Valuation of equity-indexed annuities with regime-switching jump diffusion risk and stochastic mortality risk

Qian, Linyi; Wang, Rongming; Wang, Shuai

doi:10.1007/s11425-012-4524-6

Cited by 5 publications

(5 citation statements)

References 20 publications

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“…For example, refs. [3,10,21] examined the valuation of various EIAs in a jump diffusion setting. Refs.…”

Section: Literature Reviewmentioning

confidence: 99%

“…As mentioned earlier, our market model is incomplete, and thus, lots of martingale pricing measures exist. Next, we employ the Esscher transform in [9,10] to find a martingale pricing measure for fair valuation. Define Y T = log S t S 0 .…”

Section: The Modeling Assumptionsmentioning

confidence: 99%

“…Lin et al [9] investigated the EIA valuation problems when the reference stock was driven by a regime-switching GBM. Qian et al [10] assumed that the reference risky asset obeyed the stochastic process with regime switching and studied the pricing of EIAs with stochastic mortality risk under this model. Qian et al [11] applied the local risk-minimization method to hedge EIAs when the stock followed a jump-diffusion process with regime switching.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Equity-Indexed Annuities under a Stochastic Dividend Model

Shan

Shu

2023

Mathematics

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In this paper, we examine the valuations of equity-indexed annuities (EIAs) when their reference stocks distribute stochastic dividends. Due to the fact that stocks typically pay dividends at discrete times after the payment dates are announced, pricing EIAs with dividends is deemed to be practically significant. We directly model the discrete dividend payments using the jump diffusion process with regime switching, and then determine the dynamics of the stock price. The equivalent martingale measure of fair valuation in incomplete markets is determined by employing the Esscher transform. Finally, the pricing formulas of several of the most common EIAs in the market under the stochastic dividend model are obtained. Our model incorporates and extends the present literature on EIAs with accurate and effective valuation methods.

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“…For example, refs. [3,10,21] examined the valuation of various EIAs in a jump diffusion setting. Refs.…”

Section: Literature Reviewmentioning

confidence: 99%

Section: The Modeling Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pricing Equity-Indexed Annuities under a Stochastic Dividend Model

Shan

Shu

2023

Mathematics

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“…first studied the valuation of variable annuity guarantees under a multivariate regimeswitching model. Qian et al (2012) considered the valuation of equity-indexed annuities with regime-switching jump-diffusion model and stochastic mortality, where the jump-component is described by a compound Poisson process and is independent of the modulating Markov chain. So jumps in the share price may not be triggered by state transitions.…”

Section: Introductionmentioning

confidence: 99%

Pricing annuity guarantees under a double regime-switching model

Fan

Shen

Siu

et al. 2015

Insurance: Mathematics and Economics

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“…The regime switching can be interpreted as substantial changes in the state or condition of the underlying economy, which are modeled by a continuous-time Markov process, including the adjustment in the economical structure, the evolution of the market mode as well as the cycle changes in the economy and business. In actuarial science, Yuen (2010) studied the valuation problem of Asian option and EIAs via the trinomial tree method under the assumption: the stock price dynamics were a Markov-modulated geometric Brownian motion; Lin et al (2009) considered the EIA pricing problem under a regime switching model when the dynamic of the market value of an underlying asset was driven by a generalized Markov-modulated geometric Brownian motion; Qian (2012) extended the model of Lin et al (2009) which was a regime-switching jump-diffusion model and the mortality satisfied Lévy process. Also, there are many papers in option pricing problems.…”

Section: Introductionmentioning

confidence: 99%

Pricing Equity-indexed Annuities When Discrete Dividends Follow a Markov-Modulated Jump Diffusion Model

Yan¹,

Shu²,

Kan³

2015

Communications in Statistics - Theory and Methods

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The Equity-Indexed annuities (EIAs) provide investors not only a minimum rate of return but also an opportunity to gain a potential profit that is linked to the performance of an equity index, typically S&P 500. These properties make EIAs become very popular in the market and receive considerable attention in the actuarial literature. In this article, we investigate the Equity-Indexed annuities valuation when the discrete dividend payments follow a Markov-modulated jump diffusion model. Using the generalized Itô formula, we obtain the explicit solution for dividend payments of the model. From Dividend Discount theory, which implies that the stock price should be equal to the net present value of all its future dividend payments, the stock price process is then deduced. Within this framework, closed-form solution to the point-to-point EIA pricing problem is derived via the characteristic function of the occupation times.

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Valuation of equity-indexed annuities with regime-switching jump diffusion risk and stochastic mortality risk

Cited by 5 publications

References 20 publications

Pricing Equity-Indexed Annuities under a Stochastic Dividend Model

Pricing Equity-Indexed Annuities under a Stochastic Dividend Model

Pricing annuity guarantees under a double regime-switching model

Pricing Equity-indexed Annuities When Discrete Dividends Follow a Markov-Modulated Jump Diffusion Model

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