Morini M. Understanding and Managing Model Risk: A Practical Guide for Quants, Traders and Validators

Wiley – 2011, 448 pages
ISBN 0470977612A guide to the validation and risk management of quantitative models used for pricing and hedging
Whereas the majority of quantitative finance books focus on mathematics and risk management books focus on regulatory aspects, this book addresses the elements missed by this literature the risks of the models themselves. This book starts from regulatory issues, but translates them into practical suggestions to reduce the likelihood of model losses, basing model risk and validation on market experience and on a wide range of real-world examples, with a high level of detail and precise operative indications.Part I Theory and Practice of Model Risk Management
Understanding Model Risk
What Is Model Risk?
The Value Approach
The Price Approach
A Quant Story of the Crisis
A Synthetic View on Model Risk
Foundations of Modelling and the Reality of Markets
The Classic Framework
Uncertainty and Illiquidity
Accounting for Modellers
Fair Value
The Liquidity Bubble and the Accountancy Boards
The Hidden Model Assumptions in ‘vanilla’ Derivatives
What Regulators Said After the Crisis
Basel New Principles: The Management Process
Basel New Principles: The Model, The Market and The Product
Basel New Principles: Operative Recommendations
Model Validation and Risk Management: Practical Steps
A Scheme for Model Validation
Special Points in Model Risk Management
The Importance of Understanding Models
Model Validation and Model Comparison: Case Studies
The Practical Steps of Model Comparison
First Example: The Models
The Credit Default Swap
Structural First-Passage Models
Reduced-Form Intensity Models
Structural vs Intensity: Information
First Example: The Payoff. Gap Risk in a Leveraged Note
The Initial Assessment
First Test: Calibration to Liquid Relevant Products
Second Test: a Minimum Level of Realism
The Core Risk in the Product
Structural Models: Negligible Gap Risk
Reduced-Form Models: Maximum Gap Risk
A Deeper Analysis: Market Consensus and Historical Evidence
What to Add to the Calibration Set
Performing Market Intelligence
The Lion and the Turtle. Incompleteness in Practice
Reality Check: Historical Evidence and Lack of it
Building a Parametric Family of Models
Understanding Model Implications
Managing Model Uncertainty: Reserves, Limits, Revisions
Model Comparison: Examples from Equity and Rates
Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options
Comparing Short Rate and Market Models in Pricing Interest Rate Bermudan Options
Stress Testing and the Mistakes of the Crisis
Learning Stress Test from the Crisis
The Meaning of Stress Testing
Portfolio Stress Testing
Model Stress Testing
The Credit Market and the ‘Formula that Killed Wall Street’
The CDO Payoff
The Copula
Applying the Copula to CDOs
The Market Quotation Standard
Portfolio Stress Testing and the Correlation Mistake
From Flat Correlation Towards a Realistic Approach
A Correlation Parameterization to Stress the Market Skew
Payoff Stress and the Liquidity Mistake
Detecting the Problem: Losses Concentrated in Time
The Problem in Practice
A Solution. From Copulas to Real Models
Conclusions
Testing with Historical Scenarios and the Concentration Mistake
The Mapping Methods for Bespoke Portfolios
The Lehman Test
Historical Scenarios to Test Mapping Methods
The Limits of Mapping and the Management of Model Risk
Conclusions
Preparing for Model Change. Rates and Funding in the New Era
Explaining the Puzzle in the Interest Rates Market and Models
The Death of a Market Model: August
Finding the New Market Model
The Classic Risk-free Market Model
A Market Model with Stable Default Risk
A Market with Volatile Credit Risk
Conclusions
Rethinking the Value of Money: The Effect of Liquidity in Pricing
The Setting
Standard DVA: Is Something Missing?
Standard DVA plus Liquidity: Is Something Duplicated?
Solving the Puzzle
Risky Funding for the Borrower
Risky Funding for the Lender and the Conditions for Market
Agreement
Positive Recovery Extension
Two Ways of Looking at the Problem: Default Risk or Funding
Benefit? The Accountant vs the Salesman
Which Direction for Future Pricing?
Part II Snakes in The Grass: Where Model Risk Hides
Hedging
Model Risk and Hedging
Hedging and Model Validation: What is Explained by P&L Explain?
The Sceptical View
The Fundamentalist View and Black and Scholes
Back to Reality
Remarks: Recalibration, Hedges and Model Instability
Conclusions: from Black and Scholes to Real Hedging
From Theory to Practice: Real Hedging
Stochastic Volatility Models: SABR
Test Hedging Behaviour Leaving Nothing Out
Real Hedging for Local Volatility Models
Conclusions: the Reality of Hedging Strategies
Approximations
Validate and Monitor the Risk of Approximations
The Swaption Approximation in the Libor Market Model
The Three Technical Problems in Interest Rate Modelling
The Libor Market Model and the Swaption Market
Pricing Swaptions
Understanding and Deriving the Approximation
Testing the Approximation
Approximations for CMS and the Shape of the Term Structure
The CMS Payoff
Understanding Convexity Adjustments
The Market Approximation for Convexity Adjustments
A General LMM Approximation
Comparing and Testing the Approximations
Testing Approximations Against Exact. Dupire’s Idea
Perfect Positive Correlation
Perfect Negative Correlation
Exercises on Risk in Computational Methods
Approximation
Integration
Monte Carlo
Extrapolations
Using the Market to Complete Information: Asymptotic Smile
The Indetermination in the Asymptotic Smile
Pricing CMS with a Smile: Extrapolating to Infinity
Using CMS Information to Transform Extrapolation into
Interpolation and Fix the Indetermination
Using Mathematics to Complete Information: Correlation Skew
The Expected Tranched Loss
Properties for Interpolation
Properties for Turning Extrapolation into Interpolation
Correlations
The Technical Difficulties in Computing Correlations
Correlations in Interest Rate Modelling
Cross-currency Correlations
Stochastic Volatility Correlations
Fundamental Errors in Modelling Correlations
The Zero-correlation Error
The -Correlation Error
Calibration
Calibrating to Caps/Swaptions and Pricing Bermudans
Calibrating Caplets
Understanding the Term Structure of Volatility
Different Parameterizations
The Evolution of the Term Structure of Volatility
The Effect on Early-Exercise Derivatives
Reducing Our Indetermination in Pricing Bermudans: Liquid
European Swaptions
The Evolution of the Forward Smiles
When the Payoff isWrong
The Link Between Model Errors and Payoff Errors
The Right Payoff at Default: The Impact of the Closeout Convention
How Much Will be Paid at Closeout, Really?
What the Market Says and What the ISDA Says
A Quantitative Analysis of the Closeout
A Summary of the Findings and Some Conclusions on
Payoff Uncertainty
Mathematical Errors in the Payoff of Index Options
Too Much Left Out
Too Much Left In
Empirical Results with the Armageddon Formula
Payoff Errors and Armageddon Probability
Model ArbitrageCapital Structure Arbitrage
The Credit Model
The Equity Model
From Barrier Options to Equity Pricing
Capital-structure Arbitrage and Uncertainty
The Cap-Swaption Arbitrage
Conclusion: Can We Use No-Arbitrage Models to Make Arbitrage?
Appendix
Random Variables
Generating Variables from Uniform Draws
Copulas
Normal and Lognormal
Stochastic Processes
The Law of Iterated Expectation
Diffusions, Brownian Motions and Martingales
Poisson Process
Time-dependent Intensity
Useful Results from Quantitative Finance
Black and Scholes () and Black ()
Change of Numeraire