1. Field of the Invention
The present invention generally relates to modeling operational risk for pre-emptive risk management and risk discovery in business management and, more particularly, to an approach for identifying, predicting and assessing operational risks in order to take proactive steps to manage risks.
2. Background Description
Organizations are increasingly interested in robust systems for assessing and managing operational risk. The growing interest in operational risk management has been driven by a variety of factors, including the introduction of new regulations requiring businesses to quantify and manage operational risk, such as the New Basel Capital Accord, known as Basel II (see “The New Basel Capital Accord”, Bank for International Settlements, April 2003).
A prevailing definition of operational risk is given by the Basel Committee on Banking Supervision as “the risk of loss resulting from inadequate or failed internal processes, people or systems or from external events”. (See, “Working Paper on the Treatment of Operational Risk”, Basel Committee on Banking Supervision, September 2001.)
Prior art in operational risk modeling has been based on (a) operational risk assessment methods for quantifying operational risk using statistical modeling of rare events and extreme value theory (see for example, see Advances in Operational Risk, Risk Books, 2003), and (b) Bayesian networks (see, for example, Operational Risk—Measurement and Modeling, Jack King, Wiley Publishers, 2001). Even though these approaches are able to quantify risks at the enterprise level, they do not give a clear view of the Key Risk Indicators (KRI) and specific actions that can be taken to manage operational risks. Hence they are not suitable for predicting risk and proactively managing risk on an ongoing basis. Recent industry efforts are underway to define key risk indicators for operational risk management and the KRI Exchange (www.kriex.com) has defined more than 1800 risk indicators. In order to progress towards proactive risk management, an understanding has to be gained regarding the relationships between the risk indicators and loss events that can be used as a basis to score operational risks and predict risks based on the Key Risk Indicators. Predictive modeling has been used to score risks in the fraud management, credit risk space (www.fairisaac.com), but not for predicting general operational risks and proactively managing them.
The background described above indicates the need to develop a systematic methodology for pre-emptive operational risk assessment and risk discovery, leading to a functional operational risk assessment and management system. Such a methodology can further be used as a basis to identify and deploy different countermeasures for operational risk control and mitigation. The methodology consists of five steps: (1) Identify the risk factors from many candidate variables that are typically provided by experts familiar with operational processes in the business area under consideration. (2) Model the relationship between operational loss events and risk factors. (3) Identify Key Risk Indicators that serve to predict the potential for loss events (4) Construct forecasting models for the key risk factors and assess future risk exposures by the constructed model in step (2). (5) Monitor the Key Risk Indicators using the models to provide an early warning for risk events and proactively manage loss events.
The present invention provides a system and method for pre-emptive operational risk assessment and risk discovery based on analysis of enterprise information on an ongoing basis. Information can be obtained in real-time or near real-time from runtime systems and from other enterprise information stores. According to one aspect of the invention, the method comprises the steps of:
The present invention differs from the prior art in the following respects:
The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which:
Referring now to the drawings, and more particularly to
The forecast involved in function block 108 consists of two aspects. First, forecasting the probability of future risk events; Second, forecast the severity (say, dollar amount) of future risk event should it happen. This essentially enables us to obtain an estimate of Value-at-Risk (VaR). For example, suppose we forecast the risk event would occur in the next time period with probability of 0.8, and the severity is over $1M with probability 99% should it happen, then the forecasted VaR during the next time period is over $1M with probability of 79.2% obtained through the definition of conditional probability: P(VaR>x)=P(Var>x|Risk event occurs) P(risk event occurs).
We describe here a specific embodiment of the invention for pre-emptive operational risk management and risk discovery using a simple example based on analyzing the risks in each desk for a trading scenario. The goal hiere is to identify Key Risk Indicators that can be employed in a proactive manner through ongoing monitoring to provide early warning/alerts to future risk events.
Our approach is as follows:
Many statistical techniques are readily applicable to modeling the operational risk, which corresponds to the function block 104 in
The issue of selecting key risk factors can be addressed by hypothesis testing. For instance, if we want to check whether X1, X2 are important factors in determining the probability of risky events, we may fit the model reduced from Equation (1) without X1, X2, i.e., with the constraint of β1=0, β2=0. We denote this reduced model as Model II and the complete model as Model I. We may test the significance of the reduction of log-likelihood from Model I to Model II by referring to classical generalized linear model theory (see, for example, Generalized Linear Models, P. McCullagh and J. A. Nelder, Chapman & Hall, 1989). We give a brief account of the procedure in the following. Let X1, . . . , Xn, y1, . . . ,yn be the observed data sample where Xt is the business metric as time t and yt is an indicator of risky event at time t, i.e., yt=1 if there is a risky event and 0 otherwise. The log-likelihood function of the logistic regression is
where P(Xt) is specified by Equation (1). Models I and II have different log-likelihood since they have different model formula for P(Xt). The significance of reduction of log-likelihood can be tested by the test statistic D=2[LL(Model I)—LL(Model II)]. D is usually referred as deviance. Under the null hypothesis that Model I and Model II are equivalent, D follows approximately a chi-squared distribution with degree of freedom df=number of extra parameters in Model I. Large D indicates significant reduction in the log-likelihood, which further indicates the significance of the variables not included from the complete model, i.e., Model I. In the aforementioned example, suppose the deviance D between Model I and Model II is 12.45, the corresponding P-value is P(X22>12.45)=0.002, i.e., there is only 0.2% probability of observing a deviance D as high as 12.45 should Model II be equivalent to Model I, which is very unlikely. Therefore, we reject the null hypothesis, i.e., the variables X1, X2 are key risk indicators.
It is also capable of predicting the probability of risky events in future based on the calibrated model parameters and time series forecasting of the business metrics Xt. Pt can also be interpreted as a composite score for operational risk.
Another approach of identifying a few factors that can be used to score operational risk does not require a specific model assumption like the one postulated in Equation (1). Let X1, . . . , Xn be the normalized observed business metrics through time period 1, . . . , n where Xt=(X1,t, . . . ,Xp,t) is a p-dimensional vector and each component corresponds to a risk indicator. The meaning of “normalized” is that each component of X is standardized by subtracting the mean and then dividing by the standard deviation. Since p is typically large, we may apply Principal Component Analysis (PCA) to identify s key risk indicators derived from the p components where s<<p. Principal Component Analysis (PCA) aims at reducing a large set of variables to a small set without losing much of the information in the large set (see, for example, Principal Component Analysis, Jolliffe I. T., New York: Springer, 1986). More specifically, we look for
a linear combination of X1,t, . . . , Xp,t, which has the most variation, i.e.
The problem can be solved by solving the eigenvalue decomposition of the variance-covariance matrix of X, denoted by
where T stands for transpose of vector or matrix. Let λ1≧λ2≧ . . . ≧λp≧0 be the leading eigenvalues of Σ and W1, . . . , Wp be the corresponding eigenvectors, then the first s principal components are WiTX,i=1, . . . , s. If the percentage of variation that explained by these s components,
is sufficiently high (above 95%, say), then most information carried in the original p factors are well retained by the s components. Therefore, we may model the probability of risk events as a function of these s principal components, W1TX, . . . , WsTX, where s<<p. Often it is the case that a key risk indicator is one or several nonlinear functions of the observed Xt. In this scenario, traditional PCA cannot reduce the dimensionality effectively. A nonlinear version of PCA can be performed. It is a linear PCA in a reproducing kernel Hilbert Space H. (See, for example, Learning with Kernels, B. Scholkopf and A. J. Smola, MIT Press, Cambridge, Mass., 2002). Define a mapping Φ from space of X to H such that for any X,X′ ε X, the inner product in space is defined as <Φ(X),Φ(X′)>=K(X,X′), where K(,) is a kernel function that measures similarity between X,X′. A typical choice of K(,) is polynomial kernel function K(x,x′)=(xTxt)d. Let λ1≧λ2 . . . and W1, W2, . . . be the eigenvalues and eigenvectors of the Gram matrix K=(K(Xi,Xj))1≦i,j≦n, then the kth leading principal component in space H can be written as
So rather than using all p components of X, we may just use the first s several leading principal components,
as our key risk factors provided that
is large enough (say, above 95%). In practice, the number of leading components to retain can be adjusted iteratively until satisfactory prediction power is achieved.
This model can then be used as a basis to perform risk prediction for future time periods.
Computer system 700 may include additional servers, clients, and other devices not shown. In the depicted example, the Internet provides the network 702 connection to a worldwide collection of networks and gateways that use the TCP/IP (Transmission Control Protocol/Internet Protocol) suite of protocols to communicate with one another. At the heart of the Internet is a backbone of high-speed data communication lines between major nodes or host computers, consisting of thousands of commercial, government, educational and other computer systems that route data and messages. In this type of network, hypertext mark-up language (HTML) documents and applets are used to exchange information and facilitate commercial transactions. Hypertext Transfer Protocol (HTTP) is the protocol used in these examples to send data between different data processing systems. Of course, computer system 700 also may be implemented as a number of different types of networks such as, for example, an intranet, a local area network (LAN), or a wide area network (WAN).
Referring to
Peripheral component interconnect (PCI) bus bridge 814 connected to I/O bus 812 provides an interface to PCI local bus 816. A number of modems may be connected to PCI bus 816. Typical PCI bus implementations will support four PCI expansion slots or add-in connectors. Communications links to network computers 808, 810 and 812 in
Additional PCI bus bridges 822 and 824 provide interfaces for additional PCI buses 826 and 828, from which additional modems or network adapters may be supported. In this manner, server 800 allows connections to multiple network computers. A graphics adapter 830 and hard disk 832 may also be connected to I/O bus 812 as depicted, either directly or indirectly.
Those of ordinary skill in the art will appreciate that the hardware depicted in
The data processing system depicted in
With reference now to
In the depicted example, local area network (LAN) adapter 910, Small Computer System Interface (SCSI) host bus adapter 912, and expansion bus interface 914 are connected to PCI local bus 906 by direct component connection. In contrast, audio adapter 916, graphics adapter 918, and audio/video adapter 919 are connected to PCI local bus 906 by add-in boards inserted into expansion slots. Expansion bus interface 914 provides a connection for a keyboard and mouse adapter 920, modem 922, and additional memory 924. SCSI host bus adapter 912 provides a connection for hard disk drive 926, tape drive 928, and CD-ROM drive 930. Typical PCI local bus implementations will support three or four PCI expansion slots or add-in connectors.
An operating system runs on processor 902 and is used to coordinate and provide control of various components within data processing system 900 in
Those of ordinary skill in the art will appreciate that the hardware in
Data processing system 900 may take various forms, such as a stand alone computer or a networked computer. The depicted example in
Note that the scope of this disclosure is not limited by the specific computational methods described in this document. The methodology and apparatus described herein can be combined with other computational methods for operational risk. Moreover, this disclosure is not limited by any specific system components described in this document. A pre-emptive operational risk management solution can be realized by combining the methodology described herein with other system components. Further, the scope of this disclosure is not limited by specific risk indicators or business metrics described in this document. The invention described here is applicable to any selected set of risk indicators, business metrics.
While the invention has been described in terms of a single preferred embodiment, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the appended claims.
This application is related in subject matter to copending U.S. patent application Ser. No. 10/983,641 filed Nov. 9, 2004, by Feng Cheng, David Gamarnik, Wanli Win, Bala Ramachandran, and Jonathan Miles Collin Rosenoer for “Method and Apparatus for Operational Risk Assessment and Mitigation” and assigned to a common assignee herewith. The disclosure of application Ser. No. 10/983,641 is incorporated herein by reference.