Since the initiation of the New Basel Capital Accord (Basel II) in 1999, when operational risk was introduced to the regulatory landscape, the attention to this risk type has risen substantially. The Basel Committee on Banking Supervision (Basel Committee, 2006) defines operational risk as “risk of loss resulting from inadequate or failed internal processes, people and systems or from external events.” The fact that events like bookkeeping errors and terrorist attacks are covered by this characterization illustrates the broad range of risks relative to credit or market risk. Taking this heterogeneity of loss events into account, the Basel Committee categorizes losses into seven event types and eight business lines. Banks are supposed to calculate risk measures for each of these 7 × 8 = 56 combinations, such as “Internal Fraud” in “Trading and Sales” or “Damage to Physical Assets” in “Commercial Banking”.
The risk measure specified by the Basel Committee is the Unexpected Loss at a confidence level of 99.9%. Generally speaking, this refers to the 99.9% quantile of the loss distribution (possibly reduced by the Expected Loss, that is, the mean of the distribution), commonly known as the 99.9% Value–at–Risk (VaR). It measures the maximum loss that will not be exceeded with the specified confidence level and is a widely used risk measure since the 1990s. The total required risk capital under the Advanced Measurement Approaches (AMA) is obtained by summing over all 56 event–type/business–line VaRs, a strategy implicitly expecting the joint occurrence of all loss types involved or, in other words, assuming perfect positive correlation between all loss processes. To allow for non–perfect correlations, the Basel Committee permits a bank “...to use internally determined correlations [...] provided it can demonstrate to the satisfaction of the national supervisor that its systems for determining correlations are sound, implemented with integrity, and take into account the uncertainty surrounding any such correlation estimates (particularly in periods of stress).” (Basel Committee, 2006, p. 148). Dropping the highly unrealistic assumption of perfect dependence (i.e., summing the Unexpected Losses of all cells) and relying on realistic correlation estimates should decrease the calculated risk capital. Therefore, banks should have a strong interest in developing and establishing adequate assessment approaches. This expected decrease in estimated risk capital due to less than perfect correlations of the loss processes is the focus here. Specifically, we investigate whether a general rule can be established about risk–capital requirements and less than perfect correlations. Second, we analyze how the model specification affects such a rule.
The Loss Distribution Approach (LDA) is by far the most prominent among the AMA, relying on techniques well–known from actuarial applications (Klugman et al., 2004). In its standard form, loss distributions are modeled at the event type/busniness–line level, and the resulting VaR figures are added up. However, dependencies can be introduced between cells, typically by assuming dependent frequencies of occurrence. As an example of such dependence between frequencies, one could think of storm losses (i.e., event type “Damage to Physical Assets”) which typically occur clustered during certain seasons of the year. At the same time, these damages can cause events of the type “Business Disruption and System Failures”, but also affect several business lines located closely to each other. In this paper, we focus on rare–event losses—such as natural catastrophes or terrorist attacks, rather than “everyday” losses such as common bookkeeping errors and consider risk–generating processes common in credit–risk analysis (see, e.g., Frey and McNeil, 2002, 2003). However, we assume broader parameter ranges than those typically adopted. We confine ourselves to analyzing the frequency part of operational losses to check for the impact of dependent occurrences and disregard the severity dimension by assuming fixed severities. Therefore, in our notion, “risk” is represented by the number of event occurrences.
The main finding of our paper consists of the observation that the assumption of a less than perfect correlation between loss processes does not necessarily imply a decrease in rsk capital. Specifically, for all distributional assumptions considered, there may arise situations where a decrease in correlation leads to an increase in risk capital estimates, thus reversing the desired effect.
Since the work of Artzner et al. (1999), it is well–known that VaR is not a coherent risk measure due to the lack of subadditivity. In the operational risk context, this means that the joint risk—if measured by VaR—of two event type/business–line cells may exceed the sum of the individual risks measured for the two single cells. The Expected Shortfall (ES) measure, which does fulfil the subadditivity criterion, is typically recommended as an alternative and therefore also considered within the scope of our simulation study. However, it should be pointed out that the subadditivity property is not being analyzed here. At no point in our simulations, risk measures are added up; they are rather calculated based on a sum of losses, generated under different correlation assumptions.
Download
PDF Ebook Estimating Operational Risk Capital for Correlated, Rare Events
