A First Course in Model Validation and Model Risk Management,

Edition 1

Editors: By Jonathan Schachter, Martin Goldberg and Chandrakant Maheshwari

Publication Date: 20 Apr 2026

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A First Course in Model Validation and Model Risk Management offers robust coverage for current and future financial engineers. Useful as part of a masters program, for self-study, or as a valuable reference, the textbook explains in step-by-step, practical terms how mathematical models owned by financial institutions are essential to their public activities, including sales, trading, risk management, and internal audits. Like a diverse fleet of cars maintained by a rental car location, a bank must make sure customers can "drive" any of its models for a specific financial product. The book covers both pricing and risk models. Chapters consider modeling basics, marked-to-market and marked-to-model asset classes, market risk, credit risk, portfolio risk, operational risk, capital model risk, and financial crime, along with machine learning/AI.

To support course use and practical applications, the text provides examples in Python throughout, as well as an appendix containing homework problems for all chapters, further supported by an ftp site for data and sample code. Additional appendices cover global model risk management, and a refresher in statistics.

Key Features

Offers practical concepts for learning model validation and model risk management
Explains how to use Python-based models to assess and manage model risk
Covers the US gold standard of model risk, "Federal Reserve Board SR 11-7", including testing inputs, testing outputs, benchmarking, outcomes analysis, third party models, and compensating controls
Discusses model governance, including model inventory , risk ratings, and the three lines of defense
Provides Instructor Manuals for qualified instructors via https://www.educate.elsevier.com/book/details/9780443337468

About the author

By Jonathan Schachter, CEO and Founder of Delta Vega Inc, USA; Martin Goldberg, Vice President in Model Validation, Mizuho Americas, USA and Chandrakant Maheshwari, Senior Industry Practitioner

1. Introductory Material
1.1 Why Are We Writing This Book?
1.2 Computer Code
1.3 Note on Technical Terms, Jargon, Abbreviations, and Notation
1.4 What Is Not in This Book
1.5 To the Instructor

2. Model Basics
2.1 History of MRM
2.2 What Is a Model?
2.3 What Is Model Risk?
2.4 What is MVal?
2.5 Impact of MVal
2.6 Validation Use Cases

3. Standards
3.1 Independence
3.2 Effective Challenge
3.3 Benchmarking
3.4 Testing
3.5 Vendors

4. Techniques
4.1 New Model Registration
4.2 Classification and Risk Rating
4.3 Replication
4.4 Benchmarking
4.5 Documentation
4.6 Model Governance Preview
4.7 Other Validation Testing Techniques
4.8 Postvalidation Testing, Also Called “Ongoing Monitoring”
4.9 Toolkits
4.10 Job Functions and Lines of Defense
4.11 Diplomacy and Communication
4.12 Role of Consultants
4.12 Example¿Validation of Black-Scholes

5. Marked-to-Market Asset Classes
5.1 Introduction
5.2 Fixed Income
5.3 Equity
5.4 FX
5.5 Commodities

6. Marked-to-Model Asset Classes
6.1 Bonds
6.2 Exotics
6.3 Structured Credit and Securitizations
6.4 Equity Exotics
6.5 Other Asset Classes

7. Market Risk I: Statistical Measures
7.1 Value-at-Risk
7.2 VaR Decomposition
7.3 Validating VaR Assumptions
7.4 Validating VaR Inputs
7.5 VaR Backtesting
7.6 Expected Shortfall
7.7 Curing Problematic Timeseries: EWMA

8. Market Risk II: Stress Testing
8.1 Introduction
8.2 Details of CCAR Scenarios
8.3 CCAR Models
8.4 Building Stress Scenarios and Applying the Stresses to the Bank’s Positions
8.5 Internal Stress Tests

9. Issuer Credit Risk
9.1 Introduction
9.2 Philosophy of Credit Ratings
9.3 PD, LGD, and EAD
9.4 Credit Ratings in Practice
9.5 Scorecard Models

10. Counterparty Credit Risk
10.1 Valuation Adjustments
10.2 Wrong Way Risk (WWR)
10.3 Potential Future Exposure (PFE) Basics
10.4 PFE Advanced Modeling Approach (AMA)
10.5 SIMM: The Standard Initial Margin Model

11. Correlation Credit Risk
11.1 Single-Name Credit Products
11.2 Simple Correlation Products
11.3 Tranched Correlation Products
11.4 Correlation Credit and the Great Financial Crisis

12. Portfolio Risk
12.1 Equity Performance
12.2 Statistical Arbitrage
12.3 Hedge Fund Basics
12.4 Proprietary Hedge Fund Equity Models

13. Operational Risk
13.1 The Basel OR Event Types
13.2 ORX Nonfinancial Risk Levels
13.3 Standard Approach to OR Capital
13.4 Advanced Approach: OR Models
13.5 Key Risk Indicators
13.6 OR Stress Testing

14. Capital Model Risk
14.1 Regulatory Capital
14.2 History of U.S. Bank Capital
14.3 Basel Ratios and Buffers
14.4 SIFI Tests
14.5 Economic Capital

15. Artificial Intelligence Risk
15.1 Validating Pricing and Risk AI Models
15.2 MRM Assisted by AI
15.3 AI Explainability
15.4 Essentials of AI MRM
15.5 AI Use By Central Banks
15.6 AI Standards

16. Miscellaneous Topics in Model Risk
16.1 Transition From IBORs to RFRs: SOFR
16.2 Regulatory Risk
16.3 Anti—Money Laundering/Sanctions Models
16.4 Fraud Detection Models
16.5 Model Validation at Insurance Firms
16.6 The Greeks (Sensitivities)
16.7 Monte Carlo Simulations
16.8 Mortgage Model Risk
16.9 Validation of Qualitative Models

17. Model Governance
Prologue
17.1 Introduction
17.2 Model Inventory
17.3 Model Restrictions
17.4 Internal Audit
17.5 Policies and Procedures
17.6 Role of Regulators
17.7 Personnel
17.8 Model Governance in Practice

Appendix A: Homework Problems
Appendix B: Global MRM Regulation
Appendix C: Statistics Refresher
Appendix D: Online Content
Bibliography
Index

ISBN: 9780443337468

Page Count: 582

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Instructor Guides

Students and recent graduates in financial engineering masters and Ph.D. programs, and others seeking training in model validation and model risk management