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Delta and Gamma Hedging of Mortality and Interest Rate Risk

33 Pages Posted: 31 Jan 2011 Last revised: 4 Oct 2014

Elisa Luciano

Collegio Carlo Alberto; University of Turin - Department of Statistics and Applied Mathematics

Luca Regis

University of Siena - Dipartimento di Economia Politica

Elena Vigna

University of Turin - Faculty of Economics; Collegio Carlo Alberto; CeRP

Date Written: January 27, 2011

Abstract

This paper studies the hedging problem of life insurance policies, when the mortality and interest rates are stochastic. We focus primarily on stochastic mortality. We represent death arrival as the first jump time of a doubly stochastic process, i.e. a jump process with stochastic intensity. We propose a Delta-Gamma Hedging technique for mortality risk in this context. The risk factor against which to hedge is the difference between the actual mortality intensity in the future and its "forecast" today, the instantaneous forward intensity. We specialize the hedging technique first to the case in which survival intensities are affine, then to Ornstein-Uhlenbeck and Feller processes, providing actuarial justifications for this restriction. 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, when the forward interest rate follows a constant-parameter Hull and White process. We provide a UK calibrated example of Delta and Gamma Hedging of both mortality and interest rate risk.

Suggested Citation

Luciano, Elisa and Regis, Luca and Vigna, Elena, Delta and Gamma Hedging of Mortality and Interest Rate Risk (January 27, 2011). Insurance: Mathematics and Economics, 50, 402-412, 2012; ICER Working Paper No. 1/2011. Available at SSRN: https://ssrn.com/abstract=1749426 or http://dx.doi.org/10.2139/ssrn.1749426

Elisa Luciano (Contact Author)

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

HOME PAGE: http://www.carloalberto.org/people/faculty/fellows/luciano/

University of Turin - Department of Statistics and Applied Mathematics ( email )

Corso Unione Sovietica 218 bis
Turin, I-10122
Italy
+ 39 011 6705230 (Phone)

Luca Regis

University of Siena - Dipartimento di Economia Politica ( email )

Piazza San Francesco 8
Siena, I53100
Italy

Elena Vigna

University of Turin - Faculty of Economics ( email )

Dipartimento di Statistica e Matematica Applicata
Corso Unione Sovietica 218 bis
Torino, 10134
Italy

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

CeRP ( email )

Via Real Collegio, 30
Moncalieri, Turin 10024
Italy

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