Asymmetry in mortality volatility and its implications on index-based longevity hedging. (5th September 2020)

• Record Type: Journal Article
• Authors: Zhou, Kenneth Q.; Li, Johnny Siu-Hang
• Is Part Of: Annals of actuarial science. Volume 14:Number 2(2020)
• Page Start: 278
• Page End: 301
• Publication Date: 2020-09-05
• Subjects: GARCH-type models, -- Longevity Greeks, -- S-forwards, -- Value-at-Risk, -- The Lee–Carter model; Actuarial science -- Periodicals; Insurance, Life -- Periodicals; 368.010941
• DOI: 10.1017/S174849952000010X
• Languages: English
• ISSNs: 1748-4995

Abstract

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.