Delta–Gamma hedging of mortality and interest rate risk

Luciano, Elisa; Regis, Luca; Vigna, Elena

doi:10.1016/j.insmatheco.2012.01.006

Cited by 48 publications

(21 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the risk premium will impact both assets and liabilities and will offset to a significant extent, and it will not explicitly impact the risk measures used, it is assumed zero, and we use the real world measure P for pricing and risk measures. This is the assumption made by Luciano et al [8].…”

Section: Mortality Modelmentioning

confidence: 71%

See 1 more Smart Citation

Immunization and Hedging of Post Retirement Income Annuity Products

Liu

Sherris

2017

Risks

View full text Add to dashboard Cite

Designing post retirement benefits requires access to appropriate investment instruments to manage the interest rate and longevity risks. Post retirement benefits are increasingly taken as a form of income benefit, either as a pension or an annuity. Pension funds and life insurers offer annuities generating long term liabilities linked to longevity. Risk management of life annuity portfolios for interest rate risks is well developed but the incorporation of longevity risk has received limited attention. We develop an immunization approach and a delta-gamma based hedging approach to manage the risks of adverse portfolio surplus using stochastic models for mortality and interest rates. We compare and assess the immunization and hedge effectiveness of fixed-income coupon bonds, annuity bonds, as well as longevity bonds, using simulations of the portfolio surplus for an annuity portfolio and a range of risk measures including value-at-risk. We show how fixed-income annuity bonds can more effectively match cash flows and provide additional hedge effectiveness over coupon bonds. Longevity bonds, including deferred longevity bonds, reduce risk significantly compared to coupon and annuity bonds, reflecting the long duration of the typical life annuity and the exposure to longevity risk. Longevity bonds are shown to be effective in immunizing surplus over short and long horizons. Delta gamma hedging is generally only effective over short horizons. The results of the paper have implications for how providers of post retirement income benefit streams can manage risks in demanding conditions where innovation in investment markets can support new products and increase the product range.

show abstract

Section: Mortality Modelmentioning

confidence: 71%

“…Luciano et al [8] develop delta-gamma hedging for annuity providers allowing for both stochastic interest rates and stochastic mortality rates. They use zero coupon bonds and zero coupon survival bonds as the assets in the hedging strategies and pure endowment contracts as the liability.…”

Section: Introductionmentioning

confidence: 99%

Immunization and Hedging of Post Retirement Income Annuity Products

Liu

Sherris

2017

Risks

View full text Add to dashboard Cite

show abstract

“…For each cohort of initial age x and each gender i = m, f we have extrapolated from the HMD twenty observed survival probabilities tp i x , t = 1, ..., 20; then, we have calibrated the values of the parameters µ m , µ f , σ m , σ f that appear in the theoretical survival functions S x . This calibration procedure is standard and in the actuarial context has been used to calibrate the OU intensity process in [7], [8] and [9]. Table 1 reports the calibrated values of the parameters for the generations 1950 and 1940 for both genders and Table 2 those for cohorts 1930 and 1920.…”

Section: Calibration Proceduresmentioning

confidence: 99%

A unisex stochastic mortality model to comply with EU Gender Directive

Chen

Vigna

2017

Insurance: Mathematics and Economics

Self Cite

View full text Add to dashboard Cite

EU Gender Directive ruled out discrimination against gender in charging premium for insurance products. This prohibition prevents the use of the standard actuarial fairness principle to price life insurance products. According to current actuarial practice, unisex premiums are calculated with a simple weighting rule of the gender-specific life tables. This procedure is likely to violate portfolio fairness principles. Up to our knowledge, in the actuarial literature there is no unisex mortality model that respects the unisex fairness principle. This paper is the first attempt to fill this gap. First, we recall the notion of unisex fairness principle and the corresponding unisex fair premium. Then, we provide a unisex stochastic mortality model for the mortality intensity that is underlying the pricing of a life portfolio of females and males belonging to the same cohort. Finally, we calibrate the unisex mortality model using the unisex fairness principle. We find that the weighting coefficient between the males' and females' own mortalities depends mainly on the quote of portfolio relative to each gender, on the * We thank the participants to the 19th International Congress on Insurance: Mathematics and Economics and those to the 3rd European Actuarial Journal Conference for useful remarks. We are indebted to Paolo De Angelis, Kristian Buchardt, Montserrat Guillen, Elisa Luciano, Pietro Millossovich, Luca Regis and two anonymous referees for very valuable comments that improved the paper. age, and on the type of insurance product. The knowledge of a proper unisex mortality model could help life insurance companies to better understanding the nature of the risk of a mixed portfolio.

show abstract

“…In order to model the longevity risk, we consider a second Ornstein-Uhlenbeck process for the dynamic of the force of mortality (see for instance [1], [15], [11] or [6]). We assume that the force of mortality process is non mean reverting as suggested in [3].…”

Section: Mortality Process and Survivor Indexmentioning

confidence: 99%

Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Devolder

Lebègue

2016

Dependence Modeling

View full text Add to dashboard Cite

Abstract:The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products. Secondly, for such products, we challenge the de nition of the Solvency Capital Requirement (SCR) under the Solvency II (SII) regulatory framework based on a yearly viewpoint. Several methods for the calculation of the solvency capital are presented. We start our study with risk measures as considered in the SII framework and then proceed with the ruin theory approach. Instead of considering the continuous time setting of the ruin theory, we consider the discrete time-the yearly basis-of the accounting viewpoint. Wenally give an illustration with a xed guaranteed rate product along with the equity, interest rate and longevity risks. The latter risk brings us to consider zero-coupon longevity bonds in which we invest the capital. We show that long-term guarantees might be overloaded under the SII regulation.

show abstract

Delta–Gamma hedging of mortality and interest rate risk

Cited by 48 publications

References 25 publications

Immunization and Hedging of Post Retirement Income Annuity Products

Immunization and Hedging of Post Retirement Income Annuity Products

A unisex stochastic mortality model to comply with EU Gender Directive

Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Contact Info

Product

Resources

About