eprintid: 1808
rev_number: 7
eprint_status: archive
userid: 6
dir: disk0/00/00/18/08
datestamp: 2013-09-27 13:02:28
lastmod: 2013-09-30 11:58:44
status_changed: 2013-09-30 11:58:44
type: article
metadata_visibility: show
creators_name: Luciano, Elisa
creators_name: Regis, Luca
creators_name: Vigna, Elena
creators_id: 
creators_id: luca.regis@imtlucca.it
creators_id: 
title: Delta–Gamma hedging of mortality and interest rate risk 
ispublished: pub
subjects: HB
divisions: EIC
full_text_status: none
keywords: No-arbitrage in insurance 
abstract: One of the major concerns of life insurers and pension funds is the increasing longevity of their beneficiaries. This paper studies the hedging problem of annuity cash flows when mortality and interest rates are stochastic. We first propose a Delta–Gamma hedging technique for mortality risk. The risk factor against which to hedge is the difference between the actual mortality intensity in the future and its “forecast” today, the forward intensity. We specialize the hedging technique first to the case in which mortality intensities are affine, then to Ornstein–Uhlenbeck and Feller processes, providing actuarial justifications for this selection. We show that, without imposing no arbitrage, we can get equivalent probability measures under which the {HJM} condition for no arbitrage is satisfied. Last, we extend our results to the presence of both interest rate and mortality risk. We provide a {UK} calibrated example of Delta–Gamma hedging of both mortality and interest rate risk. 
date: 2012
date_type: published
publication: Insurance: Mathematics and Economics
volume: 50
number: 3
publisher: Elsevier
pagerange: 402 - 412
id_number: 10.1016/j.insmatheco.2012.01.006
refereed: TRUE
issn:  0167-6687
official_url: http://www.sciencedirect.com/science/article/pii/S0167668712000157
citation:   Luciano, Elisa and Regis, Luca and Vigna, Elena  Delta–Gamma hedging of mortality and interest rate risk.  Insurance: Mathematics and Economics, 50 (3).  402 - 412.  ISSN  0167-6687      (2012)