TY - JOUR
T1 - Pricing longevity derivatives via Fourier transforms
AU - Bravo, Jorge M.
AU - Nunes, João Pedro Vidal
N1 - Bravo, J. M., & Nunes, J. P. V. (2021). Pricing longevity derivatives via Fourier transforms. Insurance: Mathematics and Economics, 96(January), 81-97. [Advanced online publication on 1 November, 2020]. Doi: https://doi.org/10.1016/j.insmatheco.2020.10.008 ---%ABS3%
PY - 2021/1
Y1 - 2021/1
N2 - Longevity-linked derivatives are one of the most important longevity risk management solutions for pension schemes and life annuity portfolios. In this paper, we decompose several longevity derivatives—such as geared longevity bonds and longevity-spread bonds—into portfolios involving longevity options. For instance, we show that the fair value of an index-based longevity swap can be broken down into a portfolio of long and short positions in European-style longevity caplets and floorlets, with an underlying asset equal to a population-based survivor index and strike price equal to the initial preset survivor schedule. We develop a Fourier transform approach for European-style longevity option pricing under continuous-time affine jump–diffusion models for both cohort mortality intensities and interest rates, accounting for both positive and negative jumps in mortality. The model calibration approach is described and illustrative empirical results on the valuation of longevity derivatives, using U.S. total population mortality data, are provided.
AB - Longevity-linked derivatives are one of the most important longevity risk management solutions for pension schemes and life annuity portfolios. In this paper, we decompose several longevity derivatives—such as geared longevity bonds and longevity-spread bonds—into portfolios involving longevity options. For instance, we show that the fair value of an index-based longevity swap can be broken down into a portfolio of long and short positions in European-style longevity caplets and floorlets, with an underlying asset equal to a population-based survivor index and strike price equal to the initial preset survivor schedule. We develop a Fourier transform approach for European-style longevity option pricing under continuous-time affine jump–diffusion models for both cohort mortality intensities and interest rates, accounting for both positive and negative jumps in mortality. The model calibration approach is described and illustrative empirical results on the valuation of longevity derivatives, using U.S. total population mortality data, are provided.
KW - Affine mortality models
KW - Fourier transforms
KW - Longevity bonds
KW - Longevity caps and floors
KW - Longevity Swaps
UR - http://www.scopus.com/inward/record.url?scp=85096210942&partnerID=8YFLogxK
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000608020200006
U2 - 10.1016/j.insmatheco.2020.10.008
DO - 10.1016/j.insmatheco.2020.10.008
M3 - Article
AN - SCOPUS:85096210942
SN - 0167-6687
VL - 96
SP - 81
EP - 97
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
IS - January
ER -