Delta and Gamma Hedging of Mortality and Interest Rate Risk

Luciano, Elisa; Regis, Luca; Vigna, Elena

doi:10.2139/ssrn.1749426

Cited by 20 publications

(18 citation statements)

References 23 publications

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“…Such long-dated securities do not seem appealing to capital market investors. A few researchers, including Dahl (2004), Dahl and Møller (2006), Dahl, Melchior, and Møller (2008) Cairns (2011), and Luciano, Regis, and Vigna (2012, propose dynamic longevity hedging strategies. Except the work of Cairns (2011), the existing dynamic longevity hedging strategies were developed from continuous-time models, which provide mathematical tractability but are not straightforward to implement in practice.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…The probability of survival from time t to T for a life aged x at time 0 is

S false(x + t, t, T false) = 𝔼 [(|, exp (- \int_{t}^{T} μ_{x} false(s false) normald s)) {scriptF}_{t}],

where

F_{t}

is the information filtration for mortality generated by the process up until time t (see, e.g., Luciano, Regis, and Vigna, ).…”

Section: Methodsmentioning

confidence: 99%

Natural Hedging Strategies for Life Insurers: Impact of Product Design and Risk Measure

Wong¹,

Sherris²,

Stevens³

2015

J of Risk & Insurance

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Natural hedging allows life insurers to manage long-term longevity and investment risks of life annuity products through offsetting risks in life insurance products. Benefits include a reduction in risk-based capital. We use stochastic mortality and interest rate models to assess life insurance and annuity capital requirements and to quantify the benefits of natural hedging for a range of different types of life insurance product designs and risk measures based on probability of insurer solvency. We show that level-premium life insurance products with a medium duration (around 20-30 years) can better hedge annuity products than whole life products. Renewable term life insurance products have less hedge effectiveness than level-premium term insurance. Results vary with the risk measure used, with the 1-year horizon Solvency II risk measure showing lower natural hedging benefits of life insurance compared to multiple-period risk measures. IntroductionLife annuities are recognized as an important product that protects individuals against longevity risk and investment risk in retirement. The recent global financial crisis, which resulted in significant falls and high volatility in equity markets, highlighted the benefits of such products in a retired individual's portfolio. With increasing life expectancies in most developed countries, many retirees face the risk of outliving their retirement funds and savings. Blake, Cairns, and Dowd (2008) highlight how life annuities provide retirees with a stable income that protects against longevity and also protects retirees from investment risk. Despite this, life annuity markets

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“…The lack of analytical formulas for pricing q-forwards and its derivatives, known as "Greeks", can be a significant problem in assessing hedge effectiveness since simulations within simulations are required for dynamic hedging strategies. The importance of tractable models has also been emphasised in Luciano et al (2012) who also consider dynamic hedging for longevity and interest rate risk. Hari et al (2008) apply a generalised two-factor Lee-Carter model to investigate the impact of longevity risk on the solvency of pension annuities.…”

Section: Introductionmentioning

confidence: 99%

Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

Fung

Ignatieva²,

Sherris

2019

Risks

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This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap. Although swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, also provide downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of these longevity derivatives are derived. Hedge effectiveness is considered for a hypothetical life annuity portfolio. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the market price of longevity risk, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The model is calibrated using Australian mortality data. The results provide a comprehensive analysis of longevity hedging, highlighting the risk management benefits and costs of linear and nonlinear payoff structures.

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Delta and Gamma Hedging of Mortality and Interest Rate Risk

Cited by 20 publications

References 23 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

Natural Hedging Strategies for Life Insurers: Impact of Product Design and Risk Measure

Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

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