Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws

Ulm, Eric R.

doi:10.1017/s0515036100015282

Cited by 25 publications

(19 citation statements)

References 6 publications

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“…However, finite difference methods can be avoided to solve the problem in this specific case, because the price of the VA contract has an analytical representation that includes an integral averaging Black–Scholes European put prices over the policyholder's future lifetime distribution (see, e.g.,, Hardy, ;, ).…”

Section: Pricing the Va Contractmentioning

confidence: 99%

Risk Management of Policyholder Behavior in Equity‐Linked Life Insurance

MacKay¹,

Augustyniak²,

Bernard³

et al. 2015

J of Risk & Insurance

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The financial guarantees embedded in variable annuity contracts expose insurers to a wide range of risks, lapse risk being one of them. When policyholders' lapse behavior differs from the assumptions used to hedge variable annuity contracts, the effectiveness of dynamic hedging strategies can be significantly impaired. By studying how the fee structure and surrender charges affect surrender incentives, we obtain new theoretical results on the optimal surrender region and use them to design a marketable contract that is never optimal to lapse.

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Section: Pricing the Va Contractmentioning

confidence: 99%

Risk Management of Policyholder Behavior in Equity‐Linked Life Insurance

MacKay¹,

Augustyniak²,

Bernard³

et al. 2015

J of Risk & Insurance

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“…The literature on valuation and hedging VAs is vast and includes, for example, Milevsky and Posner (2001), Boyle and Hardy (2003), Ulm (2008), Bauer et al (2008), Marquardt et al (2008), van Haastrecht et al (2009 and Bacinello et al (2011). Typically, a VA issued by an insurance company has various product features such as death benefit protection options, living benefit protection options and lifetime income options.…”

Section: Introductionmentioning

confidence: 99%

Less-Expensive Valuation and Reserving of Long-Dated Variable Annuities When Interest Rates and Mortality Rates Are Stochastic

Fergusson

2020

ASTIN Bull.

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Variable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing for dependence between financial and insurance markets. Under a simplified case of independence, the results show that when the discounted index is modelled as a time-transformed squared Bessel process, less-expensive valuation and reserving is achieved regardless of the short rate model or the mortality model.

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“…A direct way to calibrate this is to use life table data. In Ulm [16,17], he emphasized the valuation of GMDB products under mortality laws, such as the De Moivre law of mortality and the Makeham law of mortality. A similar consideration could be found in Liang et al [18].…”

Section: Introductionmentioning

confidence: 99%

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Yong

Guan

et al. 2019

Mathematics

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Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

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Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws

Cited by 25 publications

References 6 publications

Risk Management of Policyholder Behavior in Equity‐Linked Life Insurance

Risk Management of Policyholder Behavior in Equity‐Linked Life Insurance

Less-Expensive Valuation and Reserving of Long-Dated Variable Annuities When Interest Rates and Mortality Rates Are Stochastic

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

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