Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

Man Chung Fung,Katja Ignatieva,Michael Sherris

doi:10.3390/risks7010002

Man Chung Fung, Katja Ignatieva + Show 1 more

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https://doi.org/10.3390/risks7010002

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Abstract

This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures.

Highlights

Securing a comfortable living after retirement is fundamental to the majority of the working population around the world
In our model formulation, we address the fact that the mortality intensity processes for different ages are increasing as time passed
Hedging results are summarised by means of summary statistics that include mean, standard deviation, skewness, as well as Value-at-Risk (VaR) and Expected Shortfall (ES) of the discounted surplus distribution per policy of an unhedged, a swap-hedged, and a cap-hedged annuity

Summary

Introduction

Securing a comfortable living after retirement is fundamental to the majority of the working population around the world. A major risk in retirement, is the possibility that retirement savings will be outlived. Products that provide guaranteed lifetime income, such as life annuities, need to be offered in a cost effective way while maintaining the long run solvency of the provider. Annuity providers and pension funds need to manage the systematic mortality risk , associated with random changes in the underlying mortality intensity, in a life annuity or pension portfolio. Systematic mortality risk cannot be diversified away with increasing portfolio size, while idiosyncratic mortality risk, representing the randomness of deaths in a portfolio with fixed mortality intensity, is diversifiable. Reinsurance has been important in managing longevity risk for annuity and pension providers

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