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Description
ABSTRACT
Bayesian networks is an emerging tool for a wide range of risk management applications, one of which is the modeling of operational risk. This comes at a time when changes in the supervision of financial institutions have resulted in increased scrutiny on the risk management of banks and insurance companies, thus giving the industry an impetus to measure and manage operational risk. The more established methods for risk quantification are linear models such as time series models, econometric models, empirical actuarial models, and extreme value theory. Due to data limitations and complex interaction between operational risk variables, various nonlinear methods have been proposed, one of which is the focus of this article: Bayesian networks. Using an idealized example of a fictitious on line business, we construct a Bayesian network that models various risk factors and their combination into an overall loss distribution. Using this model, we show how established Bayesian network methodology can be applied to: (1) form posterior marginal distributions of variables based on evidence, (2) simulate scenarios, (3) update the parameters of the model using data, and (4) quantify in real-time how well the model predictions compare to actual data. A specific example of Bayesian networks application to operational risk in an insurance setting is then suggested.
INTRODUCTION
Bayesian networks (BNs) have recently been explored as a potential tool for various risk management applications. Its main features of combining subjective opinion with observed data and modeling cause-and-effects make it especially well suited for investigating and capturing the workings of financial institutions. Although its usage has thus far been limited to specific areas (e.g., it has been used for credit risk scoring by banks) its application to wider enterprise risks is being increasingly documented, especially in the area of operational risk (OR).
Chapter 14 of Alexander (2003) provides a brief introduction to modeling OR using BNs via a banking example. Marshall (2001), Cruz (2002), and Hoffman (2002) give brief overviews of BNs and where they fit into the whole framework of OR modeling. There is also an illustrative albeit high-level discussion on causal modeling using BNs via a banking example in King (1999).
The main purpose of this article is to consider two aspects of the application of BNs to OR in greater detail than has so far appeared in the literature. These are the theory and techniques of model updating, and the subject of model assessment. OR takes place in a dynamic setting, with more information becoming available as time progresses. Hence, it is useful to update the models used for OR to take account of this flow of information. This is feasible within the setting of BNs and was briefly mentioned in King (1999); the section on "Updating the Probabilities With New Data" of this article gives more details of how this can be implemented. In any modeling exercise, it is essential to check that the model used provides a reasonable representation of the actual experience. Again, this is best done dynamically in the OR setting, as more information arrives; this is covered in the section on "Model Assessment" of this article.
The article is set out as follows. In the section on "Changes to Supervisory Regimes as a Driver for Operational Risk Modeling," we describe recent developments in the supervision of financial institutions and how this has encouraged greater efforts in OR modeling. In the "Current Approaches to Modeling OR" section, we give a brief introduction to modeling approaches that have been used in the context of OR. The approach used in this article is that of BNs, which are introduced in the next section and applied in a general risk management context in the subsequent section. In the sections on "Updating the Probabilities With New Data" and "Model Assessment," we consider two aspects of BNs and OR that have not been covered in any detail in the literature to date: updating the models and monitoring the appropriateness of the model. In the section on "Insurance Fraud Risk Example," we briefly mention an example of how BNs can be used specifically for OR modeling in an insurance setting. The concluding section contains a discussion of the issues raised in this article.
CHANGES TO SUPERVISORY REGIMES AS A DRIVER FOR OPERATIONAL RISK MODELING
Developments in the quantification of OR has, to a significant extent, been driven by changes in the supervisory regimes for financial institutions. These changes have increased the level of supervisory scrutiny on OR and how it is managed by financial institutions--a reflection of the centrality of OR in high-profiled corporate failures in recent decades. This has become an impetus for financial institutions to develop OR models as a means to demonstrate good management and financial strength.
The banking sector paved the way when the Basel Committee for Banking Supervision (BCBS) of the Bank for International Settlements (BIS) began work in 1999 on a new framework for capital adequacy of banks, (1) also known as "Basel 2." Basel 2 comprises three "pillars." Pillar I delineates the requirements for a minimum level of capital that banks need to hold depending on their specific risk exposure. Pillar II outlines measures for supervisory review of banks to ensure that the level of capital held and risk management is commensurate with each bank's risk profile. Pillar III provides a framework for market discipline via disclosure.
Under Pillar I, explicit charges to supervisory capital were introduced for banks' exposure to credit risk and OR. These are to be either calculated as a percentage of gross income or an internal model could be used provided certain criteria have been met. It is hoped that potential savings in capital required by the supervisor would provide an incentive for banks to develop internal models with accompanying improvements in risk management. (2)
The insurance sector is also overhauling its capital adequacy framework to be more reflective of insurance companies' risk exposure. The European Commission (EC) issued a consultation for a review of its rules on prudential supervision of insurance in 1999. Also known as "Solvency II," this review aims to produce a system that would "establish a solvency margin requirement that is better matched to the true risks." (3) Solvency II will follow the basic three-pillar structure of Basel 2 albeit modified to suit the insurance industry. (4) Similar to Basel 2, Solvency II will have a solvency capital requirement (SCR), which is intended as a "target capital": a prudent level of capital that will capture all material risks and allow supervisors sufficient time to intervene in adverse circumstances. Whereas the method to arrive at the SCR is still being deliberated, the discussions show that OR will be a key component. (5)
The International Association of Insurance Supervisors (IAIS), the insurance counterpart of BIS, has issued some instructive guidance to its members on supervision of capital adequacy and solvency. According to the IAIS, solvency regimes should have regard for OR. (6) Supervisors are to intervene when an insurance company's capital breaches a predetermined "solvency control level," (7) whose sensitivity to risk may be based on stress tests. (8) With regards to these stress tests, insurers should be able to demonstrate that they have sufficiently considered OR. (9)
We have seen that OR will feature prominently in emerging capital adequacy regimes. The increased complexity of such regimes would require more intense supervision, not least in OR measurement and management. Pillar II of Basel 2 stipulates that "Supervisors should review and evaluate banks' internal capital adequacy assessments and strategies, as well as their ability to monitor and ensure their compliance with regulatory capital ratios." (10) This would also serve to assess that banks meet the criteria for usage of the Standardized Approach or Advanced Measurement Approach (11) for calculating OR capital. Findings from a 2002 report (12) (also known as the "Sharma report") commissioned by the EC as part of the Solvency II review showed that most insurer failures resulted from problems with management. This led to inadequate controls, which left insurers vulnerable to external events. Thus, the predominant root cause of insurer failures is operational. The report recommends that the Solvency II framework requires supervisors to address the underlying problems before they occur via supervisory tools such as assessment of risk management and corporate governance of insurers. (13) To facilitate this, Solvency II will broaden insurance supervisors' powers to enable them to carry out such assessments and take certain actions (such as imposing capital add-ons) where necessary. (14) Principle 13 of the IAIS Principles of Capital Adequacy and Solvency requires supervisors to consider adequacy of companies' internal risk assessment and management, alongside more established aspects of solvency assessment such as accuracy of valuations and compliance with minimum levels. (15) This has lead banks and insurers to develop more sophisticated quantitative models that serve not only to satisfy supervisory authorities of the adequacy of their capital but also to demonstrate strong risk management.
Whereas models have been developed for the purpose of internal management, it is clear from the references made to the new supervisory regimes by current literature on OR that there has not been a shortage of OR models proposed in response to such supervisory requirements. This article adds to the existing corpus by discussing the use of BNs as a framework for modeling OR. We shall see that this is an efficient and intuitively coherent methodology for incorporating expert input. In addition, BNs are useful for capturing causal dependence. This satisfies a vital requirement of any OR modeling framework: the ability to model causation (this is discussed further below). Developments in the field of graphical models (of which BNs are an example) have led to the development of several user-friendly software tools that automatically carry out the complex calculations for making inference from complex networks of causal relationships. Underlying BNs is the Bayesian statistical framework that enables the combination of subjective input with empirical observations. This lends itself very well to situations with a high degree of uncertainty, and where data are costly or sparse--two intrinsic features of OR.
CURRENT APPROACHES TO MODELING OR
Although this section is not intended as a complete survey of current models available for modeling OR, it would be instructive to briefly mention main categories of model to see where BNs fit in the spectrum.
Value-at-Risk and Ruin Theory
The broad approach to the setting of economic capital at the moment revolves around obtaining a single figure that is often defined as a high quantile of a loss distribution that is projected over a required period based on past data. This has its origins in Value-at-Risk (VaR) used by banks to measure their exposure to market risk. Thus, for example, BCBS requires that "a bank must demonstrate that its operational risk measure meets a soundness standard comparable to that of the internal ratings based approach for credit risk, (i.e., comparable to a 1-year holding period and a 99.9th percentile confidence interval)." (16) A whole body of literature exists detailing the workings of VaR in setting economic capital for market risks and credit risks (see, e.g., Jorion, 2001; Dowd, 1998).
Presently, if VaR is calculated for OR, the approach commonly ranges from the residual approach (firmwide VaR minus market VaR and credit VaR) to setting the VaR as a multiple of... |
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