An integrated inverse adaptive neural fuzzy system with Monte-Carlo sampling method for operational risk management

https://doi.org/10.1016/j.eswa.2018.01.001Get rights and content

Highlights

  • A flexible integrated inverse adaptive fuzzy inference model is proposed.

  • The model contributes to improve operational risk measurement.

  • The model combines Monte Carlo estimation of loss distribution and risk profiles.

  • The model relies on the fuzzy input that represents frequency and severity of risk.

  • The model can monitor the evolution of the risk profile of an organization.

Abstract

Operational risk refers to deficiencies in processes, systems, people or external events, which may generate losses for an organization. The Basel Committee on Banking Supervision has defined different possibilities for the measurement of operational risk, although financial institutions are allowed to develop their own models to quantify operational risk. The advanced measurement approach, which is a risk-sensitive method for measuring operational risk, is the financial institutions preferred approach, among the available ones, in the expectation of having to hold less regulatory capital for covering operational risk with this approach than with alternative approaches. The advanced measurement approach includes the loss distribution approach as one way to assess operational risk. The loss distribution approach models loss distributions for business-line-risk combinations, with the regulatory capital being calculated as the 99,9% operational value at risk, a percentile of the distribution for the next year annual loss. One of the most important issues when estimating operational value at risk is related to the structure (type of distribution) and shape (long tail) of the loss distribution. The estimation of the loss distribution, in many cases, does not allow to integrate risk management and the evolution of risk; consequently, the assessment of the effects of risk impact management on loss distribution can take a long time. For this reason, this paper proposes a flexible integrated inverse adaptive fuzzy inference model, which is characterized by a Monte-Carlo behavior, that integrates the estimation of loss distribution and different risk profiles. This new model allows to see how the management of risk of an organization can evolve over time and it effects on the loss distribution used to estimate the operational value at risk. The experimental study results, reported in this paper, show the flexibility of the model in identifying (1) the structure and shape of the fuzzy input sets that represent the frequency and severity of risk; and (2) the risk profile of an organization. Therefore, the proposed model allows organizations or financial entities to assess the evolution of their risk impact management and its effect on loss distribution and operational value at risk in real time.

Introduction

All organizations face operational risk, since this type of risk refers to the possibility of incurring losses due internal events such as deficiencies, flaws/inadequacies in processes, systems or people or due to external events (Bank for International Settlements, 2016). This means that no operation of an organization is exempt from possible losses. However, for managers and stakeholders, it is important to know when the magnitude of the losses becomes significant for an organization. Only when the magnitude of an operational risk is comprehended, it is possible to prioritize different operational risks.

Organizations need to manage operational risk to avoid or to mitigate its consequences. The management process includes the measurement of operational risk, which should lead to an understanding of the magnitude of this risk. The Basel Committee on Banking Supervision (BCBS) defined different possibilities for the measurement of operational risk. These definitions treat operational risk measurement from a regulator’s perspective. Nevertheless, in addition to complying with the regulator’s requirements, financial institutions have also to manage operational risk according to their risk appetite and tolerance.

One issue when measuring operational risk is that operational risk data is not that frequent when compared with other types of risk. Moreover, according to Reveiz and León (2009), the operational risk sources and exposures are more diverse, complex and context-dependent than those typical of other risks, in particular market and credit risk. That is one reason why supervisors require that operational risk measurement includes also qualitative methods, such as scenario analysis, Risk and Control Self Assessments (RCSA) or Key Risk Indicators (Girling, 2013).

The Value at Risk due to operational risk or operational value at risk (OpVaR) is interpreted as the maximum loss that can be expected, given a certain confidence level (α), within a certain period of time. The Loss Distribution Approach (LDA), as defined by Basel II, requires that a financial institution registers continuously all operational risk events and associated losses that occurred in a particular business line and related to a particular risk type, like fraud for example El Arif and Hinti (2014); ISO (2015); Mora Valencia (2010), to construct an empirical loss distribution (LD), which is subsequently used to estimate the OpVaR. We observe the following four development trends in the field of OpVaR that focus on estimating the LD using different methods or computational tools.

  • Bayesian risk models to identify the causes, the influence and the relations between a set of factors that define the risk exposure of an organization or financial institution (Andersen, Hager, Maberg, Naess, Tungland, 2012, Barua, Gao, Pasman, Mannan, 2016, Figini, Gao, Gindici, 2015, Lee, Park, Shin, 2009).

  • Vector models that adapt and learn from operational risk data. These models allow to identify factors, parameters and variables that are relevant to model operational risk. Within this research area, it is worth mentioning support vector machines (SVMs) that integrate various classifiers (Twala, 2010), use multiple agent systems for learning (Yu, Yue, Wang, & Lai, 2010), use experimental designs for selecting optimal weights (Yu, Yao, Wang, & Lai, 2011), or apply Bayesian concepts to identify the causes and influence between risk factors (Feki, Ben Ishak, Feki, 2012, Yu, 2014).

  • Models based on the principles of modeling and simulation of operational risk. We find models that allow to identify qualitatively the variables and parameters that can be used to model operational risk and estimate the OpVaR through the use of ontologies (Ye, Yan, Wang, Wang, & Miao, 2011) or by using data mining techniques (Koyuncugil & Ozgulbas, 2012); autoregressive models for making predictions, based on the evolution of the data, to estimate the OpVaR for both short and medium time predictions (Hernández, Opsina, 2010, Lin, Ko, 2009, Pinto, Monteiro, Nakao, 2011), as well as models that use multivariate distributions based on copulas to obtain the LD (Dorogovs, Solovjova, Romanovs, 2013, Koliali, 2016, Lopera, Jaramillo, Arcila, 2009, Mora Valencia, 2010).

  • Risk models that apply the principles of intelligent computational systems. Operational risk factors, such as those related to fraud, are complex and the data is often of a qualitative nature. Among these models, fuzzy systems stand out as they have demonstrated their effectiveness assessing risk in areas such like aviation or nutritional security (Hadjimichael, 2009). Also, we can find models that estimate risk based on fuzzy neural networks that use different learning schemes (Golmohammadi, Pajoutan, 2011, Khashman, 2010) or linguistic variables (Cooper, Piwcewicz, Warren, 2014, Deng, Sadiq, Jiang, Tesfamariam, 2011, Mitra, Karathanasopoulos, Sempinis, Dunis, 2016, Mokhtari, Ren, Roberts, Wang, 2012).

This paper contributes to the above fourth research area. With regard to measuring operational risk, we identify two ways in literature to approach this task: (1) modelling operational risk as a classification problem, e.g. by using Key Risk Indicators (Reveiz & León, 2009); (2) measuring operational risk in terms of the percentile of the loss distribution (OpVaR) following Basel II. Our work follows this second approach and proposed model’s benefits include (i) the possibility of working with qualitative risk data and (ii) the connection of risk measurement (OpVaR) with risk management, based on the risk management matrices. Thus, this paper makes a contribution that goes beyond the mere compliance with standards like Basel II by exploring new ways for operational risk management with the proposal of an Integrated Inverse Adaptive Neural Fuzzy System with Monte-Carlo sampling (IIANFSM) method that identifies the behavior and evolution of operational risk in an organization. The flexible structure of the proposed IIANFISM method can be categorized by the implementation of the following three sub-systems:

  • An Integrated Inverse Adaptive Neural Unbalanced Fuzzy System model (IIANUFSm) that identifies the structure and shape of the fuzzy input sets used to represent the frequency and severity of operational risk. Frequency refers to the number of times a risk event has occurred in a period of time, while severity refers to the impact that a particular risk event generated.

  • An Integrated Inverse Adaptive Neural Balanced Fuzzy System model (IIANBFSm) to identify the Inherited Risk Matrices (IRMs) that show the risk profile of an organization.

  • An Integrated Inverse Adaptive Neural Sampling Fuzzy System model (IIANSFSm) that identifies the evolution of a risk profile, using a Monte-Carlo sampling method for the fuzzy input sets and different Risk Impact Management Matrices (RIMMs) representing a sequence of risk impact, to show the evolution of risk impact management in an organization.

To configure the models, at the beginning (stage zero or start) a loss distribution (LD_MC) of reference is estimated. This is done according to the input variables of frequency and severity of operational risk and in compliance with Basel II definitions for AMA models (Bank for International Settlements, 2010). In a next stage (first stage), the model uses the LD_MC as a reference for the learning process. This is done in order to setup the models structure applying different RIMMs. In a second stage, the assessment of the evolution of risk impact management is carried out by the model. This is done according to the risk profile of the organization and by using Monte-Carlo sampling on the fuzzy input sets and different RIMMs.

Experimental results met expectations as the model was able to identify the risk profile of an organization, integrating three different models in one structure. The model IIANUFSm shows the structure and shape of the fuzzy input sets according to the RIMMs that define the sequence of risk. In the same way, the IRMs obtained by the model IIANBFSm represents the risk profile of an organization. After the learning process and using a neutral RIMM, the results obtained for the third model IIANSFSm revealed that the LDs evolve towards lower values of OpVaR in absence of a learning process due to a better risk impact management in an organization, preserving at all times the structure and shape of the LD distribution. These findings make the model ideal to assess the OpVaR in real time and also its evolution and risk impact management in an organization over time.

In Section 2 the conceptual and theoretical background for modelling the variables of frequency and severity of operational risk, and the estimation of LD by using the Monte-Carlo sampling method will be described. Additionally, the foundation for the estimation of OpVaRα will be explained. Section 3 presents the IIANFSM method and the behavior with respect to the estimation of the LD. Section 4 reports the experimental results regarding the behavior of the model in terms of the evolution of an operational risk profile. Finally, our main conclusions are drawn in Section 5.

Section snippets

Operational risk

The measurement of operational risk was included into the capital adequacy framework, known as Basel II, in 2004, as losses due to cases like Barings Bank and others made it necessary to include operational risk management in the regulation. Accordingly, operational risk has been defined by the Basel Committee on Banking Supervision (BCBS–Basel II) as follows:

the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition

Methodology

From the perspective of a financial institution there is a need and an opportunity as well to better integrate different elements and aspects of operational risk. On the one hand, an institution always needs to gain and preserve a good understanding of the magnitude of this type of risk by determining the OpVaR for the different business lines and eventually for the entire organization. On the other hand, operational risk has also to be managed, for example via risk management matrices, which

Stage 1: identification of fuzzy input sets (IIANUFSm)

Table 7 shows the behavior of the model in the learning phase in the estimation of the LD_MC for each risk profile in the sequence of risk. It can be observed that the model reached an IOA close to one regarding LD_MC (G.Pareto), and similar values for the IC-fingerprint indices, showing the stability of the model in the estimation of LD_MC for different risk profiles. Fig. 8 shows the structure and shape of the obtained input fuzzy sets that represent the random linguistic variable for

Conclusions

This paper presents an Integrated Inverse Adaptive Neural Fuzzy system with a Monte-Carlo structure (IIANFSM), which integrates in a single model both the Monte-Carlo sampling method and different RIMMs, which show the behavior in terms of the effect of risk impact management with regard to the LD in real time. The proposed model, in its different forms (IIANUFSm – Integrated Inverse Adaptive Neural Unbalanced Fuzzy System; IIANBFSm – Integrated Inverse Adaptive Neural Balanced Fuzzy System;

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