Modelling Longevity Bonds: Analysing the Swiss Re Kortis Bond

It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives

Insurance Mathematics and Economics ◽

10.1016/j.insmatheco.2011.02.009 ◽

2011 ◽

Vol 49 (1) ◽

pp. 100-114 ◽

Cited By ~ 60

Author(s):

Andrew Ngai ◽

Michael Sherris

Keyword(s):

Risk Management ◽

Longevity Risk ◽

Variable Annuities ◽

Static Hedging ◽

Longevity Bonds

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Pricing Longevity Bonds Under the Uncertainty Theory Framework

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001419590201 ◽

2019 ◽

Vol 33 (06) ◽

pp. 1959020

Author(s):

Jianwei Gao ◽

Huicheng Liu

Keyword(s):

Interest Rate ◽

Uncertainty Theory ◽

Calculation Algorithm ◽

Index Model ◽

Survival Index ◽

Vasicek Interest Rate Model ◽

Longevity Bonds ◽

Coupon Bond ◽

Theory Framework ◽

Pricing Formula

This paper aims to develop a new pricing approach for longevity bonds under the uncertainty theory framework. First, we describe the life expectancy by a canonical uncertain process and illustrate the dynamic of short interest rate via an uncertain Vasicek interest rate model. Then, based on these descriptions, we construct an uncertain survival index model and present its procedure for parameter estimation. By applying the chain rule, we derive a pricing formula of the uncertain zero-coupon bond. Considering that the financial market is incomplete, we put forward an uncertain distortion operator. Furthermore, based on the uncertain survival index, the uncertain zero-coupon bond pricing formula and the uncertain distortion operator, we develop a pricing formula of the uncertain longevity bond and its calculation algorithm. Finally, a numerical example is shown to illustrate the influence of parameters on the price of the uncertain longevity bond.

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Pricing of Longevity Derivatives and Cost of Capital

Risks ◽

10.3390/risks7020041 ◽

2019 ◽

Vol 7 (2) ◽

pp. 41 ◽

Cited By ~ 5

Author(s):

Fadoua Zeddouk ◽

Pierre Devolder

Keyword(s):

Financial Markets ◽

Time Horizon ◽

Cost Of Capital ◽

Solvency Ii ◽

Longevity Risk ◽

Policy Makers ◽

Academic Researchers ◽

Belgian Population ◽

One Year ◽

Longevity Bonds

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.

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Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities

British Actuarial Journal ◽

10.1017/s1357321700004736 ◽

2006 ◽

Vol 12 (1) ◽

pp. 153-197 ◽

Cited By ~ 172

Author(s):

D. Blake ◽

A. J. G. Cairns ◽

K. Dowd

Keyword(s):

Detailed Analysis ◽

Pension Plans ◽

Longevity Risk ◽

Over The Counter ◽

New Class ◽

Credit Risks ◽

Longevity Bonds ◽

The Universe ◽

Over Time ◽

The Way

ABSTRACTThis paper addresses the problem of longevity risk — the risk of uncertain aggregate mortality — and discusses the ways in which life assurers, annuity providers and pension plans can manage their exposure to this risk. In particular, it focuses on how they can use mortality-linked securities and over-the-counter contracts — some existing and others still hypothetical — to manage their longevity risk exposures. It provides a detailed analysis of two such securities — the Swiss Re mortality bond issued in December 2003 and the EIB/BNP longevity bond announced in November 2004. It then looks at the universe of hypothetical mortality-linked securities — other forms of longevity bonds, swaps, futures and options — and investigates their potential uses. It also addresses implementation issues, and draws lessons from the experiences of other derivative contracts. Particular attention is paid to the issues involved with the construction and use of mortality indices, the management of the associated credit risks, and possible barriers to the development of markets for these securities. It suggests that these implementation difficulties are essentially teething problems that will be resolved over time, and so leave the way open to the development of flourishing markets in a brand new class of securities.

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