Variable annuities: A unifying valuation approach

Bacinello, Anna Rita; Millossovich, Pietro; Olivieri, Annamaria; Pitacco, Ermanno

doi:10.1016/j.insmatheco.2011.05.003

Cited by 157 publications

(113 citation statements)

References 22 publications

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“…In particular, [9] studied the case of stochastic interest rate and stochastic volatility corresponding to a 1 = 1/2, a 2 = 0, a 3 = 1/2. In [11], the authors considered the case of deterministic interest rate and stochastic volatility with a 2 = {0, 1} and a 3 = {1/2, 1, 3/2}.…”

Section: Stochastic Modelmentioning

confidence: 99%

“…where B * λ (t) is the Wiener process and some specific forms for the drift µ λ (·) and volatility σ λ (·) are considered in, for example, [9,24]. If we need to model a portfolio of the contracts, then the dependence between the policyholder deaths can be introduced via models for the number of deaths in a given population driven by some common factors as in the Lee-Carter model and its extensions reviewed in, e.g., [34], or under the CreditRisk+ framework for mortality developed recently in [37,38].…”

Section: Stochastic Modelmentioning

confidence: 99%

“…The direct integration method was developed further in [7,8] using the Gauss-Hermite quadrature and cubic interpolations. The authors of [9] consider many VA riders under the stochastic interest rate and stochastic volatility if the policyholder withdraws at the pre-defined contractual rate or completely surrenders the contract. Their pricing is accomplished either by the ordinary MC or Least-Squares MC to account for the optimal surrender.…”

Section: Introductionmentioning

confidence: 99%

“…Their pricing is accomplished either by the ordinary MC or Least-Squares MC to account for the optimal surrender. Often, pricing of the VA riders is considered under the assumption of a geometric Brownian motion for the risky asset underlying the contract, though a few papers looked at extensions such as stochastic interest rate and/or stochastic volatility, see, e.g., [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

Shevchenko

Luo

2016

Risks

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Abstract:In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework and review the existing numerical methods. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is easier to implement and faster when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation.

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Section: Stochastic Modelmentioning

confidence: 99%

Section: Stochastic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

Shevchenko

Luo

2016

Risks

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“…This is not to say that actually determining the optimal strategies within a risk-neutral valuation framework is trivial. It may require the solution of optimal control problems akin to the valuation of American or Bermudan options, and a great number of contributions in actuarial science have taken this approach to evaluate various types of contracts (Milevsky and Salisbury, 2006;Ulm, 2006;Bauer et al, 2008;Dai et al, 2008;Bauer et al, 2010;Bacinello et al, 2011, among many others).…”

Section: What Potentially Drives Policyholder Behavior? a Review Of Tmentioning

confidence: 99%

Policyholder Exercise Behavior in Life Insurance: The State of Affairs

Bauer

Gao²,

Moenig

et al. 2017

North American Actuarial Journal

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The paper presents a review of structural models of policyholder behavior in life insurance.We first discuss underlying drivers of policyholder behavior in theory and survey the implications of different models. We then turn to empirical behavior and appraise how well different drivers explain observations. The key contributions lie in the synthesis and the systematic categorization of different approaches. The paper should provide a foundation for future studies, and we describe some important directions for future research in the conclusion.

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Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Sharma

Selvamuthu

Natarajan

2022

Appl Stoch Models Bus & Ind

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Pricing a variable annuity (VA) is traditionally based on models with standard Brownian motion (BM). The assumption of independent increments in the BM is not always realistic as the price process of the risky assets exhibit a long-range dependency. To model such assets, a fractional Brownian motion (FBM) with Hurst parameter)is an appropriate model. However, due to arbitrage in an FBM model and jumps in stock returns, we consider in this work a mixed FBM (MFBM) model with jumps and evaluate variable annuities with different riders. We analyze the proposed model numerically to see the impact of mortality risk. We perform a comparison between eight stochastic models to obtain the best-suited mortality model, for a dataset of the US male population. Finally, we obtain the price of VA guarantees using the forecasted values from the fitted mortality model.

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Variable annuities: A unifying valuation approach

Cited by 157 publications

References 22 publications

A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework

Policyholder Exercise Behavior in Life Insurance: The State of Affairs

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

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