Table of Contents 1 Introduction PART I Database Modeling 2 Database Modeling Introduction Building a Data Model Duration of Operational Risk Events Model Risk - Model, Inputs and Price Verification The Impact of Operational Risk in Market and Credit Risks Basic Database Framework for Risk Integration Including Insurance/ Hedging in the Database Provisioning Treatment of Operational Losses Developing an Operational Risk Policy PART II Stochastic Modeling 3 Severity Distributions Introduction General Approach Basic Concepts in Probability Theory Goodness-of-Fitness Tests List of Distributions Application to a Legal Events Database 4 Extreme Value Theory Introduction Risk Management and the Statistics of Extremes Extreme Distributions and EVT Application to Operational Risk Goodness of Fit Tests Working with Quantiles 5 Frequency Distributions Introduction List of Distributions Goodness-of-Fit Tests Application to the Frauds Database Extreme Events Frequency Analysis 6 The Operational Risk VaR Introduction The Concept of VaR and the differences between market and operational VaR Aggregated Risk Models Aggregating Severity and Frequency Coherent Measures of Risk Backtesting Operational VaR Models 7 Stochastic Processes in Operational Risk Introduction Risk Theory and Ruin Processes in OR Ruin Theory Applied to Hedging an OR Portfolio Markov Chain Renewal Processes Queuing Theory Reliability and Mean Time Between Failures (MTBF) Stopping Times Mixtures PART III Causal Models 8 Causal Models : Applying Econometrics and Time Series Statistics to Operational Risk Introduction Basics of Multiple Regression Econometric Models Usual Problems Model Selection Criteria Spectral Analysis Multivariate Analysis Multifactor Models in Operational Risk State-Space Models and the Kalman Filter Regime-Switching Models Discriminant Analysis (OR Scores) Developing a Matrix of OR Scores Migration 9 Non-Linear Models in Operational Risk Introduction Neural Networks Bayesian Belief Networks