Tails, Risk Measures, Tail Dependencies and their Influence on Risk Based Capital (original) (raw)

Estimating the risk-adjusted capital is an affair in the tails

2010

(Re)insurance companies need to model their liabilities' portfolio to compute the risk-adjusted capital (RAC) needed to support their business. The RAC depends on both the distribution and the dependence functions that are applied among the risks in a portfolio. We investigate the impact of those assumptions on an important concept for (re)insurance industries: the diversification gain. Several copulas are considered in order to focus on the role of dependencies. To be consistent with the frameworks of both Solvency II and the Swiss Solvency Test, we deal with two risk measures: the Value-at-Risk and the expected shortfall. We highlight the behavior of different capital allocation principles according to the dependence assumptions and the choice of the risk measure.

A Multivariate Analysis for Risk Capital Estimation in Insurance Industry: Vine Copulas

Asian Development Policy Review, 2017

This paper deals with the risks aggregation issue and adequate risk capital modeling within a multivariate setting. Focusing on the non-life insurance risk module, we examine the sensitivity of capital requirement to the dependence among risks for a multi-line Tunisian insurance firm. Such a context entails a nonlinear dependence of risks problem whose resolution may be intended by means of multivariate copulas. The relevant analysis relies profoundly on the dependence modeling by the means of vine copulas which are a flexible technique to model multivariate distributions constructed using a cascade of bivariate copulas. Under various confidence levels in VaR and TailVaR, the reached findings reveal the advantages of D-Vine copula in modeling inhomogeneous structures of dependency due to its flexibility of use in a simulation context. Practitioners and regulators can explore our conclusions for the assessment of risk capital under Solvency 2, which is based on stochastic models. Contribution/ Originality: This study uses new methodology based on CD-vine copulas estimation to investigate the sensitivity of solvency capital requirement to the dependence pattern between the losses derived from non-life business lines of a Tunisian insurance company.

Risk Dependence, Solvency and Stress Testing for Insurers

SSRN Electronic Journal, 2017

Identifying the relevant risk factors and their interdependence is central to understanding the risk exposures and vulnerabilities of a financial institution. It is needed for risk management, solvency assessment and stress testing. We assemble a unique dataset of risk factors relevant for insurers which are different than for banks, although they share exposure to financial asset risks such as corporate bonds and equities. We use this dataset to estimate risk factor correlations to better understand their dependence structure. We find that correlation between non-financial risk factors is very low (usually insignificant), between financial risk factors on the order of 30-50%, and a mix between the financial and non-financial risk factors. We fit marginal distributions to each of the risk factors, and using a t-copula we present simple simulation application to analyze the solvency of three types of insurers (pure life, pure property and casualty, mixed). We do so using both the point estimates of the correlations as well as the 95% upper and lower bound estimates to explore the sensitivity of stress impact on insurers' solvency. Our analysis should help provide an empirical basis to regulators in calibrating solvency regimes and to insurers to understand their risk sensitivities and capital needs.

Operational-Risk Dependencies and the Determination of Risk Capital

SSRN Electronic Journal, 2000

With the advent of Basel II, risk-capital provisions need to also account for operational risk. The specification of dependence structures and the assessment of their effects on aggregate risk-capital are still open issues in modeling operational risk. In this paper, we investigate the potential consequences of adopting the restrictive Basel's Loss Distribution Approach (LDA), as compared to strategies that take dependencies explicitly into account. Drawing on a real-world database, we fit alternative dependence structures, using parametric copulas and nonparametric tail-dependence coefficients, and discuss the implications on the estimation of aggregate risk capital. We find that risk-capital estimates may increase relative to that derived for the LDA when accounting explicitly for the presence of dependencies. This phenomenon is not only be due to the (fitted) characteristics of the data, but also arise from the specific Monte Carlo setup in simulation-based risk-capital analysis.

Risk based capital and capital allocation in insurance

The science of capital allocation has made significant advances in our understanding of allocation and use of risk based capital. Yet there is limited theoretical guidance on which risk measure is consistent with value maximisation and no well developed economic theory underlying the risk measures. Different firms use different risk measures and there is no agreement on the appropriate risk measure. Risk measures are applied inconsistently for different risks, different lines of business, products and divisions. For insurer pricing the price of risk should vary with the type of risk under consideration yet most risk based capital approaches implicitly use a common price of risk based on a firm wide expected cost of capital for pricing. Recent developments in capital allocation of risk capital for solvency and by-line pricing indicate a new direction is required. This paper highlights the importance of risk measure and discusses the insolvency default option value. It also discusses allocation by line and fair pricing, frictional costs and market imperfections and issues of risk based capital in a value maximizing framework.

Copula models of economic capital for life insurance companies

Applied Econometrics

The objective of this project is to construct, select, calibrate and validate a practically applicable copula internal model of economic capital for insurance companies. Copula methodology makes it possible to address multiple dependent risk factors. We identify the relevant set of asset and liability variables, and suggest a copula model for the joint distribution of these variables. Estimates of economic capital can be based on the tails of this joint distribution. Models are implemented in open source software (R and Microsoft EXCEL) and tested using simulated asset/liability data. The results are presented as a finished software product which can be utilized for customization and direct user application. The novelty of the approach consists in estimating interdependent mortality, morbidity, lapse and investment risks in one multivariate model. In particular, we address the challenges that life insurance companies face in the low interest environment. This approach requires a methodology of copula model comparison and selection and implementation of Monte Carlo simulation to the estimation of economic capital.

Risk Aggregation, Dependence Structure and Diversification Benefit

SSRN Electronic Journal, 2000

Insurance and reinsurance live and die from the diversification benefits or lack of it in their risk portfolio. The new solvency regulations allow companies to include them in their computation of risk-based capital (RBC). The question is how to really evaluate those benefits.

Risk-Based Capital and Credit Insurance Portfolios

Financial Markets, Institutions & Instruments, 2010

This paper analyzes the risk-management practices of a vulnerable credit insurer by studying the effects of time-varying correlations, asset risks and loan maturities on the risk-based capital that backs credit insurance portfolios. Since asset correlations may change over a business cycle, we have analyzed these effects by means of a one-factor Gaussian stochastic model as part of an extended contingent claims analysis. Our results show the need to account for cyclical changes to correlations in the pricing of credit insurance. When compared with the reserve of risk-based capital recommended by the Basel II Internal Ratings-Based (IRB) approach, our model provides a better capital buffer against extreme credit losses, especially in times of recession and/or in a risky business environment. Using a risk-adjusted performance metric (RAPM), we find insurers perform better when insuring relatively short-term loans. We also make several policy recommendations on creating a reserve of risk-based capital to protect against possible loan losses.

Article The Impact of Reinsurance Strategies on Capital Requirements for Premium Risk in Insurance

2016

New risk-based solvency requirements for insurance companies across European markets have been introduced by Solvency II and will come in force from 1 January 2016. These requirements, derived by a Standard Formula or an Internal Model, will be by far more risk-sensitive than the required solvency margin provided by the current legislation. In this regard, a Partial Internal Model for Premium Risk is developed here for a multi-line Non-Life insurer. We follow a classical approach based on a Collective Risk Model properly extended in order to consider not only the volatility of aggregate claim amounts but also expense volatility. To measure the effect of risk mitigation, suitable reinsurance strategies are pursued. We analyze how naï ve coverage as conventional Quota Share and Excess of Loss reinsurance may modify the exact moments of the distribution of technical results. Furthermore, we investigate how alternative choices of commission rates in proportional treaties may affect the variability of distribution. Numerical results are also figured out in the last part of the paper with evidence of different effects for small and large companies. The main reasons for these differences are pointed out.

Bounds for value at risk – the approach based on copulas with homogeneous tails

The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for the detailed study of the tail behaviour of the multivariate copulas. In this paper we investigate the class of copulas having homogeneous lower tails. We show that having only such information on the structure of dependence of returns from assets is enough to get estimates on Value at Risk of the multiasset portfolio in terms of Value at Risk of one-asset portfolios.