The value of a liability cash flow in discrete time subject to capital requirements

Engsner, Hampus; Lindensjö, Kristoffer; Lindskog, Filip

doi:10.1007/s00780-019-00408-0

Cited by 11 publications

(10 citation statements)

References 28 publications

(63 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Secondly, hybrid products based on a combination of actuarial and financial components are more and more present on the markets (for instance, life insurance products with optional payoffs) and require then a new adjusted valuation principle. Different principles have been proposed in the literature in order to price these hybrid products (see, e.g., Møller, 2002;Malamud et al, 2008;Möhr, 2011;Pelsser and Stadje, 2014;Pelsser and Ghalehjooghi, 2016;Dhaene et al, 2017;Barigou and Dhaene, 2019;Delong et al, 2019a,b;Engsner et al, 2020 and many others). Our article contributes to this literature by proposing a novel decomposition method with a clear separation of risks that are hedgeable on financial markets, risks that can be reduced by pooling, and a remaining part evaluated by taking into account solvency guidelines.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel three-step projection algorithm to valuate hybrid contracts by decomposing their payoff in three parts: a financial, hedgeable part, a diversifiable actuarial part, and a residual part that is neither hedgeable nor diversifiable. The first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Möhr (2011) proposed a valuation framework based on replication over multiple one-year time periods by a periodically updated portfolio of assets. In that framework, the split of the total asset portfolio into the value of insurance liabilities and capital funds is based on an acceptability condition related to the expected return for capital investor (see also Engsner et al, 2017Engsner et al, , 2020.…”

Section: Introductionmentioning

confidence: 99%

Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

View full text Add to dashboard Cite

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.

show abstract

“…The setting and the valuation approach we consider are similar to those considered in Engsner et al [13]. An essential difference here is that we acknowledge that an agent who assigns a value to possible future dividends and capital injections from managing a run-off of a liability may consider a valuation functional depending on a set of pricing measures, in the incomplete market setting, rather than a single one.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, there is a significant literature on market-consistent insurance valuation covering single-period, multiple-period and continuous-time valuation problems with varying assumptions on the financial market forming the basis for designing replicating portfolios of varying degrees of sophistication. We refer (in chronological order) to Grosen and Jørgensen [16], Malamud et al [19], Wüthrich et al [27], Möhr [20], Tsanakas et al [26], Wüthrich and Merz [28], Pelsser and Stadje [21], Engsner et al [14], Delong et al [9], Barigou and Dhaene [3], Engsner et al [13], and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Although we assume that the replicating portfolio is chosen to ensure that the valuation of the liability cash flow is market consistent, we do not discuss market consistency in detail since this was treated in detail in Engsner et al [13] and the material on market consistency in Engsner et al [13] applies without any modification also in the present paper. However, we emphasise that we advocate choosing a replicating portfolio in agreement with what recommended by EIOPA in [10,Article 38] in Article 38(h) on the Reference Undertaking: "the assets are selected in such a way that they minimise the Solvency Capital Requirement for market risk that the reference undertaking is exposed to".…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple-prior valuation of cash flows subject to capital requirements

Engsner¹,

Lindskog²,

Thoegersen³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

The value of a liability cash flow in discrete time subject to capital requirements

Cited by 11 publications

References 28 publications

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

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

Insurance Valuation: A Two-Step Generalised Regression Approach

Multiple-prior valuation of cash flows subject to capital requirements

Contact Info

Product

Resources

About