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2015/02/01 16:49:06

Assessment of operational risks: options are possible

Importance of assessment of operational risks about which risk managers so long went on, is gradually realized by increasing number of the Russian banks - promotes it as the regulator strengthening control in the field and growth of the threats connected with operational risks (for example, statistics of frauds both clients, and employees and even heads of banks is adverse).

Content

Introduction

Importance of assessment of operational risks about which risk managers so long went on, is gradually realized by increasing number of the Russian banks - promotes it as the regulator strengthening control in the field and growth of the threats connected with operational risks (for example, statistics of frauds both clients, and employees and even heads of banks is adverse).

However the need understanding which is, certainly, the first step on the way of creation of a modern oeprational risk management system not always leads to further development of this direction. In many small Russian banks, despite existence of provisions, techniques, etc. of documents, the analysis comes down to measure definition of OR included in calculation of capital adequacy ratio and to formal filling of "base of events" on the basis of data of accounting records. And in the near future uses of information from such base for calculations and the more so, acceptance of management decisions is not planned, and work is often conducted only for formal meeting requirements of the regulator.

However, and the regulator does not hurry to designate distinct perspectives of application of the saved-up data within advanced approaches yet, all attention paying adaptations to the Russian conditions of the Basel requirements in the field of assessment of credit risks. But, in spite of the fact that (judging by the current situation in the field of credit risk management) "advanced" approaches of assessment of operating rooms if will be allowed – that in the test mode and in a small amount of the largest Russian banks, correctly organized work on collecting and internal and external data after all can pay off.

In - the first, based on the internal reporting constructed on the analysis of competently created base of events of OR it is possible to make the justified operational and strategic decisions connected with changes of organizational structure, business processes, number of staff, implementation of new services, technologies, motivation of employees, etc. already now.

Secondly, despite application at the moment (and in the short term) the simplest approach to calculation of the capital under OR, already more than 2 years the regulator in parallel with the existing regulatory requirements to the capital recommends to create in addition the "internal procedures of assessment" it sufficiency which are guided by the Basel recommendations. It is supposed that by 2017 this work will have to be carried out in all banks.

In this article the most widespread valuation methods of the capital under an operational risk, possibilities of their use, taking into account features of application in the Russian practice are described, but the conditions imposing the restrictions for application of advanced methods connected with the organization of process, corporate culture risk management in bank are not considered. However it is necessary to notice that without their accomplishment use of advanced methods the regulator is not allowed.

The naive approaches recommended by Basel committee

Approach on the basis of the basic indicator

The simplified approach on the basis of the basic indicator (basic indicator approach - BIA) to calculation of the amount of the capital under operational risks assumes direct dependence of level of an operational risk on organization activity scales which, in turn, are defined by the gained income. It is natural that at the same time neither internal procedures of control, nor risk exposure by different activities are considered though the Russian documents regulating risk management regardless of the applied method of calculation recommend to build the culture of operational risk management at perhaps higher level. The general formula recommended by Basel committee and Provision of the Central Bank of the Russian Federation. N 346-P match, but national regulators can independently define specifics of calculation of net income.

Image:Formula1.png‎
, where
Image:Formula1 1.png‎
- the gross income (the amount of net interest and net not interest income) calculated by averaging for the selected analysis period (normal three last years, for calculation of an average are used only positive values, averaging is made at the rate of amount of positive values in the selected analysis period);
Image:Formula1 2.png‎
- coefficient of reservation of the capital (this indicator is set by both Basel committee and the Russian regulator on one at the level - 15%).

The standardized approach

This approach, as well as previous, is based on logic of dependence of risk on income, however it is considered more exact at the expense of a binding of the coefficient of reservation to each business line, (standard activities) and determination on each of them separately of the amount of the reserved capital. The negative income on one business line, according to the Basel recommendations, can "be compensated" positive on other, however the national regulator can set more tough procedure of payments.

Calculation by this method is made in three last years on the following formula:

Image:Formula2.png‎
, where<
Image:Formula2 1.png‎
- the gross income from i-go of a type of activity gained in a year of t;
Image:Formula2 2.png‎
- level of reservation of the capital for i-go of a type of activity;
Image:Formula2 3.png‎
- amount of categories of an operational risk;
Image:Formula2 4.png‎
– the number of the years selected for the analysis. Value of coefficients
Image:Formula2 2.png‎
for standard activities
Activity Β, %
Bank services for individuals 12
Bank service of legal entities 15
Implementation of payments and calculations 18
Agency services 15
Transactions and transactions in security market and urgent financial instruments 18
Rendering banking services to corporate clients, public authorities and local government in capital market 15
Asset management 12
Broker activity 12


Such approach is considered more exact in comparison with approach, the based basic indicator (basic indicator approach - BIA). However among the Russian practicians it also raises a number of doubts.

First, grouping business of lines both in the Basel document, and in Russian 76-T, slightly adapted in this question to specifics of the national banking sector, is focused on excess detailing in the field of transactions in the fodovy markets and the enlarged description of work with retail and corporate clients whereas in terms of a profile of activity of most the Russian banks the last occupy the largest volume in transactions. Certainly, the bank can increase detailing for own managerial purposes, but also calculation of the capital and comparability to external data on OR are possible only in the existing framework designated for selection of activities (business lines).

Secondly - the offered sizes
Image:Formula2 2.png‎
are also a product enough old researches and compromises in the western market. Certainly, at implementation the national regulator will be able to change the sizes of coefficients. And, in this case, the danger of transition to the standardized approach to banks will consist in a possibility of sharp increase in coefficients on those business to lines which include products and transactions which growth of the offer (in terms of the regulator) is too high and needs restriction, pro-cyclical regulation, etc. (how it occurs in the field of reservation of some retail transactions now).

It is also possible to refer cost intensity of application of such method concerning calculation for the basic indicator to minuses, as from the point of view of applied by software, and costs of time of qualified employees.

Anyway, the standardized approach, in our opinion, is more useful in terms of operational risk management - it imposes serious quality requirements of this process at all stages and levels of bank management, and also sets bank thinking of efficiency of each type of the activity taking into account risk.

The alternative standardized approach

The alternative is that for activities "bank services for individuals" and "bank service of legal entities" calculation of the capital is made not based on an average gross income as in the previous option, and proceeding from the value of average balances on the corresponding balance accounts. Calculation of a reserve under possible losses for these types of activity is made on the following formula:

Image:Formula3.png‎
, where

Image:Formula3 1.png‎
– the total amount of the issued credits calculated by averaging for the selected analysis period (three years);
Image:Formula3 2.png‎
– level of reservation of the capital for the corresponding type of activity;
Image:Formula3 3.png‎
– coefficient which value is recommended by Basel committee at the level of 0.035.

For banks – monoliners such approach can be more convenient, in terms of labor input of calculations, than previous, however and all described shortcomings are inherent in it.

"Advanced" (advanced) approaches

Use of advanced approaches (AMA) concerning operational risks was offered Basel committee much earlier, than in "The international convergence of measurement of the capital and standards of the capital: new approaches - the Complete version". So, in January, 2001 in the advisory document (nowadays not operating) "Operational Risk. Supporting Document to the New Basel Capital Accord" were mentioned two methodologies – on the basis of internal estimates and distribution curve of losses. But, unlike the block of credit risks, in the document Basel II did not appear formulas, only the conditions of application of advanced approaches and the requirement to banks and supervisory authorities were concretized. Afterwards they were specified in the next document "Principles of proper management of an operational risk and a role of supervision" in 2011.

Besides, the Basel committee with a certain frequency issued the separate documents devoted to practice on single questions of application of different methods of calculation of the capital under operational risks. At the moment it is possible to speak about creation and application of different techniques by the western banks within such types of the advanced approaches as:
– Internal assessment (IMA)
– Assessment of distribution curve of losses (LDA)
– Assessment on the basis of scoring cards
– Scenario analysis

At the same time the methodology elements which initially appeared within some campaigns can be applied in others, for example, to compensation of a lack of data. Data, can be received from internal and external bases of events, from experts whose surveys are conducted on the special technologies, in turn, which are a component of methodology and directed to identification of factors of a business environment and level of internal control and their influence on risks.

Further it is offered to consider in more detail some techniques of assessment of the capital under OR within the most widespread AMA which automation is possible by own forces or using purchase of the corresponding software.

Internal assessment

This approach is close to the standardized approach (i.e. selection of business lines which, however, can not match eight, offered by the regulator by quantity and structure is supposed) and allows to estimate capital level on the basis of the probability of implementation of an operational risk, the wastage rate estimated by bank in case of its implementation, and also - specifics risk profile of bank and the coefficient offered by the regulator connecting unexpected and expected losses. Calculation of the capital under OR for these types of activity is made on the following formula:

Image:Formula4.png‎
, where

Image:Formula4 1.png‎
- (exposure indicator) indicator of risk exposure of j-go of a type of activity of i-y of category of an operational risk;
Image:Formula4 2.png‎
- probability of implementation of an operational risk of j-go of a type of activity of i-y of category of an operational risk;
Image:Formula4 3.png‎
- the wastage rate in case of implementation of an operational risk of j-go of a type of activity of i-y of category of an operational risk;
Image:Formula4 4.png‎
- level of reservation j-go of a type of activity i-y of category of an operational risk - the factor reflecting a ratio of the amount of unforeseen and foreseeable losses with expected, UL allowing to include in calculation of the capital (is defined by the regulator);
Image:Formula4 5.png‎
- the factor defining the profile of risk of the specific organization allowing to adjust industry average, determined by the regulator taking into account specifics of risk of specific bank;
Image:Formula4 6.png‎
- quantity of types of activity;
Image:Formula4 7.png‎
- amount of categories of an operational risk.

It should be noted that for determination of an individual profile of risk of bank, it actually should do extra work - on plotting of distribution of losses and to define as expected, and unforeseen losses. However economy on a difference in the amount of the capital calculated by two specified methodologies can appear for benefit of internal estimates.

Expression
Image:Formula4 8.png‎
reflects value of expected losses
Image:Formula4 1.png‎
which can be found using the following formula:

Image:Formula5.png‎
, where
Image:Formula5 1.png‎
- mid frequency of emergence of unfavorable events of an operational risk of i-y of category of an operational risk of j-go of a type of activity within a year (is calculated with the help of the second approach described below for map development of risks);
Image:Formula5 2.png‎
- the average value of losses as a result of emergence of an unfavorable event of i-y of category of an operational risk of j-go of a type of activity within a year (is calculated with the help of the second approach described for map development of risks).

Mark and weight (scoring) approach

Sometimes this approach is called also method of scoring cards as one of methods of collection of data on risks is questioning of experts using specially created polling cards reflecting levels of risks and their importance for the specific organization, and also qualities of risk management. Assessment (it is not formalized by Basel committee) capital level under an operational risk of i-y of category of an operational risk of j-go of a type of activity in this case can be written by the following general formula:

Image:Formula6.png‎
, where
Image:Formula6 1.png‎
- (exposure indicator) indicator of risk exposure of j-go of a type of activity of i-y of category of an operational risk;
Image:Formula6 2.png‎
- the scaling coefficient;
Image:Formula6 3.png‎
- risk assessment (value of scoring).

At the same time on the basis of approach of internal assessment value of the capital under an operational risk:

Image:Formula7.png‎
, or
Image:Formula8.png‎


Comparing this expression to the general formula of assessment of the capital under an operational risk, we will note that expression
Image:Formula8 1.png‎
reflects risk assessment, i.e. value
Image:Formula6 3.png‎
, and
Image:Formula8 2 2.png‎
- the scaling coefficient
Image:Formula6 2.png‎
. I.e. the equation of calculation of expected losses
Image:Formula6 1.png‎
includes both a risk indicator value, and risk assessment, for example value of regression model (scoring).

Calculation of the capital under an operational risk offered in this article is made also, as well as in a method of Internal assessment except that expected losses, are estimated using regression (scoring) model:

Image:Formula9.png‎
, where
Image:Formula9 1.png‎
- expected losses of an operational risk of i-y of category of an operational risk of j-go of a type of activity which can be received within a year in timepoint of t;
Image:Formula9 2.png‎
- k-go value of the indicator of an operational risk (risk exposure) which theoretically or is empirically connected with the level of the operational risk accepted by the organization in timepoint of t;
Image:Formula9 3.png‎
- the modified weight of k-go of the indicator of an operational risk of model of multiple regression of j-y of the business line of the organization i-oh categories of an operational risk;
Image:Formula9 4.png‎
- a total quantity of the indicators of risk used in model.

For assessment of values of scales
Image:Formula9 3.png‎
it is used methods of a multiple linear regression. As the analyzed variable (the resulting sign) at creation of model assessment of expected losses
Image:Formula9 1.png‎
of an operational risk calculated on the basis of the analysis of events of an operational risk for the set retrospective period is used. As the risk indicators
Image:Formula9 2.png‎
(explaining factors of regression model) different indicators of risk, financial and/or economic performance, expert and/or objective evaluations of level of control over an operational risk, scoring estimates of risk level, etc. which had or could have an impact on events of an operational risk during the same retrospective period for which assessment of expected losses was calculated can be used.

Thus final calculation of value of the capital under an operational risk by a mark and weight (scoring) method can be written by the following formula:

Image:Formula10.png‎


In addition to assessment of value of the capital this formula allows to exercise also monitoring and control of an operational risk on the basis of the analysis of values of the corresponding indicators used in regression model.

Assessment of distribution curve of losses

The method of recovery of distribution function of losses allows to make more exact assessment of the capital under an operational risk, than the methods mentioned above. Information of the database of the suffered losses of the organization and/or expert evaluations on the basis of which are defined rate of emergence of unfavorable events are for this purpose used and distribution function of losses, in case of these events is estimated.

Assessment of parameters

Mid frequency of emergence of unfavorable events as it was shown above, is defined as follows:

, where

  • weight of expert evaluations of the organization;
  • expert evaluation of frequency of emergence of unfavorable events within a year of the i-y organization of category of an operational risk j-go business of the direction which value of losses belongs to d-mu to the range of losses in timepoint of t;
  • r-I am estimation of frequency of emergence of unfavorable events within a year of the i-y organization of category of an operational risk j-go business of the direction;

  • D – total quantity of ranges of losses of expert evaluations of the organization;

a total quantity of estimations of the i-y organization of category of an operational risk j-go business of the direction on the horizon of the analysis of statistical data.

As expert evaluations data of third parties can be used. In this case expert evaluations are calculated as follows. According to the organizations participating in calculations the maximum amount of the suffered Lmax losses is defined. The necessary number of ranges of losses of D for which mid frequencies of emergence of events of an operational risk which losses from implementation get to the corresponding ranges will be defined is set:

, where


In calculations can are used, both data of events of an operational risk of the organizations, and their expert evaluations. Mid frequency of emergence of the events relating to d-mu to the range of losses is defined as follows:

, where

  • d-y range of losses;
  • expert evaluation of losses as a result of emergence of an unfavorable event of n-y of the i-y organization of category of an operational risk j-go business of the direction relating to l-mu to the range of losses;
  • r-I am estimation of average losses as a result of emergence of unfavorable events of n-y of the i-y organization of category of an operational risk j-go business of the direction;
  • expert evaluation of frequency of emergence of an unfavorable event of n-y of the i-y organization of category of an operational risk j-go business of the direction which value of losses belongs to l-mu to the range of losses, within a year;
  • scale of transactions of the reference organization j-go business of the direction;
  • scale of the transactions n-y of the j-go organization business of the direction;
  • the weight of expert evaluations of n-y of the organization participating in calculations;
  • expert evaluation of frequency of emergence of unfavorable events within a year of n-y of the i-y organization of category of an operational risk j-go business of the direction which value of losses belongs to l-mu to the range of losses;
  • r-I am estimation of frequency of emergence of unfavorable events within a year of n-y of the i-y organization of category of an operational risk j-go business of the direction;

total quantity of ranges of losses of expert evaluations of n-y of the organization; total quantity of estimations of n-y of the organization;

  • N – a total quantity of the organizations, including head.

The average value of losses as a result of emergence of the unfavorable events relating to d-mu to the range of losses is defined by the following formula:

, where

  • scale of the transactions n-y of the j-go organization business of the direction;
  • scale of the transactions n-y of the j-go organization business of the direction;
  • the weight of expert evaluations of n-y of the organization participating in calculations;
  • expert evaluation of losses as a result of emergence of an unfavorable event of n-y of the i-y organization of category of an operational risk j-go business of the direction relating to l-mu to the range of losses;
  • r-I am estimation of average losses as a result of emergence of unfavorable events of n-y of the i-y organization of category of an operational risk j-go business of the direction;
  • expert evaluation of frequency of emergence of an unfavorable event of n-y of the i-y organization of category of an operational risk j-go business of the direction which value of losses belongs to l-mu to the range of losses, within a year;
  • to - I am estimation of frequency of emergence of unfavorable events of n-y of the i-y organization of category of an operational risk j-go business of the direction within a year;
  • mid frequency of emergence of the events relating to d-mu to range;

total quantity of ranges of losses of expert evaluations of n-y of the organization; total quantity of estimations of n-y of the organization;

  • N – a total quantity of the organizations which data participate in calculations.


As distribution of frequency of emergence of unfavorable events we will use distribution of Poisson which function of probability is set by the following formula:

, where

  • n – the number of the taken place events for the period;
  • K - mid frequency of emergence of events within a year.

For assessment of distribution function of losses in case of an unfavorable event the parametrical method of recovery will also be used. As distribution function of losses "mix" of two distributions, one of which describes the most part of data, usually is accepted, and the second describes distribution of a zone of extreme values (distribution "tail"). As the distribution describing the main part of data we will use logarithmic normal distribution which frequency curve is set by the following formula.

, where

  • mean value of logarithms of losses as a result of emergence of unfavorable events for the set time period;
  • page to. about logarithms of losses as a result of emergence of unfavorable events for the set time period.

For the description of a conditional distribution of a zone of "tail" of distribution of losses the Theory of Extreme Values (EVT) according to which such conditional distribution asymptotically is described by the generalized distribution of Pareto (GDP) which frequency curve is set by the following formula is usually used:

, where

  • distribution parameters.

The GPD parameters are estimated for each set threshold defining the beginning of "tail" of distribution of losses.

Final frequency curve of losses can be written as follows:


, where

  • the set threshold of losses;
  • function of probability of standard normal distribution.

Parameters of final distribution () are estimated at two stages. At the first stage according to all available data distribution parameters, describing the main part of data are estimated ():

,

, where

  • mean value of logarithms of losses of i-y of category of an operational risk of j-y of the business line;
  • root mean square deviation of logarithms of losses of i-y of category of an operational risk of j-y of a business unit;

a total quantity of the analyzed loss estimates (both settlement, and expert) i-y of category of an operational risk j-y of a business unit;

  • k-I am assessment of frequency of emergence of an unfavorable event of i-y of category of an operational risk of j-y of the business line (or or);
  • k-I am the value of losses i-y of category of an operational risk j-y of a business unit (or or).

At the second stage the maximum likelihood method estimates other parameters of final distribution. The log-likelihood function of final distribution function can be provided as follows:

, where

  • the number of the analyzed losses of i-y of category of an operational risk of j-y of the business line which value is strict less threshold value;
  • the number of the analyzed losses of i-y of category of an operational risk of j-y of the business line which value is more than threshold value ();
  • threshold value which divides distribution to the basic and a zone of extreme values ("tail");

  • and - distribution parameters of a zone of extreme values.

The problem of search of a maximum of a log-likelihood function is solved by the iterative procedure of search of possible values of value of a threshold, for each of which distribution parameters of a zone of extreme values are in turn estimated. On the basis of the received parameters intermediate values of a log-likelihood function are calculated. To the maximum function value of credibility there will correspond values of the found distribution parameters of a zone of extreme values (i). In addition the relative value of an optimal threshold which will be used in the scenario analysis is defined:


Estimation of distribution parameters of a zone of extreme values (distribution "tail")

For each selected threshold distribution parameters and zones of extreme values are estimated as follows:

, where

also should satisfy to the following equation:


or in a different way:

, where

  • it is defined for an interval of values.

The problem of determination of a root of the last equation is solved with the help of the iterative procedure of search of a root of the equation. Respectively:


If:


Thus, inverse function of final distribution which will be used for simulation modeling of possible operational losses can be described as follows:


Simulation modeling.

Now, on the basis of the found function parameters of distribution of frequency of emergence of unfavorable events and distribution function of losses as a result of emergence of an unfavorable event using simulation modeling assessment of value of the capital selected under cumulative losses from an operational risk can be made.

For the set interval, for each risk category and for each business unit to the Coin Carlo are generated by method the set quantity of options of possible losses. The amount of selection is defined by the necessary trust level. Mathematical expectation of losses is determined by the received selections (expected losses) and also the amount of unexpected and catastrophic losses. Quantity of unfavorable events in the set period in n-m option are modelled as follows:

, where


  • mid frequency of emergence of unfavorable events during the set period;
  • the random variables which are evenly distributed on an interval (0.1).

The value of losses in each case of emergence of an unfavorable event is modelled as follows:

, where

  • inverse function of distribution of losses;
  • the random variables which are evenly distributed on an interval (0.1).

The total value of losses in n-m option is defined as follows:

Expected losses for the selected period are defined as follows:

, where

  • N – total quantity of options;

  • the general losses in n-m option.

Generated N options are ranged in ascending order,


The value of losses which with the set confidential probability will not be exceeded is defined as follows:

, where

  • number of the generated option of losses in the ranged row which corresponds to the value of losses which cannot be exceeded with the set confidential probability.

Thus the capital under an operational risk i-oh of risk category of j-y of a business unit is defined as follows:


The capital under an operational risk for separate risk category, or for all organization in general is defined the same way, by generation of the general losses for separate category or for all organization in general.

Calculation of probability of catastrophic losses is in addition made. For this purpose for the set value of catastrophic losses the closest option is selected from the ranged number of options of losses. Probability of catastrophic losses can be determined by the following formula:

, where

  • number of option of losses from the ranged row which value as much as possible corresponds to the value of catastrophic losses.

The factors determining the settlement value of reservation j-go of a type of activity i-y of category of an operational risk which can be used in a method of internal assessment and in a mark and weight method are in addition estimated:


Scenario analysis

The scenario analysis allows to investigate losses from an operational risk which can result from implementation of different events which probability of emergence is small, or such events, without being observed earlier, can happen in the long term (for example, at changes of technology, implementation of new products). The main scope of the scenario analysis in this time - stress testing, Basel committee and the Russian regulator recommend creation of scenarios of rare, but heavy events.

The scenario analysis can be also applied for the purpose of determination of the different parameters applied in modeling of assessment of the capital to risk by other methods (hybrid model). Modeling in this case happens due to change of different indicators of risk (quantity and the volume of the performed operations; frequencies of emergence of unfavorable events; weights of effects from their emergence; mark estimates of the factors influencing the control environment of the organization, etc.)

The scenario analysis in a method of internal assessment

In the scenario relative changes of intensity of transactions and average value of losses on each type of activity are set that in turn cause proportional changes of estimates of mid frequency of emergence of unfavorable events and average value of losses as a result of emergence of an unfavorable event.

Depending on the selected scenario of changes calculation of ORC is made.

, where

  • mid frequency of emergence of unfavorable events of an operational risk of i-y of category of an operational risk of j-go of a type of activity;
  • the average value of losses as a result of emergence of an unfavorable event of i-y of category of an operational risk of j-go of a type of activity;
  • relative change of intensity of the transactions j-go of a type of activity;
  • relative change of average value of losses of j-go of a type of activity;
  • level of reservation j-go of a type of activity i-y of category of an operational risk;
  • the factor defining a profile of distribution j-go of a type of activity i-y of category of an operational risk;
  • quantity of types of activity;
  • amount of categories of an operational risk.

The scenario analysis in mark and weight approach

In the scenario relative changes of intensity of transactions and average value of losses on each type of activity are set that in turn cause proportional changes of estimates of mid frequency of emergence of unfavorable events and average value of losses as a result of emergence of an unfavorable event. Relative changes of indicator values of risk are set. If for any type of activity and risk category the regression model is constructed, for calculation changes of indicators of risk are used, otherwise are used frequency change and losses. Depending on the selected scenario of changes calculation of ORC is made.

, where

or, where

  • mid frequency of emergence of unfavorable events of an operational risk of i-y of category of an operational risk of j-go of a type of activity;
  • the average value of losses as a result of emergence of an unfavorable event of i-y of category of an operational risk of j-go of a type of activity;
  • relative change of intensity of the transactions j-go of a type of activity;
  • relative change of average value of losses of j-go of a type of activity;
  • relative change of j-go of the indicator of risk;
  • k-go value of the indicator of an operational risk which theoretically or is empirically connected with the level of the operational risk accepted by the organization in timepoint of t;
  • absolute term of model of multiple regression of j-y of a business unit of the organization i-oh categories of an operational risk;
  • the modified weight of k-go of the indicator of an operational risk of model of multiple regression of j-y of the business line of the organization i-oh categories of an operational risk;

error of model of multiple regression.

  • level of reservation j-go of a type of activity i-y of category of an operational risk;
  • the factor defining a profile of distribution j-go of a type of activity i-y of category of an operational risk;
  • quantity of types of activity;
  • amount of categories of an operational risk.

The scenario analysis in the valuation method of distribution curve

In the scenario relative changes of intensity of transactions and average value of losses on each type of activity are set that in turn cause proportional changes of estimates of mid frequency of emergence of unfavorable events and average value of losses as a result of emergence of an unfavorable event (a logarithm of losses).

,

,


Depending on the selected scenario of changes calculation of ORC and probability of catastrophic losses is made.

Card of risks

Representation of results of assessment of an operational risk by perhaps different methods, formats which frequency and other features should be reflected in internal documents of credit institution. Such versatile tool of data visualization as the card of risks is of interest.

The card of risks – rather wide concept meaning the tabular or graphical representation of the risk level assumed by the organization, created taking into account the frequency (probability) of emergence of unfavorable events and also the value of possible losses in case of implementation of these events. Usually the card of risks is presented in the form of the rectangular table in which cells foreseeable losses for the set time period are reflected. Coordinates of cells of the table correspond to the set ranges of frequency rates of emergence of unfavorable events on the set temporary period, on one axis, and the set ranges of value of losses as a result of emergence of an unfavorable event, on another.

This tool is rather flexible concerning the used data. For map development of an operational risk of the organization results of statistical analysis of the database of events of an operational risk, in particular value of mid frequency of emergence of events of an operational risk for the set time period (normal one calendar year) and values of losses as a result of implementation of unfavorable events are used. Also there is a possibility of use of external data, i.e. data on events of OR which happened in other organizations. Such data can be used for the purposes of calculation of exposure of OR only after their adaptation to specifics of activity of own bank what mechanisms of so-called scaling are used to.

It is offered to apply two approaches using the mechanism of a task of scale of transactions to accounting of external data. At the same time it is supposed that the scale of transactions defines relative difference of volumes of operating activities of the different organizations. The scale of transactions of the organization which will use external data of events of an operational risk in the calculations, for example, can be accepted equal to unit (the "reference" organization). The scale of transactions of other organizations is set in relative units in direct ratio to the volume of transactions of the "reference" organization. For example, if the volume of transactions of any organization which data will be used as external by 10 times exceeds the volume of transactions of the "reference" organization, then the scale of transactions of such organization is set equal 10. The scale of transactions of the organizations is set for each activity separately.

In such approach directly in calculation both internal data of the reference organization, and external data of third parties are used. Thus, the mid frequency of emergence of unfavorable events can be defined as follows:

, where

  • scale of transactions of the reference organization j-go business of the direction;
  • scale of the transactions n-y of the j-go organization business of the direction;
  • r-I am estimation of frequency of emergence of unfavorable events within a year of n-y of the i-y organization of category of an operational risk j-go business of the direction;

total quantity of estimations of n-y of the organization;

  • N – a total quantity of the organizations, including head.

The average value of losses as a result of emergence of an unfavorable event is defined by the following formula:

, where

  • scale of the transactions n-y of the j-go organization business of the direction;
  • r-I am estimation of average losses as a result of emergence of unfavorable events of n-y of the i-y organization of category of an operational risk j-go business of the direction;
  • to - I am estimation of frequency of emergence of unfavorable events of n-y of the i-y organization of category of an operational risk j-go business of the direction within a year;

total quantity of estimations of n-y of the organization;

  • N – a total quantity of the organizations, including head.

Cards of risks can be constructed by risk categories for all organization in general, or separately for everyone business of the line. Also cards of risk for each risk category by business of lines of all organization can be constructed.

For map development of risk by risk categories for all organization in general the mid frequency of emergence of unfavorable events of i-y of category of an operational risk for the set time frame is defined as follows:

, where

  • mid frequency of emergence of unfavorable events of i-y of category of an operational risk for all organization for the set time frame;
  • total quantity business of lines of the organization;
  • mid frequency of emergence of unfavorable events of an operational risk of i-y of category of an operational risk of j-y business of the line within a year.

The average value of losses as a result of emergence of an event of i-y of category for all organization are defined as follows:

, where

  • the average value of losses as a result of emergence of an event of i-y of category for all organization within a year;
  • the average value of losses as a result of emergence of an unfavorable event of i-y of category of an operational risk of j-y business of the line within a year;
  • mid frequency of emergence of unfavorable events of an operational risk of i-y of category of an operational risk of j-y business of the line within a year;
  • mid frequency of emergence of unfavorable events of i-y of category of an operational risk for all organization within a year.

Foreseeable losses are defined as follows:

, where

  • K – mid frequency of emergence of unfavorable events for the set time frame;
  • L – the average value of losses as a result of emergence of an unfavorable event.

Conclusion

The approaches offered by Basel Committee on Banking Supervision are differentiated on degree of complexity of calculations, and respectively - to requirements to data, giving as a result very different estimates of the capital.

For the credit institutions forced to spend considerable resources for ensuring accomplishment of all conditions connected with "advanced" approaches, the main incentive of implementation of the last is the hypothetical prize in the amount of the necessary capital concerning application of naive approaches. However in practice the bank can come up against a reverse situation - and calculation of the capital under OR by "advanced methods" will deliver bank before need of recapitalization.

Possibility of comparison of the potential results received by different methods of calculation (including specified in this article), and also optimization of holding analytical procedures become especially relevant in these conditions.

Banks should select the approach allowing to estimate most adequately the capital and to manage an operational risk, and also independently to develop or purchase assessment models allowing to implement these methods.

Authors

Farrakhov I.T., RISKFIN LLC, deputy CEO for development
Rozanova E.Yu., independent expert