Abstract
Annuities providers become more and more exposed to longevity risk due to the increase in life expectancy. To hedge this risk, new longevity derivatives have been proposed (longevity bonds, q-forwards, S-swaps…). Although academic researchers, policy makers and practitioners have talked about it for years, longevity-linked securities are not widely traded in financial markets, due in particular to the pricing difficulty. In this paper, we compare different existing pricing methods and propose a Cost of Capital approach. Our method is designed to be more consistent with Solvency II requirement (longevity risk assessment is based on a one year time horizon). The price of longevity risk is determined for a S-forward and a S-swap but can be used to price other longevity-linked securities. We also compare this Cost of capital method with some classical pricing approaches. The Hull and White and CIR extended models are used to represent the evolution of mortality over time. We use data for Belgian population to derive prices for the proposed longevity linked securities based on the different methods.
Highlights
Significant improvements in longevity have been experienced in most developed countries.For annuity providers, longevity risk, i.e., the risk that future mortality trends differ from those anticipated constitutes an important risk factor.Under the new European regulatory environment for the insurance industry, SolvencyII, it becomes a requirement for insurers to measure and evaluate longevity risks (Levantesi and Menzietti (2006))
We study the consistency between this Cost of Capital approach (COC) and three important classical pricing methods used in finance: risk-neutral pricing, Wang transform and Sharpe ratio
To be more consistent with the logic of Solvency II, we propose to adopt another formulation: the Solvency Capital Requirement (SCR) at time i should cover with 99.5% probability the unexpected losses on a one-year time horizon, and we consider mortality evolution’s up to time i, and from i + 1 to T according to their best estimates (Figure 4) : Figure 4
Summary
Significant improvements in longevity have been experienced in most developed countries. These products are based on mortality/longevity rates, similar to those existing in the financial market (Blake et al 2011). Longevity swaps are considered better because their transaction costs are lower, are more flexible and could be customized to suit individual circumstances Like the interest rate swaps, the survival swaps can be broken down into a collection of more simple derivative: the Survival-forwards (Coughlan et al 2007) These derivatives have attracted many researchers and practitioners who have published many papers on this subject, but because of the pricing difficulties, and the fact that these products remove only the longevity risk, they are still not widely traded in the financial market (Lin et al 2015).
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