Article2012

Longevity/Mortality Risk Modeling and Securities Pricing

Yinglu Deng · Patrick L. Brockett · Richard D. MacMinn

79 citations0/0 files storedJournal of Risk & Insurance

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Insurance, Mortality, Demography, Risk Management Insurance and Financial Risk Management Stochastic processes and financial applications

Abstract

Abstract Securitizing longevity/mortality risk can transfer longevity/mortality risk to capital markets. Modeling and forecasting mortality rate is key to pricing mortality‐linked securities. Catastrophic mortality and longevity jumps occur in historical data and have an important impact on security pricing. This article introduces a stochastic diffusion model with a double‐exponential jump diffusion process that captures both asymmetric rate jumps up and down and also cohort effect in mortality trends. The model exhibits calibration advantages and mathematical tractability while better fitting the data. The model provides a closed‐form pricing solution for J.P. Morgan’s q‐forward contract usable as a building block for hedging.

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References

1992Modeling and Forecasting U. S. Mortality 2006A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration 2002A Poisson log-bilinear regression approach to the construction of projected lifetables 2004Option Pricing Under a Double Exponential Jump Diffusion Model 2005Affine processes for dynamic mortality and actuarial valuations 2004Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts 2006Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk 2001Mortality derivatives and the option to annuitise

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2013The New Life Market 2013Pricing Standardized Mortality Securitizations: A Two‐Population Model With Transitory Jump Effects 2015The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds 2013Incorporating Longevity Risk and Medical Information Into Life Settlement Pricing 2016Dynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives

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