Pricing longevity derivatives via Fourier transforms

2021

Eur. Actuar. J.

Participating longevity-linked life annuities (PLLA) in which benefits are updated periodically based on the observed survival experience of a given underlying population and the performance of the investment portfolio are an alternative insurance product offering consumers individual longevity risk protection and the chance to profit from the upside potential of financial market developments. This paper builds on previous research on the design and pricing of PLLAs by considering a Bayesian Model Ensemble of single population generalised age-period-cohort stochastic mortality models in which individual forecasts are weighted by their posterior model probabilities. For the valuation, we adopt a longevity option decomposition approach with risk-neutral simulation and investigate the sensitivity of results to changes in the asset allocation by considering a more aggressive lifecycle strategy. We calibrate models using Taiwanese (mortality, yield curve and stock market) data from 1980 to 2019. The empirical results provide significant valuation and policy insights for the provision of a cost effective and efficient risk pooling mechanism that addresses the individual uncertainty of death, while providing appropriate retirement income and longevity protection.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pricing participating longevity-linked life annuities: a Bayesian Model Ensemble approach

2021

Eur. Actuar. J.

“…CPI inflation values are simulated using a random walk with drift model. The PLLA contract is priced using a longevity option decomposition approach considering 10000 simulations of mortality and financial market risk factors [16][17]. 2…”

Section: Financial Marketsmentioning

confidence: 99%

“…3 An alternative approach is to use a Bayesian Model Ensemble (model combinations) of stochastic mortality models [2,6,22,27,35] or continuous-time affine-jump diffusion models [17,30].…”

Section: Stochastic Mortality Modelingmentioning

confidence: 99%

Drawing Down Retirement Financial Savings: A Welfare Analysis using French data

Proceedings of the 5th International Conference on E-Commerce, E-Business and E-Government

2021

In recent decades, most countries have responded to increased longevity, population ageing, and low market returns with systemic and/or gradual parametric pension reforms. The trend towards individual accounts in public and private funded pension schemes augmented the importance of studying the decumulation phase of pensions. This paper uses a simulation design to empirically investigate the individual welfare generated from alternative annuitization and self-managed fixed, variable and hybrid drawdown strategies. A time-separable utility function is used to represent an individual's preferences towards consumption and bequest, risk aversion, and intertemporal discounting and to quantitively assess the range of retirement outcomes from competing decumulation designs. The setting comprises a stochastic mortality and investment risk framework calibrated to French interest rate, stock market, and mortality data from 2010 to 2019. The results show that self-managed variable decumulation strategies may generate higher income at the expense of high risk-taking, more volatile income streams, and no longevity insurance. Annuitization strategies involving longevity-linked life annuities and hybrid solutions provide higher expected lifetime utility at the expense of bequest motives.CCS CONCEPTS • Modeling and simulation • Continuous mathematics • Law, social and behavioral sciences

“…In recent years, several capital-market-based solutions for mortality and longevity risk management have been proposed and, some, successfully launched. They include insurance securitization, mortality-or longevity-linked securities such as CAT mortality bonds, survivor/longevity bonds [5], and derivatives with both linear and nonlinear payoff structures, e.g., Index-based Capital-market longevity swaps [6][7], q-forwards [8], S-forwards, K-forwards [9], mortality options, survivor options [7], survivor swaptions [10], K-options [11] and call-spreads [12].…”

Section: Introductionmentioning

confidence: 99%

Pricing Survivor Bonds with Affine-Jump Diffusion Stochastic Mortality Models

Proceedings of the 5th International Conference on E-Commerce, E-Business and E-Government

2021

Capital-market-based solutions are an interesting alternative to reinsurance-based options for managing systemic longevity risk in pension funds, insurance companies, and annuity providers. The pricing of longevity-linked securities depends both on the stochastic process for the underlying risk factors (age-specific mortality rates, interest rate) and on the investor's risk attitude.This paper proposes a pricing approach for survivor bonds using affine-jump diffusion stochastic mortality models. The model structure uses a non-mean reverting square-root jump-diffusion Feller process combined with a Poisson process with double asymmetric exponentially distributed jumps to account for both negative and positive jumps. The model offers analytical tractability, fits well data, and allows for closed-form expressions for the survival probability. Illustrative empirical results on the pricing of survivor bonds are provided using U. S. mortality data for representative cohorts. The results suggest the cost of hedging longevity risk by issuing survivor bonds would be acceptable for the issuer.CCS CONCEPTS • Continuous mathematics • Law, social and behavioral sciences • Modeling and simulation