Valuation of Hybrid Financial and Actuarial Products in Life Insurance by a Novel Three-Step Method

Deelstra, Griselda; Devolder, Pierre; Gnameho, Kossi; Hieber, Peter

doi:10.1017/asb.2020.25

Cited by 21 publications

(36 citation statements)

References 34 publications

(37 reference statements)

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“…Pelkiewicz et al, 2020 for a review on the Solvency II risk margin). In the literature, different approaches were considered to value the residual risk, either by an Esscher valuation operator (Deelstra et al, 2020), a standard-deviation principle (Barigou and Delong, 2020, Ghalehjooghi and Pelsser, 2021, Chen et al, 2020, Delong et al, 2019b, or a cost-of-capital principle (Pelsser, 2011).…”

Section: Discussionmentioning

confidence: 99%

“…However, there is still an open debate on how to appropriately treat the residual part and define an appropriate "risk margin" (see e.g., Pelkiewicz et al, 2020 for a review on the Solvency II risk margin). In the literature, different approaches were considered to value the residual risk, either by an Esscher valuation operator (Deelstra et al, 2020), a standard-deviation principle (Delbaen et al, 2019b;Barigou and Delong, 2020;Chen et al, 2020;Ghalehjooghi and Pelsser, 2021) or a cost-of-capital principle (Pelsser, 2011).…”

Section: Discussionmentioning

confidence: 99%

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Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

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Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

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“…Hereto, we identify the hedgeable part of a product's payoff and identify the remaining types of risk. This is of importance in a fair valuation study of hybrid financial and actuarial products in life insurance as in, for example, [2][3][4][5][6]. We consider a financial setting consisting of an initial market, characterized by its flow of information F and its underlying traded assets S, and a random time-the death time τ-that might not be observed through F when it occurs.…”

Section: Introductionmentioning

confidence: 99%

Mortality/Longevity Risk-Minimization with or without Securitization

2021

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This paper addresses the risk-minimization problem, with and without mortality securitization, à la Föllmer–Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes situations in which the correlation between the market model and the time of death is arbitrary general, and hence leads to the case of a market model where there are two levels of information—the public information, which is generated by the financial assets, and a larger flow of information that contains additional knowledge about the death time of an insured. By enlarging the filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction. Our key tool lies in our optional martingale representation, which states that any martingale in the large filtration stopped at the death time can be decomposed into precise orthogonal local martingales. This allows us to derive the dynamics of the value processes of the mortality/longevity securities used for the securitization, and to decompose any mortality/longevity liability into the sum of orthogonal risks by means of a risk basis. The first main contribution of this paper resides in quantifying, as explicitly as possible, the effect of mortality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtration. Our second main contribution consists of finding risk-minimizing strategies with insurance securitization by investing in stocks and one (or more) mortality/longevity derivatives such as longevity bonds. This generalizes the existing literature on risk-minimization using mortality securitization in many directions.

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“…In Artzner et al [2] and Deelstra et al [8] it is argued that diversifiable insurance risk should only be assigned a value corresponding to the P-expectation of such risk since the law of large numbers applies if the insurance company may form arbitrarily large portfolios. In our setting this argument is not valid since the corporate entity to which the insurance company's aggregate liability is transferred is a separate entity (referred to as reference undertaking in Solvency II) that may not be merged with other corporate entities.…”

Section: Introductionmentioning

confidence: 99%

Multiple-prior valuation of cash flows subject to capital requirements

Engsner¹,

Lindskog²,

Thoegersen³

2021

Preprint

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We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound economic properties that applies to any liability cash flow. Whereas a replicable cash flow is assigned the market value of the replicating portfolio, a cash flow that is not fully replicable is assigned a value which is the sum of the market value of a replicating portfolio and a positive margin. The margin is a direct consequence of considering a hypothetical transfer of the liability cash flow from an insurance company to an empty corporate entity set up with the sole purpose to manage the liability run-off, subject to repeated capital requirements, and considering the valuation of this entity from the owner's perspective taking model uncertainty into account. Aiming for applicability, we consider a detailed insurance application and explain how the optimisation problems over sets of probability measures can be cast as simpler optimisation problems over parameter sets corresponding to parameterised density processes appearing in applications.

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Valuation of Hybrid Financial and Actuarial Products in Life Insurance by a Novel Three-Step Method

Cited by 21 publications

References 34 publications

Insurance Valuation: A Two-Step Generalised Regression Approach

Insurance Valuation: A Two-Step Generalised Regression Approach

Mortality/Longevity Risk-Minimization with or without Securitization

Multiple-prior valuation of cash flows subject to capital requirements

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