Abstract:
The method and system enable risk assessment and presentment. The assessment includes estimation of a loss probability distribution of possible losses arising from the failure of business processes. The loss probability distributions of processes can be aggregated according to respective attribute hierarchies. The risk implications of changes within an organization can be assessed due to the linking of process change and operational risk. Control effectiveness, process value at risk, and a comparison of self-assessment against independent assessment can also be measured. The presentment includes an integrated, hierarchical process view of business operations and associated operational and compliance risks and controls, including the relationship between summary level process maps and the underlying detailed level process maps. The hierarchy contains risk and control attributes associated with any particular process. Process attributes in the hierarchy link bottom level processes to the individual business line, department, product, customer segment, or any other aspects of a business operation.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application claims priority to Australian Patent Application No. 2005902734 filed on May 27, 2005, and entitled “Methods, Devices And A Computer Program For Creating Information For Use In Facilitating A Risk Assessment,” which is incorporated herein by reference in its entirety. 
       BACKGROUND 
       [0002]    Risk is inherent in every type of business and commercial activity. Heretofore, systems and methods have been developed to calculate, measure, and manage risk. Such systems and methods have included assigning loss probability distributions to risks associated with processes employed by an organization. These loss probability distributions are intended to better assess and predict risks. 
         [0003]    By way of example, U.S. Patent Application Publication No. 2003/0149657 entitled “System and Method for Measuring and Managing Operational Risk,” describes assigning a loss probability distribution to a risk. In Paragraph [0042], it describes a loss event that can be modeled as a frequency or severity distribution. As another example, U.S. Patent Application Publication No. 2003/0236741 entitled “Method for Calculating Loss on Business, Loss Calculating Program, and Loss Calculating Device,” describes business-specific loss probability distributions. It provides an example in Paragraphs [0075]-[0079] of a loss probability distribution in the loan business. 
       SUMMARY 
       [0004]    Described herein are exemplary embodiments that present an integrated, hierarchical process view of business operations and associated operational and compliance risks and controls. The presentation hierarchy shows the relationship between summary level process maps and the underlying detailed level process maps. The hierarchy contains risk and control attributes associated with any particular process. Process attributes in the hierarchy link bottom level processes to the individual business line, department, product, customer segment, or any other aspects of a business operation. 
         [0005]    The exemplary embodiments enable the estimation of a probability distribution of possible losses arising from the failure of business processes. The loss probability distributions of bottom level processes can be aggregated according to respective attribute hierarchies, providing a more integrated and summary view of operational risk and control effectiveness. The hierarchy allows for the examination of specific processes for their risk and compliance relevance and improvement needs. The risk implications of changes within an organization can be assessed due to the linking of process change and operational risk. Control effectiveness, process value at risk, and a comparison of self-assessment against independent assessment can also be measured. 
         [0006]    Currently, it is contemplated that the exemplary embodiments can be implemented using a computer program product that receives multiple parameters, can cross correlate these parameters, and present parameters within a framework having attributes corresponding to an organization. 
         [0007]    The methodology described herein is applicable to all industry sectors but it is worth noting one particular application within the financial services industry. In the financial services industry, the Basel II operational risk compliance guidelines require various levels of operational risk measurement sophistication depending on the size and complexity of the financial services operations. The most sophisticated guidelines are referred to as the advanced measurement approach (AMA). The particular bottom up approach of the exemplary embodiments is likely to inform and interact with AMA operational risk quantification methods to provide additional insight into operational risk behavior. 
         [0008]    The exemplary embodiments can use the Basel II definition of operational risk, which states that “Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events.” Alternatively, this definition could be changed to exclude losses arising from external events so that only those risk events arising from within the organisation are considered. 
         [0009]    Another area where the exemplary embodiments can provide input and complement AMA methods is its capacity to isolate the contribution of regulatory compliance risk to operational risk. For example, the Sarbanes Oxley Act of 2002 (SOX), is effectively a prescription for a set of controls that manages a category of operational risk. The operational risk that SOX seeks to manage is the risk of misrepresenting the underlying assets and liabilities of the organization in the financial reports. The exemplary embodiments can provide a detailed insight into the process, risk and control issues associated with compliance risk in general and therefore enable organizations to manage it more effectively. 
         [0010]    Another application of the exemplary embodiments is information technology (IT) infrastructure integration, process standardization, centralized controls, event management and other operational risk management benefits. There is a large risk exposure in IT infrastructure support business processes and the failure of these systems. One such risk is the management of numerous disparate IT systems. The lack of a centralized data base or mechanism to co-ordinate their management is costly, complex and represents considerable operational risk to the business. The exemplary embodiments described herein enable the measurement of operational risk exposure, which can be used to justify the introduction of solutions based on cost and operational risk behaviour. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0011]      FIG. 1  is a general diagram of a risk assessment and presentment system in accordance with an exemplary embodiment. 
           [0012]      FIG. 2  is a hierarchy presentation of process levels generated by a software application in the exemplary system of  FIG. 1 . 
           [0013]      FIG. 3  is a flow diagram depicting operations performed in the exemplary system of  FIG. 1 . 
           [0014]      FIG. 4  is a flow diagram depicting operations performed to determine probability of an event and an amount of event balance based on different frequency levels and severity intervals in the exemplary system of  FIG. 1 . 
           [0015]      FIG. 5  is a tree diagram depicting different possible event conditions. 
           [0016]      FIG. 6  is a tree diagram depicting different possible event conditions where the worst event is one of a yearly event. 
           [0017]      FIG. 7  is a flow diagram of operations performed in an inter-process aggregation technique used in the system of  FIG. 1 . 
           [0018]      FIG. 8  is a flow diagram depicting operations performed in a likelihood distribution method. 
           [0019]      FIG. 9  is an organizational schematic depicting an exemplary embodiment implemented into an organizational setting. 
           [0020]      FIG. 10  is a cross function process map for a credit default swap process 
           [0021]      FIG. 11  is a parent child process map hierarchy for a credit default swap process 
           [0022]      FIG. 12  is a parent child process hierarchy for a credit default swap process showing a top to bottom orientation. 
           [0023]      FIG. 13  is a parent child process hierarchy for a credit default swap process showing a left to right orientation. 
           [0024]      FIG. 14  is a screen display of an interface of a software application with functionality for constructing a parent child process hierarchy. 
           [0025]      FIG. 15  is a number different computer interfaces containing a variety of different hierarchies. 
           [0026]      FIG. 16  is a display depicting intra-aggregation of two risks for the selection valuation model process. 
           [0027]      FIG. 17  is a display depicting inter-aggregation of risks for all child processes associated with a trade assessment process. 
           [0028]      FIG. 18  is a display depicting intra-aggregation of all internal fraud risks associated with credit default swap processes. 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0029]      FIG. 1  illustrates an exemplary risk assessment and presentment system  100 . The system  100  includes a computer  102  and a database  104 . The system  100  also includes a network  106  to which the computer  102  and database  104  are connected. The computer  102  has software including an operating system that provides various system-level operations and provides an environment for executing application software. In this regard, the computer  102  is loaded with a software application that provides information for use in facilitating a risk assessment. The database  104  stores data that is used by the computer  102  in creating the information for use in facilitating the risk assessment. 
         [0030]    The software application on computer  102  allows a user to identify various processes performed by an organization. For instance, the user could identify that the organization performs a credit check process on all new clients. The software application allows the user to arrange the various identified processes into a tree-like structure or hierarchy  200 , which is illustrated in  FIG. 2 . 
         [0031]    Each of the nodes in the hierarchy  200  represents the various processes identified by the user. The hierarchy  200  illustrates the relationship (child/parent) between the various processes performed by the organization. It is noted that the software application can store the identified processes according to the hierarchy  200 . The software application is such that it provides a graphical user interface (GUI) that enables a user to identify the processes and arrange them in to the hierarchy  200 . 
         [0032]    According to an exemplary embodiment, the user constructs the hierarchy  200  utilizing a standard hierarchy from a library. Alternatively, a hierarchy creation tool can be used, such as the Corporate Modeler computer software available from Casewise Systems and described on the Internet at www.casewise.com. 
         [0033]    There are numerous ways to represent a process in graphical form. For example, a credit default swap process which typically occurs in a financial service institution could be documented as a: cross functional process map (see  FIG. 11 ); a parent child process map hierarchy (see  FIG. 12 ); a parent child process hierarchy with a top to bottom orientation (see  FIG. 13 ); a parent child process hierarchy with a left to right orientation (see  FIG. 14 ). All of these representations and numerous other possible process documentation conventions can be used to convey important process information for various management purposes, such as, documentation, resource allocation, control, performance measurement and so on. The choice of representation is dependant on management&#39;s specific requirements. The exemplary embodiments are not dependant on one process representation. For example, the credit default swap examples described with reference to  FIGS. 12-14  demonstrates how the parent child process relationships could be established. As such, there is flexibility in utilizing third party process mapping software to create the parent child process hierarchy. But if third party software is not available, then the parent child process hierarchy can be established using software with functionality similar to that described with reference to  FIGS. 14-18 . The construction of the process hierarchy can be achieved through importing process data from other programs or constructed by nominating the various child processes as defined by the business and attaching these to the relevant parent processes, also defined by the business, via the add and delete function. 
         [0034]    An advantage of allowing the processes to be arranged into the hierarchy  200  is that it can be used to reflect the decision making structure of the organization. Processes are represented by nodes  202 ,  204 ,  206 , and  208 . For example, nodes  204  represent the “level 1” processes which can be those processes relevant to upper management while nodes  206  represent the “level 2” processes which can be those processes relevant to middle management. Nodes  208  represent the bottom level processes which are identified to a granular level and granted additional attributes such as “process owner/manager,” “business line,” “department/cost center,” “product,” and so on. Further attributes such as “branch,” “sales channel,” etc. can be added to the list so far as they are of interest to management for reporting purpose. The hierarchy  200  allows for “process costs,” “operational risks,” and “control measures” to be attached to bottom level processes. Overall, this “tagging system” facilitates the generation of tailored management reports for any set or combination of process attributes. It should also be noted that any number of process attributes such as those previously described, except for risks and controls, can be attached to parent processes. 
         [0035]    In addition to allowing the user to identify the various processes performed by the organization and arrange those processes in to the hierarchy  200 , the software application loaded on the personal computer  102  allows the user to identify one or more risks associated with each of the processes identified in the hierarchy  200  and assign to each of those risks several loss probability distributions (which can be either discrete or continuous distributions). In this regard, the risk might be, for example, that a credit check performed on new clients of the organization may in some instances be flawed. As with the hierarchy  200 , the graphical user interface (GUI) provided by the software application is arranged to allow the user to specify the risks. 
         [0036]    Example loss probability distributions assigned to the risks associated with each process can be identified as LPD[ 1 ], LPD[ 2 ] and LPD[ 3 ]. Additional loss probability distributions may be used in alternative embodiments. LDP[ 1 ] represents the probability of a loss occurring as a result of the associated risk without the application of any mechanisms for controlling the risk. In the context of the exemplary embodiments, “without risk control mechanisms” can mean “no controls” or “minimum controls” as defined by management, depending on the circumstances and the preferred treatment of the respective management. Generally, the process owner and an independent appraiser should agree on the LPD[ 1 ]. The LPD[ 1 ] is a baseline where control effectiveness is measured. LPD[ 2 ] represents the probability of a loss occurring as a result of the associated risk when the party responsible for the process applies a technique for controlling the risk. The difference between LPD[ 2 ] and LPD[ 1 ] in the Expected Loss (EL) or Value-at-Risk (VaR) with x % confidence level pertaining to that risk, is a measure of control effectiveness expressed in $ terms set by the process owner. LPD[ 3 ] represents the probability of a loss occurring as a result of the associated risk when an independent party assesses the technique for controlling the risk. The difference between LPD[ 3 ] and LPD[ 1 ] is the Expected Loss (EL) or Value-at-Risk (VaR) with x % confidence level pertaining to that risk, is a measure of control effectiveness expressed in $ terms set by the independent appraiser. 
         [0037]    In order to establish the three loss probability distributions (LPD[ 1 ], LPD[ 2 ] and LPD[ 3 ]), the software application loaded on the personal computer  102  is arranged to perform various operations.  FIG. 3  illustrates exemplary operations performed to establish loss probability distributions. Additional, fewer, or different operations may be performed depending on the embodiment. In an operation  310 , an occurrence probability distribution or the likelihood of an event is determined. This determination can be made using historical data or, in the absence of such data, using estimations. In an operation  320 , a loss severity or the impact of the event is determined. Loss severity can be quantified using a range of loss possibilities. In an operation  330 , a loss probability distribution is determined for the predicted event. 
         [0038]    In the situations where loss event data is available to estimate loss probability distribution, the following exemplary method can be used. While such data may not be available, the exemplary method provides a framework for a set of related questions which can guide assessors in the frequency and severity estimates of loss events. Such questions would be useful when assessors have limited access to empirical data. Instead, assessors can generate estimates using proxy data, qualitative data (e.g., expert opinion), or any combination of proxy and qualitative data. The estimates can then be supported by justifications established from answers to the questions and recorded for future reference. 
         [0039]    Advantageously, the exemplary method requires assessors to scrutinize underlying assumptions. Questions relating to frequency and severity distributions are separately identified, allowing assessors to scrutinize underlying components from the loss probability distribution. Expected loss and other statistical variables can be derived from these components, as well. Conventional methods, such as the Impact-Likelihood method assumes assessors can estimated an expected loss for a risk without analyzing the risk&#39;s underlying loss probability distribution and respective frequency and severity distributions. 
         [0040]      FIG. 4  illustrates operations performed in an exemplary loss probability distribution estimation method. Additional, fewer, or different operations may be performed depending on the embodiment. Further, it may be the case that certain operations can be performed in a different order. For purposes of illustration, the variable Y is the number of years for which historical data is considered. Assuming y years have no risk event, the probability of risk event occurring and not occurring (excluding worst case) are denoted by P 0  and P 1 . That is, 
         [0000]    
       
      
       P 
       0 
       =y/Y  
      
     
         [0000]      and 
         [0000]        P   1 =1 −P   0 . 
         [0041]    The number of years with at least one occurrence of a non-zero balance event is n=(Y−y). These years are arranged in ascending order of frequency of non-zero balance event. Each balance associates to a value of gain or loss. The respective sequences of year and its corresponding sequence of frequency of non-zero balance event are represented as follows: 
         [0000]      Y 1 ,Y 2 , . . . , Y n    
         [0000]      and 
         [0000]      f (1) ,f (2) , . . . , f (n) . 
         [0000]    The variables f (1)  and f (n)  are the respective minimum and maximum frequencies of the above non-zero balance event sequence. The frequency range is divided into three equal sub-intervals. The length of the sub-interval is: 
         [0000]        l   f =( f   (n)   −f   (1) )/3. 
         [0000]    The variables f x  and f y  are the two points that equally divide the interval [f (1) , f (n) ] As such, 
         [0000]        f   x   =f   (1)   +l   f  and  f   y   =f   (1) +2 l   f . 
         [0042]    In an operation  410 , frequency class intervals are defined as Low Frequency, Medium Frequency and High Frequency. The Low Frequency Class has the range from f (1)  to f x . The Medium Frequency Class has a frequency value greater than f x  and less than or equal to f y  while the High Frequency Class has a frequency value greater than f y  and less than or equal to f (n) . N L , N M , and N H  are the numbers in each respective Low, Medium and High Frequency Class. It should be noted that: N L +N M +N H =n. 
         [0043]    P N     L   , P N     M   , and P N     H    represent the probability of a low, medium and high level of event occurrence (excluding worst case and no event), respectively. They are defined as: 
         [0000]        P   N     L     =N   L   /n,P   N     M     =N   M   /n  and P N     H     =N   H   /n.    
         [0000]    The variable p is be the total number of non-zero balance event within those n years. As such, 
         [0000]    
       
         
           
             p 
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 n 
               
                
               
                   
               
                
               
                 
                   f 
                   
                     ( 
                     i 
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    In an operation  420 , non-zero balance events are arranged in descending order of their balance. The sequence of the event balances is: b (1) , b (2) , . . . , b (p) . The variables  b   (1)  and b (p)  are the respective maximum and minimum balance of the above sequence of balances. The balance range is divided into three equal sub-intervals. The length of the sub-interval is: l b =(b (1) −b (p) )/3. The two points that equally divide the interval [b (1) , b (p) ] are b x  and b y . Hence, b x =b (1) −l b  and b y =b (1) −2l b . 
         [0044]    In an operation  430 , severity class intervals are defined as Low Severity, Medium Severity and High Severity. The Low Severity Class has a range from b (1)  to b x . The Medium Severity Class has a balance value greater than b x  and less than or equal to b y  while the High Severity Class has a balance value greater than b y  and less than or equal to b (p) . Each b (i)  falls into one of the severity classes and it also associates to a particular year. Depending on the frequency of event occurrence of that year being considered, b (i)  belongs to the corresponding Frequency class. Table 1 shows a three by three Table of Frequency Occurrence Class and Severity of balance incurred. If the number of b (i)  in each cell is counted, each symbol in Table 1 represents the total count of a particular cell. If all the b (i)  &#39;s value in each cell are added, each symbol in Table 2 shows the total balance of a particular cell. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 Severity 
                   
               
             
          
           
               
                   
                 Frequency 
                 Low 
                 Medium 
                 High 
                 Total 
               
               
                   
                   
               
               
                   
                 Low 
                 n LL   
                 n LM   
                 n LH   
                 N L   
               
               
                   
                 Medium 
                 n ML   
                 n MM   
                 n MH   
                 N M   
               
               
                   
                 High 
                 n HL   
                 n HM   
                 n HH   
                 N H   
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
             
             
               
                   
                   
               
               
                   
                 Severity 
                   
               
             
          
           
               
                   
                 Frequency 
                 Low 
                 Medium 
                 High 
                 Total 
               
               
                   
                   
               
               
                   
                 Low 
                 A LL   
                 A LM   
                 A LH   
                 A L   
               
               
                   
                 Medium 
                 A ML   
                 A MM   
                 A MH   
                 A M   
               
               
                   
                 High 
                 A HL   
                 A HM   
                 A HH   
                 A H   
               
               
                   
                   
               
             
          
         
       
     
         [0045]    The worst case scenario happens every t years. The worst case of loss amount is denoted as T. It is assumed that the worst case scenario is independent to the yearly event.  FIG. 5  shows different possible event conditions. In an operation  440 , the probability of an event is determined, in an operation  450 , the amount of event balance is determined. The probability of getting a different event condition is shown in Table 3 with the corresponding amount of event balance.  FIG. 6  illustrates different event conditions where the worst event is part of a yearly event. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                 Amount of Event 
               
               
                 Event 
                 Probability of Event 
                 Balance 
               
               
                   
               
             
             
               
                 Worst Case and no event 
                 (1/t) × P 0   
                 T 
               
               
                 occurrence 
               
               
                 Worst case, non-zero 
                 (1/t) × P 1  × P N   L   
                 T + A L   
               
               
                 balance events and low 
               
               
                 frequency occurrence 
               
               
                 Worst case, non-zero 
                 (1/t) × P 1  × P N   M   
                 T + A M   
               
               
                 balance events and medium 
               
               
                 frequency occurrence 
               
               
                 Worst case, non-zero 
                 (1/t) × P 1  × P N   H   
                 T + A H   
               
               
                 balance events and high 
               
               
                 frequency occurrence 
               
               
                 No worst case and no event 
                 (1 − 1/t) × P 0   
                 0 
               
               
                 occurrence 
               
               
                 No worst case, non-zero 
                 (1 − 1/t) × P 1  × P N   L   
                 A L   
               
               
                 balance event and low 
               
               
                 frequency occurrence 
               
               
                 No worst case, non-zero 
                 (1 − 1/t) × P 1  × P N   M   
                 A M   
               
               
                 balance events and medium 
               
               
                 frequency occurrence 
               
               
                 No worst case, non-zero 
                 (1 − 1/t) × P 1  × P N   H   
                 A H   
               
               
                 balance events and high 
               
               
                 frequency occurrence 
               
               
                   
               
             
          
         
       
     
         [0046]    Once the software application on the computer  102  has calculated the loss probability, the software application can provide information for facilitating a risk assessment. In this regard, the software application is arranged to allow the user to select one or more of the processes represented in the hierarchy  200  (see  FIG. 2 ) via a graphical user interface (GUI). 
         [0047]    On determining which of the nodes in the hierarchy  200  have been selected by the user, the software application uses the selection to calculate a resultant loss probability distribution, which represents the information for facilitating a risk assessment. In this regard, the software application is arranged to perform at least two aggregating operations on the loss probability distributions associated with the risks associated with the nodes in the hierarchy  200 . 
         [0048]    A first of the aggregating operations is an ‘inter-process’ aggregation which involves aggregating all the loss probability distributions that are associated with the child nodes of a particular node (process) in the hierarchy  200 . For example, with reference to  FIG. 7 , the inter-process aggregation involves aggregating the loss probabilities associated with R i  for processes P x , P y , and P z , R iii  for processes P x  and P y , etc. Thus, the resultant loss probability distribution for business unit B a  would be the aggregate of the loss probabilities associated with R i  for P x , P y , and P z , the aggregate of the loss probabilities R iii  for P x  and P y , etc. Table 4 shows example loss distributions of R i  for P x , P y  and P z  to illustrate this aggregation methodology. 
         [0000]                                                                                                            TABLE 4                           P x         P y         P z                      Prob.   $ Loss   Prob.   $ Loss   Prob.   $ Loss                            0.3   10   0.9   5   0.5   10           0.4   20   0.05   10   0.5   30           0.3   30   0.03   50                   0.02   100           1       1       1                        
Table 5 shows the loss distribution of R i  for P w  using the figures from Table 4.
 
         [0000]                                                              TABLE 5                       Probability of loss       $ Amount loss                                        0.135   = 0.3 × 0.9 × 0.5   25   = 10 + 5 + 10           0.135   = 0.3 × 0.9 × 0.5   45   = 10 + 5 + 30           0.0075   = 0.3 × 0.05 × 0.5   30   = 10 + 10 + 10           0.0075   = 0.3 × 0.05 × 0.5   50   = 10 + 10 + 30           0.0045   = 0.3 × 0.03 × 0.5   70   = 10 + 50 + 10           0.0045   = 0.3 × 0.03 × 0.5   90   = 10 + 50 + 30           0.003   = 0.3 × 0.02 × 0.5   120   = 10 + 100 + 10           0.003   = 0.3 × 0.02 × 0.5   140   = 10 + 100 + 30           0.18   = 0.4 × 0.9 × 0.5   35   = 20 + 5 + 10           0.18   = 0.4 × 0.9 × 0.5   55   = 20 + 5 + 30           0.01   = 0.4 × 0.05 × 0.5   40   = 20 + 10 + 10           0.01   = 0.4 × 0.05 × 0.5   60   = 20 + 10 + 30           0.006   = 0.4 × 0.03 × 0.5   80   = 20 + 50 + 10           0.006   = 0.4 × 0.03 × 0.5   100   = 20 + 50 + 30           0.004   = 0.4 × 0.02 × 0.5   130   = 20 + 100 + 10           0.004   = 0.4 × 0.02 × 0.5   150   = 20 + 100 + 30           0.135   = 0.3 × 0.9 × 0.5   45   = 30 + 5 + 10           0.135   = 0.3 × 0.9 × 0.5   65   = 30 + 5 + 30           0.0075   = 0.3 × 0.05 × 0.5   50   = 30 + 10 + 10           0.0075   = 0.3 × 0.05 × 0.5   70   = 30 + 10 + 30           0.0045   = 0.3 × 0.03 × 0.5   90   = 30 + 50 + 10           0.0045   = 0.3 × 0.03 × 0.5   110   = 30 + 50 + 30           0.003   = 0.3 × 0.02 × 0.5   140   = 30 + 100 + 10           0.003   = 0.3 × 0.02 × 0.5   160   = 30 + 100 + 30           Total = 1                        
After arranging the loss amount into ascending order and adding together the probabilities for the same loss amounts (i.e., 45, 50, 70, 90, and 140), the loss distribution of R i  for P w  becomes as shown in Table 6.
 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 $ Loss amt. 
                 Prob. 
                 Cumulative Prob. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 25 
                 0.135 
                 0.135 
               
               
                 30 
                 0.0075 
                 0.1425 
               
               
                 35 
                 0.18 
                 0.3225 
               
               
                 40 
                 0.01 
                 0.3325 
               
               
                 45 
                 0.27 
                 0.6025 
               
               
                 50 
                 0.015 
                 0.6175 
               
               
                 55 
                 0.18 
                 0.7975 
               
               
                 60 
                 0.01 
                 0.8075 
               
               
                 65 
                 0.135 
                 0.9425 
               
               
                 70 
                 0.012 
                 0.9545 
               
               
                 80 
                 0.006 
                 0.9605 
               
               
                 90 
                 0.009 
                 0.9695 
               
               
                 100 
                 0.006 
                 0.9755 
               
               
                 110 
                 0.0045 
                 0.98 
               
               
                 120 
                 0.003 
                 0.983 
               
               
                 130 
                 0.004 
                 0.987 
               
               
                 140 
                 0.006 
                 0.993 
               
               
                 150 
                 0.004 
                 0.997 
               
               
                 160 
                 0.003 
                 1 
               
               
                   
                 1 
               
               
                   
               
             
          
         
       
     
         [0049]    A second of the aggregating operations is an ‘intra-process’ aggregation, which involves aggregating loss probability distributions of various risks associated with a process. For example, again referring to  FIG. 7 , the intra-process aggregation involves aggregating the loss probabilities associated with R i , R ii , and R iii . Thus, the resultant loss probability distribution for process P would be the aggregate of the loss probability distributions for R i , R ii , and R iii . When aggregating loss probability distributions, the software application is arranged to take into account the effect that different probability distributions can have on each other. This is achieved by processing a correlation coefficient, which the computer  102  can obtain from the database  104  via the communication network  106 . Once the resultant loss probability distribution has been calculated, the software application displays the resultant distribution on the monitor of the computer  102 , or prints on paper, so that a risk assessor can use it when considering the impact of risk. 
         [0050]    For a set of distributions where the total number of possible combinations becomes unmanageable to compute, a number of alternate strategies can be used to estimate an aggregate distribution for expected loss. One strategy reduces the number of outcomes in each of the individual low level distributions prior to starting the aggregation process. For example, where a particular low level distribution contains five possible outcomes, then the number can be reduced down to a lower number of outcomes using one of the methods described below. In this way, whereas we may have a set of ten low level distributions to be aggregated, with each distribution starting out with five possible outcomes, we can reduce the number of computations down from n=5̂10=9.765 million to n=3̂10=59,049 by aggregating within each of the low level distributions prior to starting the process of aggregating the entire set of 10 distributions. 
         [0051]    When the distribution of a parent process is constructed, the number of possible loss values increases. This parent process can be the child process of another parent process. This parent and children relationship can be propagated into many levels. The number of calculations involved to evaluate the loss distribution from one level to another increases drastically. Therefore, it is desirable to restrict the number of loss values for the distribution at each level so that the time to complete all the calculation for all levels within a system is within a realistic timeframe. A method of probability aggregation together with their expected loss values is here described. 
         [0052]    P(W=w i )=p i  is defined as the probability from a loss distribution, W, of a parent process (P w ) where i  1 ,  2 , . . . , n. Each p i  corresponds to a loss value of w i . The product of w i  and p i  is the expected loss when W=w i . The largest possible in is used such that: 
         [0000]    
       
         
           
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 m 
               
                
               
                   
               
                
               
                 p 
                 i 
               
             
             ≤ 
             
               0.5 
               . 
             
           
         
       
     
         [0053]    Three equal intervals are obtained by sub-dividing the interval [w l , w m ]. Similarly, divide the interval [w m , w n ] is divided into 3 equal sub-intervals. The variables r and s are the respective length of the first three sub-intervals and the remaining three intervals. Hence, 
         [0000]        r =( w   m   −w   l )/3 
         [0000]      and 
         [0000]        S =( w   n   −w   n )/3. 
         [0054]    Where w a  and w b  are the two points that equally divide the interval [w l , w m ]. Also, w c  and w d  are the two points that equally divide the interval [w m , w n ]. Hence, 
         [0000]    
       
      
       w 
       a 
       =w 
       l 
       +r,  
      
     
         [0000]        w   b   =w   l +2 r,    
         [0000]    
       
      
       w 
       c 
       =w 
       m 
       +s  
      
     
         [0000]      and 
         [0000]        w   d   =w   m +2 s.    
         [0055]    A set of new probabilities are calculated by considering different range of loss values. Each new probability (P(U=u j )) is the sum of probabilities from the distribution W that their loss values fall into a particular loss range being considered. The sum of their corresponding expected loss values (l i ) becomes the expected loss of this new probability (L j ). The new loss probability distribution and its expected loss values are shown in Table 7. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                   
                 Expected Loss 
                   
               
               
                 Probability Distribution of U 
                 (L j ) 
                 Loss Value (u j ) 
               
               
                   
               
             
             
               
                 P(U = u 1 ) = P(w 1  ≦ W ≦ w a ) 
                 L 1   
                 u 1  = L 1 /P(U = u 1 ) 
               
               
                 P(U = u 2 ) = P(w a  &lt; W ≦ w b ) 
                 L 2   
                 u 2  = L 2 /P(U = u 2 ) 
               
               
                 P(U = u 3 ) = P(w b  &lt; W ≦ w m ) 
                 L 3   
                 u 3  = L 3 /P(U = u 3 ) 
               
               
                 P(U = u 4 ) = P(w m  &lt; W ≦ w c ) 
                 L 4   
                 u 4  = L 4 /P(U = u 4 ) 
               
               
                 P(U = u 5 ) = P(w c  &lt; W ≦ w d ) 
                 L 5   
                 u 5  = L 5 /P(U = u 5 ) 
               
               
                 P(U = u 6 ) = P(w d  &lt; W ≦ w n ) 
                 L 6   
                 u 6  = L 6 /P(U = u 6 ) 
               
               
                   
               
             
          
         
       
     
         [0056]    If a loss distribution is symmetric, w m  can be the mid-point between w l  and w n . However, assuming the loss distribution is positively skewed, as is typically the case, the selection of w m  is based on the cumulated probability closed to 0.5. Totally, six intervals are defined. If the number of interval is still too high, it can be reduced further, for example to four, by defining a mid-point between w l  and w m  and another mid-point between w m  and w n . 
         [0057]    The number of values in a distribution can also be reduced by minimizing the sum of squared error and/or assigning a functional form. The form is done by computing the mean (M 0 ) and standard deviation (S 0 ) of the initial distribution, defining a new distribution with fewer possible outcomes, systematically selecting values of these outcomes U and computing the mean (Sn) and standard deviation (Sn) of each new distribution for each new combination of U. Then, the sum of squared errors is computed as sum[(Mn−M 0 )̂2+(Sn−S 0 )̂2], the vector of values U=(u 1 ,u 2 , . . . , un) is identified that minimize the sum of squared errors defined above, and the initial distribution is replaced with this vector U and the associated cumulative probabilities. The latter technique (assigning a functional form) involves identifying the general functional form and the specific values of any corresponding parameters that most closely approximates the original discrete distribution. This can be done for a particular discrete probability distribution by first computing the cumulative probability function of the distribution. This cumulative distribution function is compared with the relevant corresponding cumulative distribution functions of a range of continuous distributions to identify the most appropriate approximation. The most appropriate continuous distribution is selected to serve as an approximation to the original discrete probability distribution. The selection can be based upon either ( 1 ) correlation coefficient or (2) minimizing the squared error of estimation, both of these measures being computed on the basis of the cumulative distribution functions of the original and the approximate distributions. 
         [0058]    A second strategy for reducing the number of values in the distribution invokes the Central Limit Theorem (CLT) to facilitate the summation of each lower level distribution into an overall aggregate distribution. The CLT states that the mean and variance of a sum of random variants tends toward normality, with an aggregate mean equal to the sum of the means and an aggregate variance equal to the sum of the variances. This strategy can be applied to aggregate distributions where the range of loss severities are similar, such that the range of possible outcomes in any given distribution does not dominate the range of possible outcomes in all other distributions and where each distribution to be summed has finite mean and variance. 
         [0059]    Where there exists a subset of low level distributions to be aggregated, each member of the subset having a range of possible outcomes that are within the same order of magnitude, then the CLT can be invoked to estimate the moments of the aggregated distribution. The shape and confidence intervals for an aggregated distribution can then be computed using the aggregate mean and variance together with a table of percentiles for the appropriate “attractor” distribution. In the most general case this will be the standard normal distribution. Where there exists more than one subset within a given set, then the CLT method can be applied separately to each subset to generate an aggregate distribution for each subset. Then the method of aggregation described in Strategy  1  above can be used to aggregate these distributions. 
         [0060]    Yet another strategy for reducing the number of values in a distribution involves any combination of strategies  1  and  2  above, selected in part or whole and in sequence so as to produce the best possible aggregation taking into account the number and characteristics of distributions to be aggregated. 
         [0061]      FIG. 8  illustrates operations performed in an exemplary likelihood distribution method. Additional, fewer, or different operations may be performed depending on the embodiment. Further, it may be the case that certain operations can be performed in a different order. In an operation  810 , a likelihood probability distribution (LPD) is determined with reference to historical data, assuming existing controls. The LPD can be determined in accordance with operations such as those described with reference to  FIGS. 3-4 . In an operation  820 , likelihood indicators and impact indicators are identified. The LPD with reference to manager&#39;s expectations is determined assuming existing controls in an operation  830 . Managers are requested to look ahead into the next 12 months (for example) to consider whether the values of the “likelihood indicators” and “impact indicators” will change. Any changes and comments are recorded. An example of this type of analysis is presented for a reconciliation process, see Table 8 and 9. On the basis of this new information the operations in  FIGS. 3-4  are revisited so that a new LPD is determined. 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Likelihood 
                   
                   
                   
                   
               
               
                 Indicators 
                   
                 Current 
                 Expected 
               
               
                 (LI N ) 
                 Definition 
                 Value 
                 Value 
                 Comments 
               
               
                   
               
             
             
               
                 LI 1   
                 % of staff in reconciliation 
                 10% 
                 17% 
                 New staff to be recruited 
               
               
                   
                 team with &lt;3 months training 
               
               
                 LI 2   
                 number of items processed 
                 1 mil 
                 1.5 mil 
                 Expansion of business 
               
               
                 LI 3   
                 average outstanding duration 
                 3 days 
                 3 days 
                 NA 
               
               
                   
                 of unreconciled items 
               
               
                 LI 4   
                 amount of staff resources 
                 10 FTE&#39;s 
                 12 FTE&#39;s 
                 Plan to employ new staff 
               
               
                   
                 assigned to perform 
               
               
                   
                 reconciliation task 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                 Impact 
                   
                   
                   
                   
               
               
                 Indicators 
                   
                 Current 
                 Expected 
                   
               
               
                 (II N ) 
                 Definition 
                 Value 
                 Value 
                 Comments 
               
               
                   
               
             
             
               
                 II 1   
                 average $ amount of items 
                 10000 
                 10000 
                 NA 
               
               
                   
                 processed 
               
               
                 II 2   
                 additional handling fees, 
                 5% 
                 5% 
                 NA 
               
               
                   
                 interest or charges on 
               
               
                   
                 unreconciled items 
               
               
                   
               
             
          
         
       
     
         [0062]    In an operation  840 , managers are asked to consider whether the “likelihood indicators” and “impact indicators” are likely to change if the controls of the process are relaxed one by one. This approach can be illustrated using the reconciliation process example similar to operation  830 . In the example below (see Tables 10 and 11), the controls are relaxed and the managers expected cumulative changes recorded. The managers are then in a better position to revisit operations described with reference to  FIGS. 3-4  with a list of event loss drivers that will direct their responses to the relevant likelihood and impact questions. Hence, the LPD assuming without controls can be determined. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Likelihood 
                   
                   
                   
                   
                   
                   
               
               
                 Indicators 
                   
                 Expected 
                 Relax 
                 Relax 
                 Relax 
                 Cumulative 
               
               
                 (LI N ) 
                 Definition 
                 Value 
                 C 1   
                 C 1 , C 2   
                 C 1 , C 2 , C 3   
                 changes 
               
               
                   
               
             
             
               
                 LI 1   
                 % of staff in 
                 17% 
                   
                   
                   
                 17% 
               
               
                   
                 reconciliation team 
               
               
                   
                 with &lt;3 months training 
               
               
                 LI 2   
                 number of items 
                 1.5 mil 
                   
                   
                   
                 1.5 mil 
               
               
                   
                 processed 
               
               
                 LI 3   
                 average outstanding 
                 3 days 
                 4 days 
                 5 days 
                 7 days 
                 7 days 
               
               
                   
                 duration of unreconciled 
               
               
                   
                 items 
               
               
                 LI 4   
                 amount of staff 
                 12 FTE&#39;s 
                   
                   
                   
                 12 
               
               
                   
                 resources assigned to 
               
               
                   
                 perform reconciliation 
               
               
                   
                 task 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 Impact 
                   
                   
                   
                   
                   
                   
               
               
                 Indicators 
                   
                 Expected 
                 Relax 
                 Relax 
                 Relax 
                 Cumulative 
               
               
                 (II N ) 
                 Definition 
                 Value 
                 C 1   
                 C 1 , C 2   
                 C 1 , C 2 , C 3   
                 changes 
               
               
                   
               
             
             
               
                 II 1   
                 average $ amount of 
                 10000 
                   
                   
                   
                 10000 
               
               
                   
                 items processed 
               
               
                 II 2   
                 additional handling fees, 
                 5% 
                 6% 
                 7% 
                 8% 
                 8% 
               
               
                   
                 interest or charges on 
               
               
                   
                 unreconciled items 
               
               
                   
               
             
          
         
       
     
         [0063]    The operations may reveal that some controls do not impact on any of the likelihood impact indicators. This result may indicate one or more of the following situations: (i) the controls are “detective” rather than “preventative,” (ii) some indicators are not properly identified, or (iii) the controls are redundant. 
         [0064]      FIG. 9  illustrates an exemplary process for integrating operational and compliance risk into risk adjusted performance metrics. Additional, fewer, or different operations may be performed depending on the embodiment. Further, it may be the case that certain operations can be performed in a different order. In an operation  910 , data and performance metrics are defined. Such metrics can be different for different groups of an organization. For example, business divisions or departments, line management, process owners, auditors, board members, compliance officers, and the such can define different data and performance metrics. Process owners can gather data, identify key risk indicators, assess risk and control, and generate process maps. Line management can review the process maps, review risk and control assessment, and identify process metrics. Other functions can be carried out by different entities within the organization, as appropriate. 
         [0065]    In an operation  920 , an operational risk calculation is performed. This operational risk calculation can include the risk calculations described with reference to the Figures herein. The board of directors can set the operational and compliance risk appetite and confidence levels. Auditors can review the board&#39;s decisions and directions. In an operation  930 , there is an allocation of operational risk capital and a calculation of risk adjusted performance metrics (RAPM). For example, operational risk capital can be allocated to relevant owners. Incentives for line managers and process owners can be set. Metrics can be calibrated and adjustments made based on results from the risk calculations. 
         [0066]    In an operation  940 , a variety of different reports are generated and analysis performed at all levels of the organization. In an operation  950 , risk adjusted productivity is managed. For example, process owners can collect risk data and deploy resources in accordance with operational risk metrics and risk adjusted performance metrics objectives. Line management can deploy resources in accordance with these objectives and divisions or departments can align resources according to these objectives. In an operation  960 , process structures and/or risk profiles are updated and the evaluation process continues. 
         [0067]      FIG. 10  illustrates a cross-function process map for a credit default swap process. The process map graphically illustrates operations behind a credit default swap, including a trade assessment, trade negotiation, and trade execution.  FIG. 11  illustrates a parent child process map hierarchy for the credit default swap process. The hierarchy presents the various component parts that make us the credit default swap.  FIG. 12  illustrates a top to bottom orientation to the credit default swap process.  FIG. 13  illustrates a left-to-right orientation to the credit default swap process. Such a left-to-right orientation can be depicted in a computer user interface, using collapsible and expandable folder and sub-folder structures. An example computer interface having the hierarchy depicting in a left-to-right orientation is shown in  FIG. 14 .  FIG. 15  illustrates a number different computer interfaces containing a variety of different hierarchies. 
         [0068]      FIG. 16  illustrates a computer interface showing inter-aggregation of two risks for a selection valuation model.  FIG. 17  illustrates a computer interface showing intra-aggregation of risks for all child processes associated with a trade assessment process.  FIG. 18  illustrates a computer interface showing inter-aggregation of internal fraud risks associated with credit default swap processes. 
         [0069]    The methodology described herein with respect to the exemplary embodiments provides a number of advantages. For example, the exemplary methodology attaches operational risk attributes and loss probability distributions (LPDs) to bottom level processes. Operational risks; controls; budget/actual costs; and LPDs due to the individual operational risks are associated with the bottom level processes which also have attributes including but not limited to: owner process ID, parent process ID, process owner/manager, department to which the process belongs, business unit to which the process belongs, and product to which the process is supporting. 
         [0070]    Further, the exemplary methodology enables multiple party evaluation/validation for the risk and control details of bottom level processes. Process owners and independent reviewers need to agree on the state and correctness of operational risk and control information prior to constructing the set of LPDs. The exemplary-methodology is designed to support the modeling of multiple LPDs for each operational risk at bottom level processes to enhance the quality of independent reviews. The use of LPDs (LPD[ 1 ]: assumed without control (or, as discussed above, with minimum controls defined by management); LPD[ 2 ]: assumed with control assessed by process owner; LPD[ 3 ]: assumed with control assessed by independent reviewer, . . . etc.) to capture multiple parties&#39; assessment on risk and control effectiveness enhances the process/quality of independent review, making it more standardized, accurate, and transparent across the organization. 
         [0071]    The exemplary methodology enables the inter-aggregation of the set of LPDs for individual risks of the bottom level processes along the respective hierarchies of the various attributes (e.g. process/business unit/department/product/ . . . etc.) in order to establish a set of LPDs for every risk at each process/business unit/department/product . . . etc. in their respective hierarchies. The exemplary methodology aggregates sets of LPDs (i.e. LPD[ 1 ]: assumed without control (or minimum control); LPD [ 2 ]: assumed with control assessed by process owner; LPD [ 3 ]: assumed with control assessed by independent reviewer, etc.) for individual operational risks of the bottom level processes to their parent processes up the process hierarchy such that every parent process has a corresponding set of aggregated LPDs for the respective operational risk. This aggregation is also performed according to the respective hierarchy of other attributes (e.g. individual business line, department, product, . . . etc). As far as their effects are updated in the respective LPDs and then aggregated up the respective hierarchies, changes to the risk/control profile at the bottom level processes are automatically reflected to all parent processes, business units, departments, and products. 
         [0072]    The exemplary methodology enables the intra-aggregation of the sets of LPDs for all operational risks at each process/business unit/department/product . . . etc. into 1 set of LPDs (i.e. LPD[ 1 ], LPD[ 2 ], LPD[ 3 ]) for every process/business unit/department/product . . . etc. PRIM aggregates sets of LPDs for the various operational risks under a process into one set of LPDs for that particular process. The same is also performed for other attributes, i.e. individual business line, department, product . . . etc. This enables the reporting of ‘Expected Loss’ (EL) and ‘Value at Risk with x % of confidence level’ (VaR) in dollar terms for every process/business unit/department/product . . . etc. 
         [0073]    The exemplary methodology can provide reports quantifying the organizations risk capital allocation requirement. Quantitative measures of operational risks such as ‘Expected Loss’ (EL) and ‘Value at Risk with x % confidence level’ (VaR) are expressed in dollar terms, and are readily available with the LPDs for processes, departments, business units, and products. As a result, a basis for operational risk capital allocation is readily available for processes, departments, business units, and products levels using ‘EL’ or ‘VaR’ as an allocation basis. 
         [0074]    The exemplary methodology provides a means to identify the component of the organizations risk capital allocation requirement that is attributed to compliance risk. The process, risk and control analysis prescribed by the methodology, which includes the application of LID, enables the aggregation of only those LPDs associated with compliance risks. The exemplary methodology measures control effectiveness based on LPDs and in dollar terms. By comparing LPD ‘assumed with control’ and LPD ‘assumed without control’, the methodology enables the measurement of control effectiveness to be based on LPDs and expressed in dollar terms (e.g. “Expected Loss (EL) is reduced by $n” and “Value-at-Risk with a x % confidence level (VaR) is reduced by $n”) for individual process, business unit, department, product . . . etc. Control effectiveness measurement expressed in dollar terms facilitates the cost-benefit analysis for controls. 
         [0075]    The exemplary methodology recognizes the complex operational risk behavior that can arise from an interdependent network of business processes. Network effect refers to the situation where the successful performance of a process (e.g., Process A) is dependant on the success of another process (e.g., Process B). Therefore the failure of Process B represents a risk to Process A. As such, the outsourcing, for example, of Process B only removes the risks directly associated with it, but cannot remove the network effect that it has on Process A. The exemplary methodology handles this by allowing the user to specify for Process A the risk of Process B failing. 
         [0076]    The exemplary methodology captures correlation among different risks by correlation factors. The correlation factors are applied when performing LPD aggregation of the risks involved. The exemplary methodology is not exclusively reliant on the availability of quantitative data. The exemplary methodology provides management with the choice to use quantitative or qualitative data or a blend of both to develop LPDs. In this sense, the methodology is not completely reliant on historical operational loss data alone. 
         [0077]    The exemplary methodology&#39;s data capture methodology can simplify management&#39;s task of characterizing the risk and control attributes for processes where there is little or no data. Processes which have a rich source of high quality data to characterize risk and control can be used to characterize similar processes for which there is little or no data. In one exemplary embodiment, an organization has already developed a robust business process view of the organization, where process definitions are standardized, mapped and well documented, such that a process hierarchy similar to the hierarchy  200  of  FIG. 2  is already available or can be easily produced. 
         [0078]    The hierarchy  200  represents the way business processes are actually managed and captures the network of process relationships within the organization i.e., how the various processes interact. From hierarchy  200 , a chart  210  is derived which is the parent-child process hierarchy and is the basic structure defining how the various LPDs are aggregated. The relationship between the hierarchy  200  and chart  20  in  FIG. 2  can be understood by examining the corresponding process notation. 
         [0079]    In a second exemplary embodiment, a business process program is not in place. A process map hierarchy does not necessarily need to be created before the parent-child process hierarchy is created. Creating the parent-child process hierarchy is not a complex exercise because the complicated, time consuming process relationship detail is not required. Advantage can be gained by utilizing existing process information and any remaining gaps quickly obtained by requesting the input from various line managers and subject matter experts. It is possible to simply identify only the bottom level child processes perform LPD aggregations without the parent-child process hierarchy to place some predefined definitions to LPD aggregation. Under this scenario the information can still provide valuable management insights to operational risk adjusted productivity, operational risk and control behavior. 
         [0080]    Those skilled in the art will appreciate that the invention described herein is susceptible to variations and modifications other than those specifically described. It should be understood that the invention includes all such variations and modifications which fall within the spirit and scope of the invention.