Natural delta gamma hedging of longevity and interest rate risk
The paper presents closed-form Delta and Gamma hedges for an- nuities and death assurances, in the presence of both longevity and interest-rate risk. Longevity risk is modelled through an extension of the classical Gompertz law, while interest rate risk is modelled via an Hull-and-White process. We theoretically provide natural hedg- ing strategies, considering also contracts written on di erent genera- tions. We provide a UK-population and bond-market calibrated exam- ple. We compute longevity exposures and explicitly calculate Delta- Gamma hedges. Re-insurance is needed in order to set-up portfolios which are Delta-Gamma neutral to both longevity and interest-rate risk.
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- Robert Jarrow & Stuart Turnbull, 1994. "Delta, gamma and bucket hedging of interest rate derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 21-48.
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