Approaches to modeling operational risks of frequency and severity in insurance (original) (raw)
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Scenario Analysis Approach for Operational Risk in Insurance Companies
ACTA VŠFS, 2020
The article deals with the possibility of calculating the required capital in insurance companies allocated to operational risk under Solvency II regulation and the aim of this article is to come up with model that can be use in insurance companies for calculating operational risk required capital. In the article were discussed and compared the frequency and severity distributions where was chosen Poisson for frequency and Lognormal for severity. For the calculation, was used only the real scenario and data from small CEE insurance company to see the effect of the three main parameters (typical impact, Worst case impact and frequency) needed for building the model for calculation 99,5% VaR by using Monte Carlo simulation. Article comes up with parameter sensitivity and/or ratio sensitivity on calculating capital. From the database arose two conclusions related to sensitivity where the first is that the impact of frequency is much higher in the interval (0;1) than above the interval t...
Insurance: Mathematics and Economics, 2011
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies different insurance policies in the context of capital reduction for a range of extreme loss models and insurance policy scenarios in a multi-period, multiple risk settings. A Loss Distributional Approach (LDA) for modelling of the annual loss process, involving homogeneous compound Poisson processes for the annual losses, with heavy-tailed severity models comprised of α-stable severities is considered. There has been little analysis of such models to date and it is believed, insurance models will play more of a role in OpRisk mitigation and capital reduction in future. The first question of interest is when would it be equitable for a bank or financial institution to purchase insurance for heavy-tailed OpRisk losses under different insurance policy scenarios? The second question pertains to Solvency II and addresses quantification of insurer capital for such operational risk scenarios. Considering fundamental insurance policies available, in several two risk scenarios, we can provide both analytic results and extensive simulation studies of insurance mitigation for important basic policies. The intention being to address questions related to VaR reduction under Basel II, SCR under Solvency II and fair insurance premiums in OpRisk for different extreme loss scenarios. In the process we provide closed-form solutions for the distribution of loss process and claims process in an LDA structure as well as closed-form analytic solutions for the Expected Shortfall, SCR and MCR under Basel II and Solvency II. We also provide closed-form analytic solutions for the annual loss distribution of multiple risks including insurance mitigation.
Operational Risk and Insurance: Quantitative and Qualitative Aspects
Social Science Research Network, 2004
This paper incorporates insurance contracts into an operational risk model based on idiosyncratic and common shocks. A key feature of the approach is the explicit modelling of residual risk inherent in insurance contracts, such as counterparty default, payment uncertainty and liquidity risk due to delayed payments. Compared to the standard haircut approach, the net loss distribution exhibits a larger weight on the tail. Thereby an underestimation of extreme losses and loss clusters is avoided. The difference between the models is statistically significant for the means and the 99.9%-quantiles of the distribution.
Modeling Frequency and Severity of Insurance Claims in an Insurance Portfolio
American Journal of Applied Mathematics and Statistics, 2020
Premium pricing is always a challenging task in general insurance. Furthermore, frequency of the insurance claims plays a major role in the pricing of the premiums. Severity in insurance on the other hand, can either be the amount paid due to a loss or the size of the loss event. For insurer’s to be in a position to settle claims that occur from existing portfolios of policies in future, it is necessary that they adequately model past and current data on claim experience then use the models to project the expected future experience in claim amounts. In addition, non-life insurance companies are faced with problems when modeling claim data i.e selecting appropriate statistical distribution and establishing how well it fits the claimed data. Therefore, the study presents a framework for choosing the most suitable probability distribution and fitting it to the past motor claims data and the parameters are estimated using maximum likelihood method (MLE). The goodness of fit of frequency...
Revista Mexicana de Economía y Finanzas, 2017
Main objective is to quantifying capital requirements of Operational Risk based on Bayesian inference by using an operational risk advanced measurement model, particularly when historical information is not available for a typical Mexican financial institution. The model employs a conjugated Poisson-Gamma distribution and feeds from experts interviews information so parameters can be measured. Monte Carlo simulations based on an interval for experts expected value of a loss event were generated from which following results were collected: 1) operational risk value can be gotten with insufficient information at a 95% of confidence, 2) expected losses tend to increase when experts expected events increase as well, 3) a positive correlation between operational risk and experts expected events exist, 4) frequency and severity of losses are smaller at the beginning and higher as operational risk value is been approached, then both decrease again. Described results depend highly on assumptions model and experts opinion and information available. Methodology proposed stands for an operational risk advanced measurement, so a specific strategy can be formulated for the firm to avoid losses and therefore operational risk.
A Risk Theoretical Model for Assessing the Solvency Profile of a General Insurer 1
2003
A risk theoretical simulation model is here applied in order to assess the default risk of a general insurer along a medium-term time horizon. Different ruin barriers are regarded and by the results of the simulation model is then built up a Risk vs Return trade-off to analyse the most appropriate strategies in order to satisfy the insurer targets. Clearly not only profitability level but also risk measures must be taken into account, with special reference to minimum capital levels required by the insurance regulators. At this regard different suitable strategies may be pursued and, among these, reinsurance is one of the most relevant for the insurance risk management. Only conventional covers as quota share and excess of loss reinsurance are here regarded, but it is emphasized how effective they can be on the risk/return profile of a general insurer. To increase the volume of business is a natural target for the management of an insurance company, but that may cause a need of eith...
2012
The Basel II accord requires banks to put aside a capital buffer against unexpected operational losses, resulting from inadequate or failed internal processes, people and systems or from external events. Under the sophisticated Advanced Measurement Approach banks are given the opportunity to develop their own model to estimate operational risk. This report focus on a loss distribution approach based on a set of real data. First a comprehensive data analysis was made which suggested that the observations belonged to a heavy tailed distribution. An evaluation of commonly used distributions was performed. The evaluation resulted in the choice of a compound Poisson distribution to model frequency and a piecewise defined distribution with an empirical body and a generalized Pareto tail to model severity. The frequency distribution and the severity distribution define the loss distribution from which Monte Carlo simulations were made in order to estimate the 99.9% quantile, also known as the the regulatory capital. Conclusions made on the journey were that including all operational risks in a model is hard, but possible, and that extreme observations have a huge impact on the outcome.
2009
To meet the Basel II regulatory requirements for the Advanced Measurement Approaches, the bank's internal model must include the use of internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal control systems. Quantification of operational risk cannot be based only on historical data but should involve scenario analysis. Historical internal operational risk loss data have limited ability to predict future behaviour moreover, banks do not have enough internal data to estimate low frequency high impact events adequately. Historical external data are difficult to use due to different volumes and other factors. In addition, internal and external data have a survival bias, since typically one does not have data of all collapsed companies. The idea of scenario analysis is to estimate frequency and severity of risk events via expert opinions taking into account bank environment factors with reference to events that have occurred (or may have occurred) in other banks. Scenario analysis is forward looking and can reflect changes in the banking environment. It is important to not only quantify the operational risk capital but also provide incentives to business units to improve their risk management policies, which can be accomplished through scenario analysis. By itself, scenario analysis is very subjective but combined with loss data it is a powerful tool to estimate operational risk losses. Bayesian inference is a statistical technique well suited for combining expert opinions and historical data. In this paper, we present examples of the Bayesian inference methods for operational risk quantification.
The structural modelling of operational risk via Bayesian inference: Combining loss data …
Journal of Operational Risk
To meet the Basel II regulatory requirements for the Advanced Measurement Approaches, the bank's internal model must include the use of internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal control systems. Quantification of operational risk cannot be based only on historical data but should involve scenario analysis. Historical internal operational risk loss data have limited ability to predict future behaviour moreover, banks do not have enough internal data to estimate low frequency high impact events adequately. Historical external data are difficult to use due to different volumes and other factors. In addition, internal and external data have a survival bias, since typically one does not have data of all collapsed companies. The idea of scenario analysis is to estimate frequency and severity of risk events via expert opinions taking into account bank environment factors with reference to events that have occurred (or may have occurred) in other banks. Scenario analysis is forward looking and can reflect changes in the banking environment. It is important to not only quantify the operational risk capital but also provide incentives to business units to improve their risk management policies, which can be accomplished through scenario analysis. By itself, scenario analysis is very subjective but combined with loss data it is a powerful tool to estimate operational risk losses. Bayesian inference is a statistical technique well suited for combining expert opinions and historical data. In this paper, we present examples of the Bayesian inference methods for operational risk quantification.
Statistical models for operational risk management
Physica A: Statistical Mechanics and its …, 2004
The Basel Committee on Banking Supervision has released, in the last few years, recommendations for the correct determination of the risks to which a banking organization is subject. This concerns, in particular, operational risks, which are all those management events that may determine unexpected losses. It is necessary to develop valid statistical models to measure and, consequently, predict, such operational risks. In the paper we present the possible approaches, including our own proposal, which is based on Bayesian networks.