Research

19 pages, 1435 KiB

Open AccessArticle

Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data

by Rocco Roberto Cerchiara and Francesco Acri

Risks 2020, 8(3), 74; https://doi.org/10.3390/risks8030074 - 06 Jul 2020

Cited by 1 | Viewed by 3413

We studied the volatility assumption of non-life premium risk under the Solvency II Standard Formula and developed an empirical model on real data, the Danish fire insurance data. Our empirical model accomplishes two things. Primarily, compared to the present literature, this paper innovates [...] Read more.

We studied the volatility assumption of non-life premium risk under the Solvency II Standard Formula and developed an empirical model on real data, the Danish fire insurance data. Our empirical model accomplishes two things. Primarily, compared to the present literature, this paper innovates the fitting of Danish fire insurance data using a composite model with a random threshold. Secondly we prove, by fitting the Danish fire insurance data, that for large insurance companies the volatility of the standard formula is higher than the volatility estimated with internal models such as composite models, also taking into account the dependence between attritional and large claims. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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12 pages, 848 KiB

Open AccessArticle

Systemic Risk and Insurance Regulation ^†

by Fabiana Gómez and Jorge Ponce

Risks 2018, 6(3), 74; https://doi.org/10.3390/risks6030074 - 27 Jul 2018

Cited by 5 | Viewed by 2986

Abstract

This paper provides a rationale for the macro-prudential regulation of insurance companies, where capital requirements increase in their contribution to systemic risk. In the absence of systemic risk, the formal model in this paper predicts that optimal regulation may be implemented by capital [...] Read more.

This paper provides a rationale for the macro-prudential regulation of insurance companies, where capital requirements increase in their contribution to systemic risk. In the absence of systemic risk, the formal model in this paper predicts that optimal regulation may be implemented by capital regulation (similar to that observed in practice, e.g., Solvency II ) and by actuarially fair technical reserve. However, these instruments are not sufficient when insurance companies are exposed to systemic risk: prudential regulation should also add a systemic component to capital requirements that is non-decreasing in the firm’s exposure to systemic risk. Implementing the optimal policy implies separating insurance firms into two categories according to their exposure to systemic risk: those with relatively low exposure should be eligible for bailouts, while those with high exposure should not benefit from public support if a systemic event occurs. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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38 pages, 1997 KiB

Open AccessArticle

Surrender Risk in the Context of the Quantitative Assessment of Participating Life Insurance Contracts under Solvency II

by Tobias Burkhart

Risks 2018, 6(3), 66; https://doi.org/10.3390/risks6030066 - 27 Jun 2018

Cited by 3 | Viewed by 6690

Abstract

Participating life insurance contracts entitle the policyholder to participate in the company’s annual surplus. Typically, they are also equipped with a surrender option that allows the policyholder to terminate the contract prior to maturity, receiving a predetermined surrender value. The option interacts with [...] Read more.

Participating life insurance contracts entitle the policyholder to participate in the company’s annual surplus. Typically, they are also equipped with a surrender option that allows the policyholder to terminate the contract prior to maturity, receiving a predetermined surrender value. The option interacts with (often cliquet-style) interest guarantees that are a key feature of traditional participating contracts. Surrender options can considerably affect an insurer’s liabilities and bear material risks. This paper addresses the recognition of those risks in the quantitative assessment of a heterogeneous insurance portfolio under Solvency II, taking into account the complex interrelation between minimum interest guarantees, reserving requirements, and profit sharing. The lapse risk module of the Solvency II standard formula requires the identification of portfolio segments that are exposed to a specific change of surrender rates (long-term increase/decrease, one-off increase). We provide a heuristic that identifies homogeneous risk groups in the sense that the respective stress would increase the insurer’s liabilities. Our approach can be used to derive an appropriate segmentation in practical applications. We further analyze implications of the segmentation on the Risk Margin (as part of the Technical Provisions under Solvency II) and discuss consequences of policyholder options on the calculation of Going Concern Reserve and Surplus Funds. To illustrate our findings, we set up a stochastic balance sheet and cash flow projection model for a stylized life insurance company. We conclude that current methods used for practical applications underestimate surrender risk under Solvency II and that the proposed modeling refinements may improve the appropriateness of solvency ratios for participating business. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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26 pages, 1086 KiB

Open AccessArticle

A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies

by Anne-Sophie Krah, Zoran Nikolić and Ralf Korn

Risks 2018, 6(2), 62; https://doi.org/10.3390/risks6020062 - 11 Jun 2018

Cited by 21 | Viewed by 7567

Abstract

The Solvency II directive asks insurance companies to derive their solvency capital requirement from the full loss distribution over the coming year. While this is in general computationally infeasible in the life insurance business, an application of the Least-Squares Monte Carlo (LSMC) method [...] Read more.

The Solvency II directive asks insurance companies to derive their solvency capital requirement from the full loss distribution over the coming year. While this is in general computationally infeasible in the life insurance business, an application of the Least-Squares Monte Carlo (LSMC) method offers a possibility to overcome this computational challenge. We outline in detail the challenges a life insurer faces, the theoretical basis of the LSMC method and the necessary steps on the way to a reliable proxy modeling in the life insurance business. Further, we illustrate the advantages of the LSMC approach via presenting (slightly disguised) real-world applications. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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13 pages, 878 KiB

Open AccessFeature PaperArticle

The Effect of Non-Proportional Reinsurance: A Revision of Solvency II Standard Formula

by Gian Paolo Clemente

Risks 2018, 6(2), 50; https://doi.org/10.3390/risks6020050 - 02 May 2018

Cited by 2 | Viewed by 4357

Abstract

Solvency II Standard Formula provides a methodology to recognise the risk-mitigating impact of excess of loss reinsurance treaties in premium risk modelling. We analyse the proposals of both Quantitative Impact Study 5 and Commission Delegated Regulation highlighting some inconsistencies. This paper tries to [...] Read more.

Solvency II Standard Formula provides a methodology to recognise the risk-mitigating impact of excess of loss reinsurance treaties in premium risk modelling. We analyse the proposals of both Quantitative Impact Study 5 and Commission Delegated Regulation highlighting some inconsistencies. This paper tries to bridge main pitfalls of both versions. To this aim, we propose a revision of non-proportional adjustment factor in order to measure the effect of excess of loss treaties on premium risk volatility. In this way, capital requirement can be easily assessed. As numerical results show, this proposal appears to be a feasible and much more consistent approach to describe the effect of non-proportional reinsurance on premium risk. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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17 pages, 587 KiB

Open AccessArticle

The Cascade Bayesian Approach: Prior Transformation for a Controlled Integration of Internal Data, External Data and Scenarios

by Bertrand K. Hassani and Alexis Renaudin

Risks 2018, 6(2), 47; https://doi.org/10.3390/risks6020047 - 27 Apr 2018

Cited by 1 | Viewed by 3015

Abstract

According to the last proposals of the Basel Committee on Banking Supervision, banks or insurance companies under the advanced measurement approach (AMA) must use four different sources of information to assess their operational risk capital requirement. The fourth includes ’business environment and internal [...] Read more.

According to the last proposals of the Basel Committee on Banking Supervision, banks or insurance companies under the advanced measurement approach (AMA) must use four different sources of information to assess their operational risk capital requirement. The fourth includes ’business environment and internal control factors’, i.e., qualitative criteria, whereas the three main quantitative sources available to banks for building the loss distribution are internal loss data, external loss data and scenario analysis. This paper proposes an innovative methodology to bring together these three different sources in the loss distribution approach (LDA) framework through a Bayesian strategy. The integration of the different elements is performed in two different steps to ensure an internal data-driven model is obtained. In the first step, scenarios are used to inform the prior distributions and external data inform the likelihood component of the posterior function. In the second step, the initial posterior function is used as the prior distribution and the internal loss data inform the likelihood component of the second posterior function. This latter posterior function enables the estimation of the parameters of the severity distribution that are selected to represent the operational risk event types. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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23 pages, 901 KiB

Open AccessArticle

Operational Choices for Risk Aggregation in Insurance: PSDization and SCR Sensitivity

by Xavier Milhaud, Victorien Poncelet and Clement Saillard

Risks 2018, 6(2), 36; https://doi.org/10.3390/risks6020036 - 13 Apr 2018

Viewed by 3244

Abstract

This work addresses crucial questions about the robustness of the PSDization process for applications in insurance. PSDization refers to the process that forces a matrix to become positive semidefinite. For companies using copulas to aggregate risks in their internal model, PSDization occurs when [...] Read more.

This work addresses crucial questions about the robustness of the PSDization process for applications in insurance. PSDization refers to the process that forces a matrix to become positive semidefinite. For companies using copulas to aggregate risks in their internal model, PSDization occurs when working with correlation matrices to compute the Solvency Capital Requirement (SCR). We examine how classical operational choices concerning the modelling of risk dependence impacts the SCR during PSDization. These operations refer to the permutations of risks (or business lines) in the correlation matrix, the addition of a new risk, and the introduction of confidence weights given to the correlation coefficients. The use of genetic algorithms shows that theoretically neutral transformations of the correlation matrix can surprisingly lead to significant sensitivities of the SCR (up to 6%). This highlights the need for a very strong internal control around the PSDization step. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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18 pages, 969 KiB

Open AccessArticle

On Central Branch/Reinsurance Risk Networks: Exact Results and Heuristics

by Florin Avram and Sooie-Hoe Loke

Risks 2018, 6(2), 35; https://doi.org/10.3390/risks6020035 - 12 Apr 2018

Cited by 2 | Viewed by 2735

Abstract

Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact [...] Read more.

Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact answers. Occasionally, reductions to one dimension or heuristic simplifications yield explicit approximations, which may be useful for getting qualitative insights. In this paper, we study two such problems: the ruin problem for a two-dimensional CB network under a new mathematical model, and the problem of valuation of two-dimensional CB networks by optimal dividends. A common thread between these two problems is that the one dimensional reduction exploits the concept of invariant cones. Perhaps the most important contribution of the paper is the questions it raises; for that reason, we have found it useful to complement the particular examples solved by providing one possible formalization of the concept of a multi-dimensional risk network, which seems to us an appropriate umbrella for the kind of questions raised here. Full article

(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)

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