Cliquet-style return guarantees in a regime switching Lévy model

Hieber, Peter

doi:10.1016/j.insmatheco.2016.11.009

Cited by 21 publications

(15 citation statements)

References 39 publications

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“…We recall that Fourier transform techniques have also been applied in the context of cliquet option pricing in e.g. [9] and [11].…”

Section: Cliquet Option Pricing With Fourier Transform Techniquesmentioning

confidence: 99%

Cliquet option pricing in a jump-diffusion Lévy model

Heß¹

2018

Modern Stochastics: Theory and Applications

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We investigate the pricing of cliquet options in a jump-diffusion model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a drifted Lévy process entailing a Brownian diffusion component as well as compound Poisson jumps. We also derive representations for the density and distribution function of the emerging Lévy process. In this setting, we infer semi-analytic expressions for the cliquet option price by two different approaches. The first one involves the probability distribution function of the driving Lévy process whereas the second draws upon Fourier transform techniques. With view on sensitivity analysis and hedging purposes, we eventually deduce representations for several Greeks while putting emphasis on the Vega.

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“…We recall that Fourier transform techniques have also been applied in the context of cliquet option pricing in e.g. [9] and [11].…”

Section: Cliquet Option Pricing With Fourier Transform Techniquesmentioning

confidence: 99%

Cliquet option pricing in a jump-diffusion Lévy model

Heß¹

2018

Modern Stochastics: Theory and Applications

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“…To study the valuation issue in a different perspective, scholars turned to the regime-switching model, which was used to investigate the performance of an object subject to the economic changes in financial markets. In the literature, interest readers can refer to Fan et al [19], Siu et al [5], Ignatieva et al [20], and Hieber [21].…”

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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“…Recently, more complicated settings are adopted to study the EIA valuation problem. To capture how the status of the market affects the value of an equity-linked life insurance contract, both [18] and [6] render the valuation problem under a regime-switching framework while the latter involves stochastic volatility models with jumps. [5] consider ratchet EIAs with the quanto feature.…”

mentioning

confidence: 99%

“…There are ways to specify the mortality model. Some directly use life table data, see [21] and [18], therein. Others apply analytical laws of mortality, see [27] and [28] where the constant force of mortality and De Moivre's mortality law are adopted, respectively.…”

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confidence: 99%

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Valuation of cliquet-style guarantees with death benefits

Yong

Yang

2023

JIMO

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<p style='text-indent:20px;'>In this paper, we consider the problem of valuing an equity-linked insurance product with a cliquet-style payoff. The premium is invested in a reference asset whose dynamic is modeled by a geometric Brownian motion. The policy delivers a payment to the beneficiary at either a fixed maturity or the time upon the insured's death, whichever comes first. The residual lifetime of a policyholder is described by a random variable, assumed to be independent of the asset price process, and its distribution is approximated by a linear sum of exponential distributions. Under such characterization, closed-form valuation formulae are derived for the contract considered. Moreover, a discrete-time setting is briefly discussed. Finally, numerical examples are provided to illustrate our proposed approach.</p>

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Cliquet-style return guarantees in a regime switching Lévy model

Cited by 21 publications

References 39 publications

Cliquet option pricing in a jump-diffusion Lévy model

Cliquet option pricing in a jump-diffusion Lévy model

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Valuation of cliquet-style guarantees with death benefits

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