✎✎✎ Two Operational Variables In An Operational Environment

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Two Operational Variables In An Operational Environment



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A new risk was born in the mids known as operational risk. Though its application varied by institutions—Basel II for banks and Solvency II for insurance companies—the idea stays the same. Firms are interested in operational risk because exposure can be fatal. Hence, it has become one of the major risks of the financial sector. In this study, we are going to define operational risk in addition to its applications regarding banks and insurance companies. Moreover, we will discuss the different measurement criteria related to some examples and applications that explain how things work in real life. Operational risk existed longer than we know, but its concept was not interpreted until after the year when one of the oldest banks in London, Barings bank, collapsed because of Nick Leeson, one of the traders, due to unauthorized speculations.

A wide variety of definitions are used to describe operational risk of which the following is just a sample cf. Moosa [ 1 , pages ]. The Basel II Committee, however, defined operational risk as the risk of loss resulting from inadequate or failed internal processes, people and systems, or from external events cf. Currently, the lack of operational risk loss data is a major issue on hand but once the data sources become available, a collection of methods will be progressively implemented. In , the Basel Committee started a series of surveys and statistics regarding operational risks that most banks encounter. The idea was to develop and correct measurements and calculation methods.

Additionally, the European Commission also started preparing for the new Solvency II Accord, taking into consideration the operational risk for insurance and reinsurance companies. As so, and since Basel and Solvency accords set forth many calculation criteria, our interest in this paper is to discuss the different measurement techniques for operational risk in financial companies. We will also present the associated mathematical and actuarial concepts as well as a numerical application regarding the Advanced Measurement Approach, like Loss Distribution, Extreme Value Theory and Bayesian updating techniques, and propose more robust measurement models for operational risk.

At the end, we will point out the effects of the increased use of insurance against major operational risk factors and incorporate these in the performance analyses. Basel II cites three ways of calculating the capital charges required in the first pillar of operational risk. The three methods, in increasing order of sophistication, are as follows. Regardless of the method chosen for the measurement of the capital requirement for operational risk, the bank must prove that its measures are highly solid and reliable. Each of the three approaches have specific calculation criteria and requirements, as explained in the following sections.

Banks using the BIA method have a minimum operational risk capital requirement equal to a fixed percentage of the average annual gross income over the past three years. Hence, the risk capital under the BIA approach for operational risk is given by where , stands for gross income in year , and is set by the Basel Committee. The results of the first two Quantitative Impact Studies QIS conducted during the creation of the Basel Accord showed that on average of the annual gross income was an appropriate fraction to hold as the regulatory capital. Gross income is defined as the net interest income added to the net noninterest income.

This figure should be gross of any provisions unpaid interest , should exclude realized profits and losses from the sale of securities in the banking book, which is an accounting book that includes all securities that are not actively traded by the institution, and exclude extraordinary or irregular items. The capital charge for each business line is calculated by multiplying gross income by a factor assigned to a particular business line, see Table 1. As in the Basic Indicator Approach, the total capital charge is calculated as a three-year average over all positive gross income GI as follows: The second QIS issued by the Basel Committee, covering the same institutions surveyed in the first study, resulted in , , and as appropriate rates in calculating regulatory capital as a percentage of gross income.

Before tackling the third Basel approach AMA , we give a simple example to illustrate the calculation for the first two approaches. In Table 2 , we see the Basic and Standardized Approaches for the 8 business lines. The main difference between the BIA and the SA is that the former does not distinguish its income by business lines. As shown in the tables, we have the annual gross incomes related to year 3, year 2, and year 1. With the Basic Approach, we do not segregate the income by business lines, and therefore, we have a summation at the bottom. Moreover, the Basic Indicator Approach does not take into consideration negative gross incomes. We obtain a result of Similarly to the BI Approach, the Standardized Approach has a Beta factor for each of the business lines as some are considered riskier in terms of operational risk than others.

Hence, we have eight different factors ranging between 12 and 18 percent as determined by the Basel Committee. For this approach, we calculate a weighted average of the gross income using the business line betas. Any negative number over the past years is converted to zero before an average is taken over the three years. In this case, we end up with a capital charge of around As depicted in the previous example, the capital charge relating to the Standardized Approach was lower than that of the Basic Approach. This, however, is not always the case, thus causing some criticism and raising questions such as why would a bank use a more sophisticated approach when the simpler one would cost them less?

In this section, we show that the capital charge could vary between different approaches. To start with, let and , where , is the gross income related to the business line , and is the total gross income. Compiling these equations, we have and, consequently Therefore, the BIA produces a higher capital charge than the SA under the condition that the alpha factor under the former is greater than the weighted average of the individual betas under the latter. There is no guarantee that the condition will be satisfied, which means that moving from the BIA to the SA may or may not produce a lower capital charge cf.

Moosa [ 1 ]. Several Quantitative Impact Studies QIS have been conducted for a better understanding of operational risk significance on banks and the potential effects of the Basel II capital requirements. Furthermore, to account for national impact, a joint decision of many participating countries resulted in the QIS 4 being undertaken. Before analyzing the quantitative approaches, let us take a look at the minimum regulatory capital formula and definition cf. Basel Committee on Banking Supervision [ 4 ]. Total risk-weighted assets are determined by multiplying capital requirements for market risk and operational risk by The Total Regulatory Capital has its own set of rules according to 3 tiers. The Quantitative Impact Study QIS survey requested banks to provide information on their minimum regulatory capital broken down by risk type credit, market, and operational risk and by business line.

Banks were also asked to exclude any insurance and nonbanking activities from the figures. The survey covered the years to Overall, more than banks provided some information on the operational risk section of the QIS. These banks included 57 large, internationally active banks called type 1 banks in the survey and more than 80 smaller type 2 banks from 24 countries. The RMG used the data provided in the QIS to gain an understanding of the role of operational risk capital allocations in banks and their relationship to minimum regulatory capital for operational risk. These results are summarized in Table 3.

The results suggest that on average, operational risk capital represents about 15 percent of overall economic capital, though there is some dispersion. These results suggest that a reasonable level of the overall operational risk capital charge would be about 12 percent of minimum regulatory capital. BCBS [ 5 ]. The calculation was Here, is the minimum regulatory capital for bank in year and is the gross income for bank in year. Given these calculations, the results of the survey are reported in Table 4. Table 4 presents the distribution in two ways—the statistics of all banks together and the statistics according to the two types of banks by size.

The first three columns of the table contain the median, mean, and the weighted average of the values of the alphas using gross income to weight the individual alphas. The remaining columns of the table present information about the dispersion of alphas across banks. For each business line, the capital requirement will be calculated according to a certain percentage of gross income attributed for that business line. The first three columns of the table present the median, mean and weighted average values of the betas for each business line, and the rest of the columns present the dispersion across the sample used for the study.

As with the Basic Approach, the mean values tend to be greater than the median and the weighted average values, thus reflecting the presence of some large individual beta estimates in some of the business lines. Through statistical testing of the equality of the mean and the median, the results do not reject the null hypothesis that these figures are the same across the eight business lines. These diffusions observed in the beta estimate could be reflected in the calibration difference of the internal economic capital measures of banks. Additionally, banks may also be applying differing definitions of the constitution of operational risk loss and gross income as these vary under different jurisdictions.

However, the use of these approaches must be approved and verified by the national supervisor. The AMA is based on the collection of loss data for each event type. Each bank is to measure the required capital based on its own loss data using the holding period and confidence interval determined by the regulators 1 year and In addition, the Basel II Committee decided to allow the use of insurance coverage to reduce the capital required for operational risk, but this allowance does not apply to the SA and the BIA.

A bank intending to use the AMA should demonstrate accuracy of the internal models within the Basel II risk cells eight business lines seven risk types shown in Table 7 , relevant to the bank, and satisfy some criteria including the following. The relative weight of each source and the combination of sources are decided by the banks themselves; Basel II does not provide a regulatory model. The application of the AMA is, in principle, open to any proprietary model, but the methodologies have converged over the years and thus specific standards have emerged. As a result, most AMA models can now be classified into the following.

The Loss Distribution Approach LDA is a parametric technique primarily based on historic observed internal loss data potentially enriched with external data. Established on concepts used in actuarial models, the LDA consists of separately estimating a frequency distribution for the occurrence of operational losses and a severity distribution for the economic impact of the individual losses. The implementation of this method can be summarized by the following steps see Figure 1.

For each business line and risk category, we establish two distributions cf. Dahen [ 6 ] : one related to the frequency of the loss events for the time interval of one year the loss frequency distribution , and the other related to the severity of the events the loss severity distribution. To establish these distributions, we look for mathematical models that best describe the two distributions according to the data and then we combine the two using Monte Carlo simulation to obtain an aggregate loss distribution for each business line and risk type. Finally, by summing all the individual VaRs calculated at We start with defining some technical aspects before demonstrating the LDA cf. Maurer [ 7 ]. Definition 2. The capital charge is the So with as the random number of events, the total loss is where is the th loss amount.

The capital charge would then be. Here, the capital charge would result in. The capital charge in this case would be a For the LDA method which expresses the aggregate loss regarding each business line event type as the sum of individual losses, the distribution function of the aggregate loss, noted as , would be a compound distribution cf. Frachot et al. So the capital-at-risk CaR for the business line and event type corresponds to the quantile of as follows: and, as with the second definition explained previously, the CaR for the element is equal to the sum of the expected loss EL and the unexpected Loss UL : Finally, by summing all the the capital charges , we get the aggregate CaR across all business lines and event types: see Figure 2 The Basel committee fixed an to obtain a realistic estimation of the capital required.

However, the problem of correlation remains an issue here as it is unrealistic to assume that the losses are not correlated. For this purpose, Basel II authorised each bank to take correlation into consideration when calculating operational risk capital using its own internal measures. The IMA method cf. BCBS [ 2 ] provides carefulness to individual banks on the use of internal loss data, while the method to calculate the required capital is uniformly set by supervisors.

In implementing this approach, supervisors would impose quantitative and qualitative standards to ensure the integrity of the measurement approach, data quality, and the adequacy of the internal control environment. Under the IM approach, capital charge for the operational risk of a bank would be determined using the following. The overall capital charge for a particular bank is the simple sum of all the resulting products. Let us reformulate all the points mentioned above; calculating the expected loss for each business line so that for a business line and an event type , the capital charge is defined as where represents the expected loss, is the scaling factor, and is the Risk Profile Index.

The Basel Committee on Banking Supervision proposes that the bank estimates the expected loss as follows: where is the exposure indicator, is the probability of an operational risk event, and is the loss given event. The committe proposes to use a risk profile index as an adjustment factor to capture the difference of the loss distribution tail of the bank compared to that of the industry wide loss distribution.

The idea is to capture the leptokurtic properties of the bank loss distribution and then to transform the exogeneous factor into an internal scaling factor such that By definition, the of the industry loss distribution is one. If the bank loss distribution has a fatter tail than the industry loss distribution would be larger than one. So two banks which have the same expected loss may have different capital charge because they do not have the same risk profile index. The questions are designed to focus on the principal drivers and controls of operational risk across a broad range of applicable operational risk categories, which may vary across banks.

These can vary significantly between banks due to business mix differences and may also be customized along business lines within an organization. Note that scoring of response options will often not be linear. The Basel Committee did not put any kind of mathematical equation regarding this method, but working with that method made banks propose a formula related which is where is the exposure indicator, the risk score, and the scale factor.

Risk is defined as the combination of severity and frequency of potential loss over a given time horizon and is linked to the evaluation of scenarios. Scenarios are potential future events. Their evaluation involves answering two fundamental questions: firstly, what is the potential frequency of a particular scenario occurring and secondly, what is its potential loss severity? Banks with their activities and their control environment should build scenarios describing potential events of operational risks. Then experts are asked to give opinions on probability of occurrence i. Furthermore, the overall sbAMA process must be supported by a sound and structured organisational framework and by an adequate IT infrastructure. The sbAMA comprises six main steps, which are illustrated in Figure 3.

Outcome from sbAMA will be statistically compatible with that arising from LDA so as to enable a statistically combination technique. The most adequate technique to combine LDA and sbAMA is Bayesian inference, which requires experts to set the parameters of the loss distribution see Figure 3 for illustration. Solvency II imposes a capital charge for the operational risk that is calculated regarding the standard formula given by regulators or an internal model which is validated by the right authorities. For the enterprises that have difficulties running an internal model for operational risk, the standard formula can be used for the calculation of this capital charge.

The QIS allow the committee to adjust and develop the formulas in response to the observations and difficulties encountered by the enterprises. The breakdown of the SCR is shown in Figure 4. With the calculation of the BSCR, In relation to previous surveys, respondents suggested that the following. Before going into the formula let us define some notations cf. For the purpose of this calculation, technical provisions should not include the risk margin and should be without deduction of recoverables from reinsurance contracts and special purpose vehicles. For the purpose of this calculation, technical provisions should not include the risk margin and should be without deduction of recoverables from reinsurance contracts and special purpose vehicle. Finally the standard formula resulted to be where ,.

A wide variety of risks exist, thus necessitating their regrouping in order to categorize and evaluate their threats for the functioning of any given business. The concept of a risk matrix, coined by Richard Prouty , allows us to highlight which risks can be modeled. Experts have used this matrix to classify various risks according to their average frequency and severity as seen in Figure 5. There are in total four general categories of risk. Catastrophic risks are modeled using the Extreme Value Theory and Bayesian techniques. Classifying the risks as per the matrix allows us to identify their severity and frequency and to model them independently by using different techniques and methods.

We are going to see in the following sections the different theoretical implementation and application of different theories and models regarding operational risk. Chapter 2 discusses the challenges of the operational environment from the perspective of the small unit leaders The Environmental Operating Principles relate to the human environment and apply to all aspects of business and operations. The EOPs require a recognition and acceptance of individual responsibility from senior leaders to the newest team members. In addition, operational and mission variables are discussed as a way for engineer planners to gain understanding of the environment in which base camps are planned and the operational impacts that base camp development can have.

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Karam 1 and F. Figure 12 shows that the Bayesian approach has a more stable behavior around the true value of even when just Two Operational Variables In An Operational Environment Personal Narrative: Jud Reincke My Grandpa data points are available, which is not the case with the MLE and the SW estimators. To start with, let andwhereis the gross income related to Two Operational Variables In An Operational Environment business lineand is the total Two Operational Variables In An Operational Environment income.

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