top of page

Stress Testing and Risk Integration in Banks

Table of Contents

1. Introduction to Stress Testing and Risk Integration

1.1 Antidote to the Crisis

   1.1.1 What Went Wrong

   1.1.2 Regulatory Responses

1.2 Stress Testing, Risk Integration, and Reverse Stress Testing

   1.2.1 Stress Testing

   1.2.2 Risk Integration and Reverse Stress Testing

1.3 Book Structure at a Glance

   1.3.1 Organization of the Book

1.4 Summary

2. Macroeconomic Scenario Analysis from a Bank Perspective

2.1 Introduction

2.2 Autoregression and Moving-Average Modeling

   2.2.1 AR(p) Analysis

   2.2.2 MA(q) Analysis

   2.2.3 ARMA(p, q) Analysis

   2.2.4 Box-Jenkins Time Series Analysis

2.3 Vector Autoregression and Vector Error-Correction Modeling

   2.3.1 Vector Autoregression and Vector Error-Correction Analysis

   2.3.2 Vector Autoregression and Vector Error-Correction Forecast

   2.3.3 Impulse Response Analysis

2.4 Global Vector Autoregression Modeling

   2.4.1 Introduction to the Global Vector Autoregression Model

   2.4.2 Global Vector Autoregression Analysis

   2.4.3 Global Vector Autoregression Forecast

   2.4.4 Generalized Impulse Response Analysis

2.5 Stress Testing Scenario

   2.5.1 Scenario Design

   2.5.2 Conditional Forecasting

   2.5.3 Bank Alpha’s Stress Testing Scenario

   2.5.4 Macroeconomic Modeling and Satellite Frameworks

2.6 Summary

Appendix. Robust Vector Error Correction Model: A Forward Search Approach



3. Asset and Liability Management, and Value at Risk

3.1 Introduction

3.2 Margin at Risk

   3.2.1 Margin at Risk Estimation

   3.2.2 Interest Rate Sensitivity Analysis

   3.2.3 Term Structure of Interest Rates

   3.2.4 Margin at Risk Under a Stress Testing Scenario

   3.2.5 Bank Alpha’s Stress Testing Margin at Risk

3.3 Value at Risk

   3.3.1 Variance-Covariance Value at Risk

   3.3.2 Monte Carlo Simulation Value at Risk

   3.3.3 Historical Simulation Value at Risk

   3.3.4 Stress Testing and Regulatory Value at Risk

   3.3.5 Bank Alpha’s Market RWA

3.4 Liquidity Analysis

   3.4.1 Bank Alpha’s Liquidity Analysis

3.5 Summary

Appendix A. Kalman Filter for Affine Term Structure Models

Appendix B. Robust Kalman Filter: A Forward Search Approach to Estimate Affine Term Structure Models


4. Portfolio Credit Risk Modeling

4.1 Introduction

4.2 Credit Portfolio Modeling

   4.2.1 Credit Loss Distribution

   4.2.2 CreditMetrics

   4.2.3 Credit Portfolio Modeling With Copulas

4.3 Credit Risk-Weighted Assets

   4.3.1 Standardized Credit Risk-Weighted Assets

   4.3.2 Internal Ratings-Based Credit Risk-Weighted Assets

   4.3.3 Bank Alpha’s RWAs for Credit Risk

4.4 How to Link Credit Risk Parameters and Macroeconomic Variables

   4.4.1 Default Probability and Macroeconomic Variables

   4.4.2 Loss Given Default and Macroeconomic Variables

4.5 Portfolio Credit Risk Stress Testing

   4.5.1 Stress Testing Risk-Weighted Assets

   4.5.2 Portfolio Credit Stress Testing

4.6 Summary

Appendix A: Default Probability Estimation Via Logit Regression

Appendix B: The Forward Search for Elliptical Copulas



5. Balance Sheet, and Profit and Loss Stress Testing Projections

Key Abbreviations and Symbols

5.1 Introduction

5.2 Balance Sheet Projection

   5.2.1 Credit Life Cycle

   5.2.2 Performing Portfolio Projection

   5.2.3 Nonperforming Portfolio Projection

   5.2.4 Trading Book, Other Assets, and Liabilities Projection

   5.2.5 Bank Alpha’s Stress Testing Balance Sheet

5.3 Profit and Loss Projection

   5.3.1 Profit and Loss Mechanics

   5.3.2 Bank Alpha’s Stress Testing Profit and Loss

5.4 Conduct and Operational Risk Stress Testing

   5.4.1 Projection of Conduct and Operational Losses

   5.4.2 Risk-Weighted Assets for Operational Risk

   5.4.3 Bank Alpha’s Stress Testing Operational RWA

5.5 Summary



6. Regulatory Capital, RWA, Leverage, and Liquidity Requirements Under Stress

6.1 Introduction

6.2 Regulatory Capital

   6.2.1 How to Compute the Regulatory Capital

   6.2.2 Bank Alpha’s Stress Testing Regulatory Capital

6.3 Risk-Weighted Assets and Capital Ratios

   6.3.1 Bank Alpha’s Risk-Weighted Assets (From a Silo Perspective)

   6.3.2 Risk-Weighted Asset Aggregation

   6.3.3 Bank Alpha’s Stress Testing Capital Ratios

6.4 Leverage and Liquidity Ratios

   6.4.1 Leverage Ratio

   6.4.2 Bank Alpha’s Stress Testing Leverage

   6.4.3 Liquidity Coverage Ratio

   6.4.4 Bank Alpha’s Stress Testing Liquidity Coverage Ratio

   6.4.5 Net Stable Funding Ratio

   6.4.6 Bank Alpha’s Stress Testing Net Stable Funding Ratio

6.5 Summary



7. Risk Integration

7.1 Introduction

7.2 Top-Down Risk Integration Modeling

   7.2.1 Basic Integration

   7.2.2 Top-Level Integration

   7.2.3 Base-Level Integration

7.3 Bottom-Up Economic Capital Integration Modeling

   7.3.1 Economic Capital Integration

   7.3.2 Integration Process

   7.3.3 Bank Alpha’s Integrated Economic Capital

7.4 Bottom-Up Liquidity Integration Modeling

   7.4.1 Risk Integration: Liquidity (Short-Term Perspective)

   7.4.2 Bank Alpha’s Integrated Liquidity

7.5 Summary



8. Reverse Stress Testing

8.1 Introduction

8.2 Reverse Stress Testing Objective Function

   8.2.1 Reverse Stress Testing: Economic Capital Versus Liquidity Mismatching

8.3 Integrated Risk Modeling and Vulnerability Thresholds

   8.3.1 Long- and Short-Run Risk Integration

   8.3.2 Vulnerability Thresholds

8.4 Bank-Specific Disastrous Event Fact Finding

   8.4.1 Trading Book

   8.4.2 Banking Book

   8.4.3 Liquidity and Overall Financial Structure

8.5 Exploration of Ruinous Macroeconomic Scenarios

   8.5.1 Long- and Short-Run Ruinous Scenarios

   8.5.2 Conditional Mean and Hull Contours

   8.5.3 Bank Alpha’s Ruinous Scenario Analysis

8.6 Summary


bottom of page