A lattice approach to evaluate participating policies in a stochastic interest rate framework

Costabile, Massimo; Massabó, Ivar; Russo, Emilio; Staino, Alessandro

doi:10.1016/j.cam.2020.113212

Cited by 4 publications

(6 citation statements)

References 26 publications

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“…A similar discretization for the interest rate may be also found in Costabile et al. (2021) and De Angelis et al. (2022).…”

Section: Framework and Process Discretizationssupporting

confidence: 63%

“…The interest rate process (2.1) is discretized by generating a binomial tree having a number of nodes that grows up linearly with the number of time steps, as detailed in the Costabile and Massabó (2010) approach. A similar discretization for the interest rate may be also found in Costabile et al (2021) andDe Angelis et al (2022).…”

Section: The Interest Rate Process Discretizationmentioning

confidence: 73%

“…The idea is similar to the one adopted by Costabile et al (2021) and De Angelis et al (2022) to develop their bivariate lattice, but the lattice construction is different on some aspects as detailed hereafter and, more important, it has a different aim, that is, the introduction of the mortality risk in the evaluation process. Under this perspective, we choose to evaluate survival zero coupon bonds paying one unit of money at maturity in case of survival and mortality bonds characterized by traditional fixed coupons at regular intervals and a principal at maturity becoming random and linked with realized longevity or mortality experiences.…”

Section: Valuation Of Bonds Through a Bivariate Discrete Modelmentioning

confidence: 99%

“…The values associated with the lattice nodes are generated in order to replicate the diffusion part of each process, while the probability associated with each branch is defined in a way that the first and second order local moments of the discrete model replicate, at least within the limit, the corresponding continuous-time versions. Such a methodology, originally proposed by Costabile and Massabó (2010), has been already applied in the field of financial and actuarial mathematics to discretize the processes appearing in more complex models used to solve different evaluation problems as reported in Russo and Staino (2018b), Costabile et al (2021), andDe Angelis et al (2022), to name just a few. The latter models develop different bivariate lattice models to evaluate interest sensitive claims under stochastic volatility or, when considering stochastic interest rates like the framework proposed in this manuscript, options paying discrete dividends, variable annuities in presence of guaranteed minimum withdrawal benefit, and participating policies.…”

Section: Introductionmentioning

confidence: 99%

“…Such a methodology, originally proposed by Costabile and Massabó (2010), has been already applied in the field of financial and actuarial mathematics to discretize the processes appearing in more complex models used to solve different evaluation problems as reported in Russo and Staino (2018b), Costabile et al. (2021), and De Angelis et al. (2022), to name just a few.…”

Section: Introductionmentioning

confidence: 99%

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Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach

Devolder,

Russo,

Staino

2024

ASTIN Bull.

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We propose a flexible lattice model to evaluate the fair value of insurance contracts embedding both financial and actuarial risk factors. Flexibility relies on the ability of the model to manage different specifications of the correlated processes governing interest rate, mortality, and fund dynamics, thus allowing the insurer to make the most appropriate choices. The model is also able to handle additional guarantees like a surrender opportunity for which explicit formulae are not available being it similar to an American derivative. The model discretizes mortality and interest rate dynamics through two different binomial lattices and then combines them into a bivariate tree characterized by the presence of four branches for each node. The probability of each branch is defined to replicate the correlation affecting the two processes. The bivariate model is useful to compute the value of survival zero coupon bond. When adding another source of risk, such as the fund dynamics for evaluating fund-linked insurance products, we model it through a bivariate tree that captures the influence of the interest rate on its drift term. Then, the mortality risk is embedded by defining a trivariate tree presenting eight branches emanating from each node with probabilities defined in order to capture the correlations of the processes. Extensive numerical experiments assess the model accuracy by considering some stylized policies, but the model application is not limited to them being it able to manage different contract specifications.

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“…A similar discretization for the interest rate may be also found in Costabile et al. (2021) and De Angelis et al. (2022).…”

Section: Framework and Process Discretizationssupporting

confidence: 63%

Section: The Interest Rate Process Discretizationmentioning

confidence: 73%

Section: Valuation Of Bonds Through a Bivariate Discrete Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach

Devolder,

Russo,

Staino

2024

ASTIN Bull.

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A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders

Angelis

Marchis

Martire

et al. 2022

Decisions Econ Finan

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In a market where a stochastic interest rate component characterizes asset dynamics, we propose a flexible lattice framework to evaluate and manage options on equities paying discrete dividends and variable annuities presenting some provisions, like a guaranteed minimum withdrawal benefit. The framework is flexible in that it allows to combine financial and demographic risk, to embed in the contract early exercise features, and to choose the dynamics for interest rates and traded assets. A computational problem arises when each dividend (when valuing an option) or withdrawal (when valuing a variable annuity) is paid, because the lattice lacks its recombining structure. The proposed model overcomes this problem associating with each node of the lattice a set of representative values of the underlying asset (when valuing an option) or of the personal subaccount (when valuing a variable annuity) chosen among all the possible ones realized at that node. Extensive numerical experiments confirm the model accuracy and efficiency.

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Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees

Kirkby

Aguilar²

2022

Scandinavian Actuarial Journal

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A lattice approach to evaluate participating policies in a stochastic interest rate framework

Cited by 4 publications

References 26 publications

Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach

Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach

A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders

Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees

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