Massimo Morini

Understanding and Managing Model Risk (eBook, ePUB)

A Practical Guide for Quants, Traders and Validators

• Format: ePub

Produktbeschreibung

A 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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 352
• Erscheinungstermin: 20. Oktober 2011
• Englisch
• ISBN-13: 9780470977743
• Artikelnr.: 37301394

Autorenporträt

Massimo Morini is Head of Credit Models and Coordinator of Model Research at IMI Bank of Intesa San Paolo. He has spent the last ten years inventing new models, implementing them, and helping practitioners in using them for buying, selling, and hedging derivatives. This has exposed him to the most practical side of model risk, and has led him to investigate model uncertainty, model robustness, and the management of the risk of model losses. Massimo is also Professor of Fixed Income at Bocconi University and was a Research Fellow at Cass Business School, City University London. He regularly delivers advanced training in London New York and worldwide on model risk management, credit modelling, interest rate models and correlation modelling, where he teaches cutting edge innovations in quantitative finance and discusses their implications with practitioners from the major institutions. He has led workshops on financial modelling and the financial crisis at major international conferences, including Global Derivatives, the Quant Congress, and the Fixed Income Conference. He has published papers in journals including Risk Magazine, Mathematical Finance, and the Journal of Derivatives. Massimo holds a PhD in Mathematics and an MSc in Economics.

Inhaltsangabe

Preface xi Acknowledgements xix PART I THEORY AND PRACTICE OF MODEL RISK
MANAGEMENT 1 Understanding Model Risk 3 1.1 What Is Model Risk? 3 1.1.1 The
Value Approach 4 1.1.2 The Price Approach 6 1.1.3 A Quant Story of the
Crisis 9 1.1.4 A Synthetic View on Model Risk 17 1.2 Foundations of
Modelling and the Reality of Markets 22 1.2.1 The Classic Framework 22
1.2.2 Uncertainty and Illiquidity 30 1.3 Accounting for Modellers 38 1.3.1
Fair Value 38 1.3.2 The Liquidity Bubble and the Accountancy Boards 40
1.3.3 Level 1, 2, 3 . . . go? 41 1.3.4 The Hidden Model Assumptions in
'vanilla' Derivatives 42 1.4 What Regulators Said After the Crisis 48 1.4.1
Basel New Principles: The Management Process 49 1.4.2 Basel New Principles:
The Model, The Market and The Product 51 1.4.3 Basel New Principles:
Operative Recommendations 52 1.5 Model Validation and Risk Management:
Practical Steps 53 1.5.1 A Scheme for Model Validation 54 1.5.2 Special
Points in Model Risk Management 59 1.5.3 The Importance of Understanding
Models 60 2 Model Validation and Model Comparison: Case Studies 63 2.1 The
Practical Steps of Model Comparison 63 2.2 First Example: The Models 65
2.2.1 The Credit Default Swap 66 2.2.2 Structural First-Passage Models 67
2.2.3 Reduced-Form Intensity Models 69 2.2.4 Structural vs Intensity:
Information 72 2.3 First Example: The Payoff. Gap Risk in a Leveraged Note
74 2.4 The Initial Assessment 77 2.4.1 First Test: Calibration to Liquid
Relevant Products 77 2.4.2 Second Test: a Minimum Level of Realism 78 2.5
The Core Risk in the Product 81 2.5.1 Structural Models: Negligible Gap
Risk 82 2.5.2 Reduced-Form Models: Maximum Gap Risk 82 2.6 A Deeper
Analysis: Market Consensus and Historical Evidence 85 2.6.1 What to Add to
the Calibration Set 85 2.6.2 Performing Market Intelligence 86 2.6.3 The
Lion and the Turtle. Incompleteness in Practice 86 2.6.4 Reality Check:
Historical Evidence and Lack of it 87 2.7 Building a Parametric Family of
Models 88 2.7.1 Understanding Model Implications 93 2.8 Managing Model
Uncertainty: Reserves, Limits, Revisions 95 2.9 Model Comparison: Examples
from Equity and Rates 99 2.9.1 Comparing Local and Stochastic Volatility
Models in Pricing Equity Compound and Barrier Options 99 2.9.2 Comparing
Short Rate and Market Models in Pricing Interest Rate Bermudan Options 105
3 Stress Testing and the Mistakes of the Crisis 111 3.1 Learning Stress
Test from the Crisis 111 3.1.1 The Meaning of Stress Testing 112 3.1.2
Portfolio Stress Testing 113 3.1.3 Model Stress Testing 116 3.2 The Credit
Market and the 'Formula that Killed Wall Street' 118 3.2.1 The CDO Payoff
118 3.2.2 The Copula 119 3.2.3 Applying the Copula to CDOs 122 3.2.4 The
Market Quotation Standard 124 3.3 Portfolio Stress Testing and the
Correlation Mistake 125 3.3.1 From Flat Correlation Towards a Realistic
Approach 126 3.3.2 A Correlation Parameterization to Stress the Market Skew
131 3.4 Payoff Stress and the Liquidity Mistake 136 3.4.1 Detecting the
Problem: Losses Concentrated in Time 137 3.4.2 The Problem in Practice 139
3.4.3 A Solution. From Copulas to Real Models 145 3.4.4 Conclusions 150 3.5
Testing with Historical Scenarios and the Concentration Mistake 151 3.5.1
The Mapping Methods for Bespoke Portfolios 152 3.5.2 The Lehman Test 156
3.5.3 Historical Scenarios to Test Mapping Methods 157 3.5.4 The Limits of
Mapping and the Management of Model Risk 164 3.5.5 Conclusions 168 4
Preparing for Model Change. Rates and Funding in the New Era 171 4.1
Explaining the Puzzle in the Interest Rates Market and Models 171 4.1.1 The
Death of a Market Model: 9 August 2007 173 4.1.2 Finding the New Market
Model 174 4.1.3 The Classic Risk-free Market Model 178 4.1.4 A Market Model
with Stable Default Risk 182 4.1.5 A Market with Volatile Credit Risk 192
4.1.6 Conclusions 200 4.2 Rethinking the Value of Money: The Effect of
Liquidity in Pricing 201 4.2.1 The Setting 204 4.2.2 Standard DVA: Is
Something Missing? 206 4.2.3 Standard DVA plus Liquidity: Is Something
Duplicated? 207 4.2.4 Solving the Puzzle 207 4.2.5 Risky Funding for the
Borrower 208 4.2.6 Risky Funding for the Lender and the Conditions for
Market Agreement 209 4.2.7 Positive Recovery Extension 210 4.2.8 Two Ways
of Looking at the Problem: Default Risk or Funding Benefit? The Accountant
vs the Salesman 211 4.2.9 Which Direction for Future Pricing? 214 PART II
SNAKES IN THE GRASS: WHERE MODEL RISK HIDES 5 Hedging 219 5.1 Model Risk
and Hedging 219 5.2 Hedging and Model Validation: What is Explained by P&L
Explain? 221 5.2.1 The Sceptical View 222 5.2.2 The Fundamentalist View and
Black and Scholes 222 5.2.3 Back to Reality 224 5.2.4 Remarks:
Recalibration, Hedges and Model Instability 226 5.2.5 Conclusions: from
Black and Scholes to Real Hedging 228 5.3 From Theory to Practice: Real
Hedging 229 5.3.1 Stochastic Volatility Models: SABR 231 5.3.2 Test Hedging
Behaviour Leaving Nothing Out 232 5.3.3 Real Hedging for Local Volatility
Models 238 5.3.4 Conclusions: the Reality of Hedging Strategies 241 6
Approximations 243 6.1 Validate and Monitor the Risk of Approximations 243
6.2 The Swaption Approximation in the Libor Market Model 245 6.2.1 The
Three Technical Problems in Interest Rate Modelling 245 6.2.2 The Libor
Market Model and the Swaption Market 247 6.2.3 Pricing Swaptions 250 6.2.4
Understanding and Deriving the Approximation 253 6.2.5 Testing the
Approximation 257 6.3 Approximations for CMS and the Shape of the Term
Structure 264 6.3.1 The CMS Payoff 265 6.3.2 Understanding Convexity
Adjustments 266 6.3.3 The Market Approximation for Convexity Adjustments
267 6.3.4 A General LMM Approximation 269 6.3.5 Comparing and Testing the
Approximations 271 6.4 Testing Approximations Against Exact. Dupire's Idea
276 6.4.1 Perfect Positive Correlation 278 6.4.2 Perfect Negative
Correlation 280 6.5 Exercises on Risk in Computational Methods 283 6.5.1
Approximation 283 6.5.2 Integration 285 6.5.3 Monte Carlo 285 7
Extrapolations 287 7.1 Using the Market to Complete Information: Asymptotic
Smile 288 7.1.1 The Indetermination in the Asymptotic Smile 288 7.1.2
Pricing CMS with a Smile: Extrapolating to Infinity 292 7.1.3 Using CMS
Information to Transform Extrapolation into Interpolation and Fix the
Indetermination 293 7.2 Using Mathematics to Complete Information:
Correlation Skew 295 7.2.1 The Expected Tranched Loss 295 7.2.2 Properties
for Interpolation 298 7.2.3 Properties for Turning Extrapolation into
Interpolation 298 8 Correlations 303 8.1 The Technical Difficulties in
Computing Correlations 303 8.1.1 Correlations in Interest Rate Modelling
305 8.1.2 Cross-currency Correlations 307 8.1.3 Stochastic Volatility
Correlations 312 8.2 Fundamental Errors in Modelling Correlations 315 8.2.1
The Zero-correlation Error 316 8.2.2 The 1-Correlation Error 319 9
Calibration 323 9.1 Calibrating to Caps/Swaptions and Pricing Bermudans 324
9.1.1 Calibrating Caplets 325 9.1.2 Understanding the Term Structure of
Volatility 326 9.1.3 Different Parameterizations 329 9.1.4 The Evolution of
the Term Structure of Volatility 332 9.1.5 The Effect on Early-Exercise
Derivatives 334 9.1.6 Reducing Our Indetermination in Pricing Bermudans:
Liquid European Swaptions 335 9.2 The Evolution of the Forward Smiles 340
10 When the Payoff isWrong 347 10.1 The Link Between Model Errors and
Payoff Errors 347 10.2 The Right Payoff at Default: The Impact of the
Closeout Convention 348 10.2.1 How Much Will be Paid at Closeout, Really?
350 10.2.2 What the Market Says and What the ISDA Says 352 10.2.3 A
Quantitative Analysis of the Closeout 353 10.2.4 A Summary of the Findings
and Some Conclusions on Payoff Uncertainty 360 10.3 Mathematical Errors in
the Payoff of Index Options 362 10.3.1 Too Much Left Out 364 10.3.2 Too
Much Left In 365 10.3.3 Empirical Results with the Armageddon Formula 365
10.3.4 Payoff Errors and Armageddon Probability 367 11 Model Arbitrage 371
11.1 Introduction 371 11.2 Capital Structure Arbitrage 373 11.2.1 The
Credit Model 373 11.2.2 The Equity Model 375 11.2.3 From Barrier Options to
Equity Pricing 377 11.2.4 Capital-structure Arbitrage and Uncertainty 381
11.3 The Cap-Swaption Arbitrage 391 11.4 Conclusion: Can We Use
No-Arbitrage Models to Make Arbitrage? 394 12 Appendix 397 12.1 Random
Variables 397 12.1.1 Generating Variables from Uniform Draws 397 12.1.2
Copulas 397 12.1.3 Normal and Lognormal 398 12.2 Stochastic Processes 399
12.2.1 The Law of Iterated Expectation 399 12.2.2 Diffusions, Brownian
Motions and Martingales 400 12.2.3 Poisson Process 403 12.2.4
Time-dependent Intensity 404 12.3 Useful Results from Quantitative Finance
405 12.3.1 Black and Scholes (1973) and Black (1976) 405 12.3.2 Change of
Numeraire 407 Bibliography 409 Index 417