Valuing guaranteed minimum accumulation benefits by a change of numéraire approach

Huang, Yiming; Mamon, Rogemar; Xiong, Heng

doi:10.1016/j.insmatheco.2021.11.002

Cited by 5 publications

(3 citation statements)

References 42 publications

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“…The financial instrument denoted by Equation (12) bears a resemblance to a variable annuity that incorporates a GMAB‐type rider. It pertains to a unit‐linked product that disburses to the annuitant the value of the contract at the time of retirement, which could potentially be augmented by an extra premium, see, for example, Reference 24 for further details.…”

Section: Option Pricing With Portfolio Insurance Strategiesmentioning

confidence: 99%

“…the risk-neutral measure Q. For our purposes, in addition to the derivative whose price was defined in (24), we consider additional contingent claims with maturity T, whose underlyings are the portfolio insurance strategies introduced in Section 2, namely the CPPI, TIPP, G-CPPI, G-TIPP strategies. To make the TA B L E 4 Parameters used in the numerical experiments for the stochastic interest rate model (Vasicek) and the stochastic volatility model (Heston model).…”

Section: The Modelmentioning

confidence: 99%

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Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

Persio

Mancinelli

Oliva

et al. 2023

Appl Stoch Models Bus & Ind

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We introduce a new exotic option to be used within structured products to address a key disadvantage of standard time‐invariant portfolio protection: the well‐known cash‐lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option‐based structure with a dynamic allocation logic as underlying. We provide an in‐depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek‐type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time‐invariant portfolio protection strategies, meanwhile being also afraid to experience a cash‐lock event triggered by market turmoils.

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Section: Option Pricing With Portfolio Insurance Strategiesmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

Persio

Mancinelli

Oliva

et al. 2023

Appl Stoch Models Bus & Ind

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“…A policyholder of a guaranteed minimum income benefit (GMIB) contract receives at least a pre-specified stream of lifetime income after annuitizing the VA. A guaranteed minimum withdrawal benefit (GMWB) ensures a steady stream of periodical withdrawals regardless of investment performance. There is a rich literature on the fair valuation and risk management of life insurance contracts with embedded guarantees, for example, Boyle and Hardy (2003), Pelsser (2003), Bauer et al (2008), Van Haastrecht et al (2010), Hyndman and Wenger (2014), Shen et al (2016), Mamon et al (2021) and Huang et al (2022). Stochastic optimal control problems for insurance policies with various forms of guaranteed minimum benefits have been studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

Hedging longevity risk in defined contribution pension schemes

2023

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Pension schemes all over the world are under increasing pressure to efficiently hedge longevity risk imposed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme that decides to hedge longevity risk using a mortality-linked security, typically a longevity bond. The pension scheme promises a minimum guarantee which allows the members to purchase lifetime annuities upon retirement. The scheme manager invests in the risky and riskless assets available on the market, including the longevity bond. We transform the corresponding constrained optimal investment problem into a single investment portfolio optimization problem by replicating future contributions from members and the minimum guarantee provided by the scheme. We solve the resulting optimization problem using the dynamic programming principle. Through a series of numerical studies, we show that the longevity risk has an important impact on the investment strategy performance. Our results add to the growing evidence supporting the use of mortality-linked securities for efficient hedging of longevity risk.

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Efficient valuation of guaranteed minimum accumulation benefits in regime switching jump diffusion models with lapse risk

Zhang,

Zhong

2024

Applied Mathematics and Computation

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Valuing guaranteed minimum accumulation benefits by a change of numéraire approach

Cited by 5 publications

References 42 publications

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

Hedging longevity risk in defined contribution pension schemes

Efficient valuation of guaranteed minimum accumulation benefits in regime switching jump diffusion models with lapse risk

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