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Operational Risk Capital Models

Edited By Rafael Cavestany, Brenda Boultwood and Laureano F. Escudero


Operational Risk Capital Models is a guide for the implementation of state of the art operational risk capital models suitable for regulatory approval.

For insurers, Solvency II implementation has created the need, in both highly developed and less developed markets, for the development of these models that help to better understand risks, safe capital and compliance. For the banking industry, regulators in many countries in Africa, Asia and Latin America (as well as Europe) are pressing their local banks to implement advanced operational risk capital models. Banks that have made early implementation are looking to improve their capital models with new advances to match the increasing regulatory requirements.

Take a detailed look at what this book covers here with the Introduction from Rafael Cavestany.

"I found the quantitative methods presented in “Operational Risk Capital Models” to be not only rigorous, but also understandable and actually useable and useful, which can be said of shockingly few books treating operational risk. Amidst a wasteland of operational risk management pie charts and unactionable and subjective heat maps, books like this are an oasis of practical, applied solutions for capital estimation and stress testing. If your objective is to directly and measurably mitigate and manage operational risk using scientifically defensible, objective methodology, as opposed to red-amber-green traffic ‘analyses,’ the methods herein are the kind you need."

J.D. Opdyke, author of multiple Journal of Operational Risk papers and winner of OR&R’s “Operational Risk Paper of the Year” Award in 2012 and 2015.


Publish date: 30 Apr 2015

Availability: In stock

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Book description

Operational Risk Capital Models enables you to model your operational risk capital to ensure the model meets regulatory standards. It describes the process end to end, from the capture of the required data to the modelling and VaR calculation, as well as the integration of capital results into your institution’s daily risk management.

Chapters include:

•    Modelling Challenges
•    Regulatory Compliance and Supervision
•    Operational Loss Modelling
•    External Data Rescaling
•    Scenario Analysis Framework and Modelling
•    BEICFs Modelling and Integration into Capital Model
•    Capital Results Integration into Business Planning and Risk Appetite
•    Hybrid Model Construction: Integrating ILD, ED and SA

Operational Risk Capital Models is essential for the creation of op risk capital models for both regulatory compliance and improving risk management practices.The book addresses and resolves the challenges in the implementation of advanced operational risk capital models by presenting a highly detailed end-to-end process for the capital model construction, compliance and integration into management.

The first part of the book describes a robust framework for the definition and capture of the four data elements: Internal Loss Data, External Data, Scenario Analysis and Business Environment Internal Control Factors. This part includes topics such as the validation of scenario analysis and the use of business environment and internal control factors as inputs to the capital model. It provides insights for mitigating cognitive biases in scenario analysis and defines a common understanding for operational loss. It also presents state-of-the-art methods for expert judgment elicitation (Structured Expert Judgment) and their application into operational risk scenario analysis.

The second part presents the exhaustive modelling and integration of the four data elements to compute operational risk VaR, capital and depict the operational risk profile of the institution. This part addresses all standard and more advanced topics, such as the modelling of BEICFs and their use in capital allocation, correlation calculation and ex-post capital adjustment; modelling of scenario analysis including GoF, tail control and more; determination of the optimal modelling granularity and threshold (up to 8 different methods); fitting distributions with old and new loss data by the use of a decay factor; analysis of capital instability (the resampling and what-if methods); various methods for external data re-scaling; construction of a hybrid model using credibility theory; operational risk dependencies including frequency-severity dependence and the use of expert judgment in their elicitation; different methods for capital allocation (contribution to expected shortfall, Heuler allocation, incremental analysis and others); backtesting of severities, frequencies and total losses; stress testing under different approaches including the modified LDA, regression, historical analysis, scenario analysis based and more.

In the third part, the work turns into the integration of capital results into the day to day management: embedding of the operational risk profile into strategic and operational business planning process; operational risk appetite definition, cascading down, monitoring and adherence; and the risk/reward evaluation of the effectiveness of controls and mitigation plans (insurance, action plans, critical infrastructure protection, operational risk predictive models and the determination of the optimal mitigation strategy using adversarial risk analysis).

Finally, the book's appendices examine in detail the distributions used in operational risk modelling including truncated, shifted, mixtures, empirical and plain vanilla parametric distributions; different credibility theory models, optimization methods used in operational risk modelling and business risk modelling.

Book details

Book - 9781782722014 / eBook 9781782722373
Publish date
30 Apr 2015
155mm x 235mm

Editor biography

Rafael Cavestany, Brenda Boultwood and Laureano F. Escudero

Rafael Cavestany has over fifteen years of experience in the financial services industry covering the banking and insurance sectors.  He currently works as a director in True North Partners Group and SKITES. Before, Rafael worked at Everis as Executive Director of the risk management practice and PwC as Senior Manager. He has worked on projects for a number of leading financial institutions in USA, Canada, UK, Spain, Italy, LatAm and South Africa and his experience is focused on consulting projects for the development of risk management tools and the corresponding methodologies, workflows and data requirements, etc. with special emphasis on operational risk modelling. Rafael Cavestany received the MBA degree from University of Michigan in 1997, a degree in Economics from Universidad Autónoma de Madrid and is currently finishing his PhD thesis in Statistics.

Brenda Boultwood is the Senior VP of Industry Solutions at MetricStream. Previously, Brenda served as Senior Vice President and Chief Risk Officer at Constellation Energy. Prior to that, she served as Global Head of Strategy, Alternative Investment Services, at J.P. Morgan Chase & Company. At Bank One Corporation, she served as Head, Corporate Market Risk Management and Counterparty Credit, and Head of Corporate Operational Risk Management, before advancing to Head, Global Risk Management for the company’s Global Treasury Services group.

Brenda has also worked with PricewaterhouseCoopers and Chemical Bank Corporation. In addition, she has spent time teaching at the University of Maryland’s MBA program. Brenda was a member of the CFTC Technology Advisory Committee, and has also served on the Board of the Global Association of Risk Professionals (GARP).  She currently serves on the Board of the Committee of Chief Risk Officers (CCRO). Brenda graduated with honors from the University of South Carolina with a Bachelor’s degree in International Relations. She also earned a Ph.D. in Economics from the City University of New York.

Professor Laureano F. Escudero received the PhD. Degree in Economics from the Universidad de Deusto, Bilbao, Spain, in 1974 and a degree in Computer Science from Universidad Politecnica de Madrid, Spain, 1972. He has been Professor of Statistics and Operations Research at the Universidad Rey Juan Carlos, Spain, 2007-2013. In the period 2003-04 he was the President of EURO (Association of European Operational Research Societies).  He has worked at IBM Research, Scientific and Development Centers in Madrid (Spain), Palo Alto (California), Sindelfingen (Germany) and Yorktown Heights (NY), 1972-1991. He taught Mathematical Programming at the Mathematical Sciences School, Universidad Complutense de Madrid, Spain, 1992-2000 and Stochastic Programming at the Universidad Miguel Hernandez, Spain, 2000-2007. He is the author of 5 books, has co-edited 5 others, and has published over 135 scientific papers in leading journals and over 30 chapters in edited books. He has worked in different mathematical programming fields (linear, integer, nonlinear, stochastic) and its risk management applications to finance, energy, supply chain management and air traffic, among other sectors.

Table of contents

Marcelo Cruz

Rafael Cavestany

PART I - Capture and Determination of the Four Data Elements

1. Collection of Operational Loss Data: ILD and ED
Brenda Boultwood

  • Towards a Common Understanding of Operational Loss
  • Completeness of Data Collection
  • Consistency with Accounting
  • External Data

2. Scenario Analysis Framework and BEIFCs Integration
Rafael Cavestany, Brenda Boultwood and Daniel Rodriguez

  • Scenario Support Data and Preparation
  • Scenario Rating
  • Scenario Validation
  • BEICFs as an Input into Scenario Analysis

PART II - General Framework for Operational Risk Capital Modelling

3. Loss Data Modelling: ILD and ED
Rafael Cavestany and Daniel Rodriguez

  • Exploratory Analysis and Selection of a Homogeneous Data Sample
  • Optimal Modelling Granularity
  • Tail Shape and Threshold Determination through Extreme Value Theory
  • Severity Distributions Fitting
  • Frequency Distribution Fitting
  • Goodness-of-Fit (GoF) Evaluation
  • Stability Analysis of Capital Estimates, Distribution Parameters, and GoF
  • Evaluating if the Capital Estimates are Realistic
  • External Data Rescaling
  • Definition of the Loss Data Modelling Process

4. Scenario Analysis Modelling
Rafael Cavestany

  • Translating Scenario Analysis Questions into Distribution Characteristics
  • Fitting a Full Distribution to Scenario Analysis
  • Distribution Shape Control during the Scenario Distribution Fit
  • Goodness of Fit in Scenario Analysis
  • Splitting Scenario into Lower Organizational Entities

5. BEICFs Modelling and Integration into Capital Model
Rafael Cavestany

  • Ex-post Capital Adjustment Driven by BEICFs
  • Modelling BEICFs
  • Qualitative and Structured Determination of Correlations based on BEICFs
  • Capital Attribution Driven by BEICFs

6. Hybrid Model Construction: Integration of ILD, ED and SA
Rafael Cavestany, Daniel Rodriguez and Fabrizio Ruggeri

  • Credibility Theory: Determining the Weights for ILD, ED and SA in the Hybrid Model
  • The Mixture Approach
  • The Bayesian Approach
  • Tail Complementing with External Data Losses
  • Tail Complementing with Scenarios
  • Mixing Distribution Properties from Different Data Elements during the Fit

7. Derivation of the Joint Distribution and Capitalisation of Operational Risk
Rafael Cavestany

  • Monte Carlo Simulation
  • Single Loss Approximation: Analytical Derivation of the Loss Distribution
  • Operational Risk Correlations
  • Using Copulas for Replicating Operational Risk Dependencies
  • Capitalization of Operational Risk
  • Allocation of Operational Risk Capital
  • Operational Risk Profile Measurement

8. Backtesting, Stress Testing and Sensitivity Analysis
Rafael Cavestany and Daniel Rodriguez

  • Backtesting of Severities
  • Backtesting of Annual Frequency
  • Backtesting of Annual Total Losses
  • Stress-testing of Severities and Frequencies
  • Stress-testing of Operational Risk Correlations

9. Evolving from a Plain Vanilla to a State of the Art Model
Rafael Cavestany

PART III - Use Test, Integrating Capital Results into the Institution´s Day-To-Day Risk Management

10. Strategic and Operational Business Planning and Monitoring
Lutz Baumgarten, Rafael Cavestany and Brenda Boultwood

  • Integrating the Operational Risk Profile into the Strategic and Operational Planning
  • Integrating Capital Results into the GRC Risk Reporting
  • ORA for Monitoring the Strategic and Business Plan

11. Risk/reward Evaluation of the Mitigation and Control Effectiveness
Rafael Cavestany and Javier Moguerza

  • Insurance Programmes: Evaluation of their Mitigation Impact
  • Risk/reward Evaluation of the Mitigation Impact of Action Plans
  • Internal Audit Non-Conformities Evaluation
  • Process Improvement: Six Sigma and Operational Risk
  • Operational Loss Prediction Analytics
  • Adversarial Risk Analysis: Linking Risk Measurement with Optimal Mitigation

Appendix I - Distributions for Modelling Operational Risk Capital
Daniel Rodriguez

Appendix II - Credibility Theory
Daniel Rodriguez

Appendix III – Mathematical Optimization Methods Required for Operational Risk Modelling and Other Risk Mitigation Processes
Laureano Escudero

Appendix IV – Business Risk Quantification
Lutz Baumgarten


"The book covers in detail all the building blocks of operational risk modelling with a very pragmatic, step-by-step, view from industry practitioners so the reader can see how the operational risk capital is actually calculated and stress tested. The authors move from the technicalities of capital calculation to the integration of this capital into the strategic and tactical decisions of the financial institution. In my view, this book is a strong contribution to operational risk management in this new era."

Marcelo Cruz, Professor, New York University Stern School of Business and Editor-in-Chief, Journal of Operational Risk

Customer Reviews

Average customer reviews for Operational Risk Capital Models

Meeting the theoretical with the practical

The book provides an excellent view into how to practically model operational risk, showing alternative methods that have all been tried and tested. While many theoretical texts are out there, few are able to distill down into something pragmatic enough to implement in practice being able to trade off statistical reliability with issues of lack of data and expert judgement. This book covers these issues and a full range of possible ways depending on what is available to the modeler.
Review by Andrew Morgan - Quantitative Risk Analyst, Old Mutual plc , 26/10/2015

A very practical and implementable approach to operational risk modelling

The book includes interesting and innovative topics such as structured scenario analysis, techniques for determining optimal level of granularity for modelling, methods for qualitative derivation of correlation, and the modelling of correlation between frequency and severity. The outputs of proposed quantitative methods can be integrated into daily risk management practices and performance measures, making the book very relevant for modern day financial institutions.
Review by Flippie Snyman, Enterprise Risk Management, FirstRand , 26/10/2015

A practical book to start building Op Capital models

An easy to read book that covers all relevant topics on how to build operational risk capital models. Its easy to pick up this book and start designing and planning your model implementation. The authors are practitioners in the field and hence the book gets to implementation issues quickly with practical ways to solve common challenges we face in the course of our work. I recommend this book to anyone wanting to start implementing models.
Review by Niru , 24/10/2015

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