A market- and time-consistent extension for the EIOPA risk-margin

A.S. Ghalehjooghi; A. Pelsser

doi:10.1007/s13385-023-00343-7

A market- and time-consistent extension for the EIOPA risk-margin

A.S. Ghalehjooghi^*, A. Pelsser

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this paper, we investigate market- and time-consistent valuation of life-insurance liabilities, which are long-dated by nature. To obtain a market- and time-consistent value, the "two-step market evaluation" introduced by Pelsser and Stadje (Math Finance 24:25-65, 2014) is used to evaluate a hybrid payoff with underlying hedgeable financial and (partially) unhedgeable actuarial risks. The resulting time-consistent and market-consistent (TCMC) price captures the dynamics of the risk drivers over the lifetime of the contract. We show that the EIOPA standard-formula for the risk-margin is not time-consistent, and we construct a time-consistent version of the risk-margin that captures the extra uncertainties from the process dynamics. EIOPA's standard-formula for the Risk-Margin is compared to the TCMC price for a simple unit-linked contract and we show that the effects of time-inconsistency are increasing with maturity and are significant for long-dated contracts.

Original language	English
Number of pages	23
Journal	European Actuarial Journal
DOIs	https://doi.org/10.1007/s13385-023-00343-7
Publication status	E-pub ahead of print - 1 Feb 2023

Keywords

MERGING ACTUARIAL JUDGMENT
VALUATION
COHERENT
OPTIONS

Access to Document

10.1007/s13385-023-00343-7

Cite this

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title = "A market- and time-consistent extension for the EIOPA risk-margin",

abstract = "In this paper, we investigate market- and time-consistent valuation of life-insurance liabilities, which are long-dated by nature. To obtain a market- and time-consistent value, the {"}two-step market evaluation{"} introduced by Pelsser and Stadje (Math Finance 24:25-65, 2014) is used to evaluate a hybrid payoff with underlying hedgeable financial and (partially) unhedgeable actuarial risks. The resulting time-consistent and market-consistent (TCMC) price captures the dynamics of the risk drivers over the lifetime of the contract. We show that the EIOPA standard-formula for the risk-margin is not time-consistent, and we construct a time-consistent version of the risk-margin that captures the extra uncertainties from the process dynamics. EIOPA's standard-formula for the Risk-Margin is compared to the TCMC price for a simple unit-linked contract and we show that the effects of time-inconsistency are increasing with maturity and are significant for long-dated contracts.",

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N2 - In this paper, we investigate market- and time-consistent valuation of life-insurance liabilities, which are long-dated by nature. To obtain a market- and time-consistent value, the "two-step market evaluation" introduced by Pelsser and Stadje (Math Finance 24:25-65, 2014) is used to evaluate a hybrid payoff with underlying hedgeable financial and (partially) unhedgeable actuarial risks. The resulting time-consistent and market-consistent (TCMC) price captures the dynamics of the risk drivers over the lifetime of the contract. We show that the EIOPA standard-formula for the risk-margin is not time-consistent, and we construct a time-consistent version of the risk-margin that captures the extra uncertainties from the process dynamics. EIOPA's standard-formula for the Risk-Margin is compared to the TCMC price for a simple unit-linked contract and we show that the effects of time-inconsistency are increasing with maturity and are significant for long-dated contracts.

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