risk transfer market

“…Mortality data sorted by the IMD is frequently used to investigate and model socioeconomic mortality differences in England, compare, for example, Lyu et al (2023) or Wen et al (2023). Freimann (2021) for all technical details, including the resulting model parameters. Throughout this work, we rely on 2500 outer simulation paths along with additional 2500 inner 1-year simulations for the computations of SCRs and economic capital.…”

“…For the simulation of future mortality, we follow Freimann (2021) and rely on his calibration of our stochastic mortality model to data of English and Welsh males. The corresponding national population represents the natural choice for the reference population, and we use data of English males sorted by quintiles of the Index of Multiple Deprivation (IMD) for the calibration of $${N}_{Sub}=5$$ suitable subpopulations of different socioeconomic status.…”

“…The corresponding national population represents the natural choice for the reference population, and we use data of English males sorted by quintiles of the Index of Multiple Deprivation (IMD) for the calibration of $${N}_{Sub}=5$$ suitable subpopulations of different socioeconomic status. We refer the reader to Freimann (2021) for all technical details, including the resulting model parameters. Throughout this work, we rely on 2500 outer simulation paths along with additional 2500 inner 1‐year simulations for the computations of SCRs and economic capital.…”

“…Börger (2010) argues that (re)insurers typically evaluate and price longevity transactions with regard to the tied‐up economic capital. This so‐called cost‐of‐capital pricing approach is implemented and further refined by Freimann (2021), Levantesi and Menzietti (2017), and Zeddouk and Devolder (2019). However, all of these works have in common that they do not explicitly account for potential diversification effects within the reinsurer's business mix even though these may constitute a decisive competitive advantage.…”