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

TL;DR

This paper evaluates the effectiveness of index-based longevity swaps and caps in hedging mortality risk for life annuities, using a stochastic model calibrated with Australian data to analyze various market scenarios.

Contribution

It introduces a tractable stochastic mortality model with analytical pricing formulas for longevity derivatives and assesses hedge effectiveness for different market conditions.

Findings

Longevity swaps provide effective downside risk protection.

Longevity caps offer additional risk management benefits.

Hedge effectiveness varies with market risk premiums and contract maturities.

Abstract

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