This paper provides the static, swap-based hedge for an annuity, and compares it with the dynamic, delta-based hedge, achieved using longevity bonds. We assume that the longevity intensity is distributed according to a CIR-type process and provide closed-form derivatives prices and hedges, also...

This paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk- return frontier and shows that hedging strategies - such as the transfer of...

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....

The paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and...

Longevity risk transfer is a popular choice for annuity providers such as pension funds. This paper formalizes the trade-off between the cost and the risk relief of such choice, when the annuity provider uses value- at-risk to assess risk. Using first-order approximations we show that, if the...

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....

This paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk-return frontier and shows that hedging strategies–such as the transfer of...

The paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and...

This paper uses copula functions in order to evaluate tail probabilities and market risk trade-offs at a given confidence level, dropping the joint normality assumption on returns. Copulas enable to represent distribution functions separating the marginal distributions from the association...