# Advanced Measurement Approach to Operational Risk

### Operational Risk: Definition and Approaches

- The risk of direct or indirect loss resulting from inadequate or failed internal processes, people and systems or from external events
- strategic and reputational risk is not included

- Alternative approaches
- Basic Indicator Approach (BIA)
- Standardized Approach (SA)
- Advanced Measurement Approach (AMA)

- All approaches target for calibration of capital requirement for (next) 12 months time horizon, which is compatible with the treatment of credit risk

### Incentives to Move to AMA

- Capital requirement for operational risk is a new element of regulation of the financial sector; hence more capital is required for this purpose from all regulated institutions
- AMA is viewed by many national regulators as the long-term goal for most institutions
- FSA (and some other national regulators) have presented the idea of negative incentives, to be possibly introduced under Pillar 2
- Institutions to use simple approaches for capital savings (or investment savings) can be made subject to additional capital requirements sufficient to justify adopting the AMA

### Advanced Measurement Approach

- Continues to be a very fluid structure, even after Basel II final document
- Basic idea is to apply the business line – loss type matrix as developed for the Standardized Approach
- Minimum capital requirements are to be determined for each cell of the matrix using Advanced Methodologies
- Total capital requirement for operational risk is then obtained as the direct sum of the capital requirements for the individual cells (no offsetting through correlations allowed)
- 12 months time horizon is to be used as reference period

### FSA interpretation on AMA (CP 189)

- An important interpretation on the AMA was introduced in the year 2003, presented e.g. by FSA in CP 189
- consequential losses of market risk and credit risk type from operational risk events have to be included in operational risk capital requirement calculations

- This implies e.g. that delays in corrective measures – such as detecting and executing a failed hedge – will potentially generate operational losses through market movements or through deterioration of credit quality of assets
- Consequently, portfolio market-credit value simulations may be included in AMA calculations

### Business line – loss type matrix

- 48 cell matrix combining 8 lines of business (Level 1) and 6 types of losses
- Exposure indicators are suggested for the qualitative entries of cells
- these include volume of trades, volume of transactions, value of assets, value of transactions etc.

- Business lines can be further mapped into Level 2
- With insurance operations included this mapping increases the number of Level 1 lines of business to 9 and the number of Level 2 lines of business to 24
- Corresponding number of cells of matrix are 54 and 144 for the Level 1 and Level 2 mappings

### Advanced Methodologies

- Internal Measurement Approach (IMA)
- Key parameters are EI (exposure indicator), PE (probability of loss event) and LGE (loss given event)
- EL (expected loss) = EI*PE*LGE
- Authorities will determine the g (gamma) function which transforms EL into capital requirement for each cell

- Loss Distribution Approach (LDA)
- Bank estimates the above three probability distribution functions for each cell
- Based on these distributions bank then computes the probability distribution function of the cumulative operational loss
- Capital charge is based on the simple sum of the VaRs of cells
- Correlations may also be allowed if verified by bank

### Implementing IMA in CDFT Platform

- Implementing straight IMA in CDFT R/V Platform involves relatively simple steps:
- for each cell of matrix, obtain values of exposure indicator variables
- for each cell of matrix, obtain point estimates of probabilities of events
- for each cell of matrix, obtain point estimates of losses given events
- each estimates are to be forecasts for the next 12 months period
- for each cell of matrix, compute expected losses and values of g functions
- the Minimum Capital Requirement to cover operational risk is then obtained as the straight sum of the values of g functions for individual cells

### Extending IMA in CDFT Platform

- Straight IMA calculates just the MCR for operational risk in the standard case
- IMA can be extended in two ways in CDFT R/V Platform:
- First, let loss given events for each cell of matrix be random and simulated variables – capital requirements can then be computed at different confidence levels, which may help the bank in planning for its potential capitalization pressures
- Secondly, let loss given event random variables be correlated with each other in general terms, i.e. so that correlation coefficients may deviate from +1 (the implied case in computing direct sum of cells)
- These calculations are likely to turn out useful for economic capital and pricing purposes and allow computing the Risk Profile Index for MCR adjustment for bank-specific operational risk profile

### Implementing LDA in CDFT Platform

- Steps to be taken in implementing LDA in CDFT R/V Platform:
- for each cell of matrix obtain distribution functions for the frequency of operational risk events for 12 months time horizon
- for each cell of matrix obtain distribution functions for the single operational risk event impact for 12 months time horizon
- simulate the distributions to obtain the cumulative operational loss distribution function
- compute the regulator-specified VaR number to obtain directly an estimate for the capital charge for each cell
- sum up the VaR numbers of cells to obtain the MCR for the whole bank

### Advantages of LDA

- LDA yields a better risk sensitivity than IMA
- LDA measures unexpected loss directly and not through an RPI adjustment
- No need for gamma function
- The bank can determine the business line – loss type matrix itself and can use but is not limited to the regulator-presented sample matrices

### Extending LDA in CDFT Platform

- LDA can be extended in CDFT R/V Platform in different ways:
- general correlation structure can be introduced between (any) random variables – this improves accuracy of calculations for economic capital/pricing purposes
- operational risk control measures can be modeled as mathematical control rules – this helps in quantifying the benefits of controls