On the calibration of mortality forward curves

Li, Johnny Siu-Hang; Ng, Andrew; Chan, Wai-Sum

doi:10.1002/fut.20500

Cited by 6 publications

(3 citation statements)

References 32 publications

(31 reference statements)

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“…It thus warrants a separate study to investigate how much the proposed risk management methods may cost. To determine the cost associated with the dynamic longevity hedge, one may replace

q^{f}

with a forward mortality rate that is derived from the pricing methods proposed by Chuang and Brockett (), Li, Ng, and Chan (), Deng, Brockett, and MacMinn (2012) and Li and Hardy (). As a reinsurance treaty, the customized surplus swap may be priced under the Solvency II framework.…”

Section: Discussionmentioning

confidence: 99%

Dynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives

Zhou¹,

Li²

2016

J of Risk & Insurance

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In this article, we study the feasibility of dynamic longevity hedging with standardized securities that are linked to broad‐based mortality indexes. On the technical front, we generalize the dynamic “delta” hedging strategy developed by Cairns (2011) to incorporate the situation when population basis risk exists. On the economic front, we discuss the potential financial benefits of an index‐based hedge over a bespoke risk transfer. By considering data from a large group of national populations, we find evidence supporting the diversifiability of population basis risk. We further propose a customized surplus swap—executed between a hedger and reinsurer—to utilize the diversifiability. As standardized instruments demand less illiquidity premium, a combination of a dynamic index‐based hedge and the proposed customized surplus swap may possibly be a more economical (and equally effective) alternative to a bespoke risk transfer.

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“…It thus warrants a separate study to investigate how much the proposed risk management methods may cost. To determine the cost associated with the dynamic longevity hedge, one may replace

q^{f}

Section: Discussionmentioning

confidence: 99%

Dynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives

Zhou¹,

Li²

2016

J of Risk & Insurance

Self Cite

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“…They do not distinguish the difference of the expected mortality rate and the fixed rate, so adapting their approach to calculate the premium under the LLMA model structure is not clear. Li et al (2011) apply the canonical valuation to the q-forward pricing (see Stutzer 1996). Their mortality rate modeling is constructed on the mortality odds proposed by Cairns et al (2006).…”

Section: The Fixed Ratementioning

confidence: 99%

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

Chuang

Brockett

2014

North American Actuarial Journal

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The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk-related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association.

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“…In the past decades, the type of mortality‐linked securities (e.g., longevity bonds, q ‐forwards, survivor swaps, annuity futures, mortality options, and survivor caps) to manage longevity or mortality risks has been proposed, for example, Milevsky and Promislow (2001), Menoncin (2008), Dawson et al (2009), Lin and Tzeng (2010), Li et al (2011), Lin and Tsai (2016), and Schmeck and Schmidli (2021). In the practitioner community, JP Morgan has set up LifeMetrics for the purpose of building a liquid market for longevity derivatives since 2007.…”

Section: Introductionmentioning

confidence: 99%

A new option for mortality–interest rates

Lin

Tsai

2022

Journal of Futures Markets

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We propose a new type of mortality-interest option related to a new random variable, the force of mortality-interest denoted as μ*, the addition of the force of mortality and the force of interest. We assume μ* moves approximately linearly, design the new mortality-interest option, and then derive closed-form formulas for its expected values. We show that using the new mortality-interest options, an annuity provider and a life insurer can, respectively, hedge the longevity and mortality risks with interest rate risk; a financial intermediary selling the new options can benefit from natural hedges resulted from two-side businesses with the annuity provider and life insurer.

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On the calibration of mortality forward curves

Cited by 6 publications

References 32 publications

Dynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives

Dynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

A new option for mortality–interest rates

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