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Asymmetry in mortality volatility and its implications on index-based longevity hedging

Published online by Cambridge University Press:  05 May 2020

Kenneth Q. Zhou  and
Johnny Siu-Hang Li
Kenneth Q. Zhou
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
Johnny Siu-Hang Li*
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada Department of Economics, University of Melbourne, Melbourne, Australia
*
* Corresponding author. E-mail: shli@uwaterloo.ca
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Abstract

Mortality volatility is crucially important to many aspects of index-based longevity hedging, including instrument pricing, hedge calibration and hedge performance evaluation. This paper sets out to develop a deeper understanding of mortality volatility and its implications on index-based longevity hedging. First, we study the potential asymmetry in mortality volatility by considering a wide range of generalised autoregressive conditional heteroskedasticity (GARCH)-type models that permit the volatility of mortality improvement to respond differently to positive and negative mortality shocks. We then investigate how the asymmetry of mortality volatility may impact index-based longevity hedging solutions by developing an extended longevity Greeks framework, which encompasses longevity Greeks for a wider range of GARCH-type models, an improved version of longevity vega, and a new longevity Greek known as “dynamic Delta”. Our theoretical work is complemented by two real-data illustrations, the results of which suggest that the effectiveness of an index-based longevity hedge could be significantly impaired if the asymmetry in mortality volatility is not taken into account when the hedge is calibrated.

Keywords

GARCH-type modelsLongevity GreeksS-forwardsValue-at-RiskThe Lee–Carter model
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 278 - 301
Copyright
© Institute and Faculty of Actuaries 2020

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