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Counterparty Credit Risk, Collateral and Funding

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Beschreibung

The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular ‘concrete’ financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity.

The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price  counterparty credit and funding risk, to develop a ‘feel’ for applying sophisticated mathematics and stochastic calculus to solve practical problems.

The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation.

Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.



Professor Damiano Brigo is Chair of Mathematical Finance and co-Head of Group at Imperial College, London. Damiano is also Director of the Capco Research Institute. His previous roles include Gilbart Professor and Head of Group at King's College, Managing Director and Global Head of Quantitative Innovation in Fitch, Head of Credit Models in Banca IMI, Fixed Income Professor at Bocconi University in Milan, and Quantitative Analyst at Banca Intesa. He has worked on quantitative analysis of counterparty risk, interest rates-, FX-, credit- and equity- derivatives, risk management and structured products, and funding costs and collateral modelling. Damiano has published 70+ works in top journals for Mathematical Finance, Systems Theory, Probability and Statistics, with H-index 24 on Scholar, and books for Springer and John Wiley & Sons that became field references in stochastic interest rate and credit modelling. Damiano is Managing Editor of the International Journal of Theoretical and Applied Finance, and has been listed as the most cited author in Risk Magazine in 2006 and 2010. Damiano obtained a Ph.D. in stochastic filtering with differential geometry in 1996 from the Free University of Amsterdam, following a BSc in Mathematics with honours from the University of Padua.

Massimo Morini is Head of Interest Rate and Credit Models and Coordinator of Model Research at IMI Bank of Intesa San Paolo. 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. He has led workshops on credit risk and the financial crisis at major international conferences. He has published papers in journals including Risk Magazine, Mathematical Finance, and the Journal of Derivatives, and is the author of Understanding and Managing Model Risk: A Practical Guide for Quants, Traders and Validators. Massimo holds a PhD in Mathematics and an MSc in Economics.

Andrea Pallavicini is Head of Equity, FX and Commodity Models at Banca IMI, where he has the responsibility of numerical algorithm's design, financial modelling and research activity. He is also Visiting Professor at the Department of Mathematics of the Imperial College London. Previously, he held positions as Head of Financial Models at Mediobanca and Head of Financial Engineering at Banca Leonardo, he worked also in aerospace industries and financial institutions. He has a Degree in Astrophysics and a Ph.D. in Theoretical and Mathematical Physics from the University of Pavia for his research activity at CERN laboratory in Genève. Over the years he has written books in finance and he published several academic and practitioner-oriented articles in financial modelling, theoretical physics and astrophysics on major peer-reviewed journals. He teaches regularly at professional training courses and at Master and Ph.D. courses in finance at different Universities and private institutions. His main contributions in finance concern interest-rate and credit modelling, counterparty credit risk, and hybrid derivative pricing.



Autorentext

About the authors

PROFESSOR DAMIANO BRIGO is Chair of Mathematical Finance and co-Head of Group at Imperial College, London. Damiano is also Director of the Capco Research Institute. His previous roles include Gilbart Professor and Head of Group at King's College, Managing Director and Global Head of Quantitative Innovation in Fitch, Head of Credit Models in Banca IMI, Fixed Income Professor at Bocconi University in Milan, and Quantitative Analyst at Banca Intesa. He has worked on quantitative analysis of counterparty risk, interest rates-, FX-, credit- and equity- derivatives, risk management and structured products, and funding costs and collateral modelling. Damiano has published 70+ works in top journals for Mathematical Finance, Systems Theory, Probability and Statistics, with H-index 24 on Scholar, and books for Springer and John Wiley & Sons that became field references in stochastic interest rate and credit modelling. Damiano is Managing Editor of the International Journal of Theoretical and Applied Finance, and has been listed as the most cited author in Risk Magazine in 2006 and 2010.

Damiano obtained a Ph.D. in stochastic filtering with differential geometry in 1996 from the Free University of Amsterdam, following a BSc in Mathematics with honours from the University of Padua.

MASSIMO MORINI is Head of Interest Rate and Credit Models and Coordinator of Model Research at Banca IMI of Intesa San Paolo. 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. He has led workshops on credit risk and the financial crisis at major international conferences. He has published papers in journals including Risk Magazine, Mathematical Finance, and the Journal of Derivatives, and is the author of Understanding and Managing Model Risk: A Practical Guide for Quants, Traders and Validators. Massimo holds a PhD in Mathematics and an MSc in Economics.

ANDREA PALLAVICINI is Head of Equity, FX and Commodity Models at Banca IMI, where he has the responsibility of numerical algorithm's design, financial modelling and research activity. He is also Visiting Professor at the Department of Mathematics of the Imperial College London. Previously, he held positions as Head of Financial Models at Mediobanca and Head of Financial Engineering at Banca Leonardo, he worked also in aerospace industries and financial institutions. He has a Degree in Astrophysics and a Ph.D. in Theoretical and Mathematical Physics from the University of Pavia for his research activity at CERN laboratory in Genève. Over the years he has written books in finance and he published several academic and practitioner-oriented articles in financial modelling, theoretical physics and astrophysics in major peer-reviewed journals. He teaches regularly at professional training courses and at Master and Ph.D. courses in finance at different Universities and private institutions. His main contributions in finance concern interest-rate and credit modelling, counterparty credit risk, and hybrid derivative pricing.

Klappentext

Counterparty Credit Risk, Collateral and Funding With Pricing Cases for All Asset Classes

Brigo, Morini & Pallavicini

Counterparty Credit Risk, Collateral and Funding: With Pricing Cases for All Asset Classes aims to help academic researchers, quantitative analysts and traders who need to frame and price counterparty credit and funding risk, to develop a feel for applying advanced mathematics and stochastic models to solve practical problems.

The book focuses on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book also looks at practical problems, linking particular models to particular financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging area of longevity / mortality risk. Several pricing examples and numerical case studies are presented. The implications for regulation, from Basel III to FASB and IAS, are also considered. The main models are illustrated from theoretical formulation to final implementation with calibration to market data. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are discussed.

Written by authors who are methodology thought leaders both in industry and academia, Counterparty Credit Risk, Collateral and Funding is a must-have for anyone who is interested in expanding their mathematical knowledgebase and their understanding of counterparty credit models in order to accurately price and hedge a number of financial instruments.

Inhalt

Ignition xv

Abbreviations and Notation xxiii

PART I COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING

1 Introduction 3

1.1 A Dialogue on CVA 3

1.2 Risk Measurement: Credit VaR 3

1.3 Exposure, CE, PFE, EPE, EE, EAD 5

1.4 Exposure and Credit VaR 7

1.5 Interlude: P and Q 7

1.6 Basel 8

1.7 CVA and Model Dependence 9

1.8 Input and Data Issues on CVA 10

1.9 Emerging Asset Classes: Longevity Risk 11

1.10 CVA and Wrong Way Risk 12

1.11 Basel III: VaR of CVA and Wrong Way Risk 13

1.12 Discrepancies in CVA Valuation: Model Risk and Payoff Risk 14

1.13 Bilateral Counterparty Risk: CVA and DVA 15

1.14 First-to-Default in CVA and DVA 17

1.15 DVA Mark-to-Market and DVA Hedging 18

1.16 Impact of Close-Out in CVA and DVA 19

1.17 Close-Out Contagion 20

1.18 Collateral Modelling in CVA and DVA 21

1.19 Re-Hypothecation 22

1.20 Netting 22

1.21 Funding 23

1.22 Hedging Counterparty Risk: CCDS 25

1.23 Restructuring Counterparty Risk: CVA-CDOs and Margin Lending 26

2 Context 31

2.1 Definition of Default: Six Basic Cases 31

2.2 Definition of Exposures 32

2.3 Definition of Credit Valuation Adjustment (CVA) 35

2.4 Counterparty Risk Mitigants: Netting 37

2.5 Counterparty Risk Mitigants: Collateral 38

2.5.1 The Credit Support Annex (CSA) 39

2.5.2 The ISDA Proposal for a New Standard CSA 40

2.5.3 Collateral Effectiveness as a Mitigant 40

2.6 Funding 41

2.6.1 A First Attack on Funding Cost Modelling 42

2.6.2 The General Funding Theory and its Recursive Nature 42

2.7 Value at Risk (VaR) and Expected Shortfall (ES) of CVA 43

2.8 The Dilemma of Regulators and Basel III 44

3 Modelling the Counterparty Default 47

3.1 Firm Value (or Structural) Models 47

3.1.1 The Geometric Brownian Assumption 47

3.1.2 Merton's Model 48

3.1.3 Black and Cox's (1976) Model 50

3.1.4 Credit Default Swaps and Default Probabilities 54

3.1.5 Black and Cox (B&C) Model Calibration to CDS: Problems 55

3.1.6 The AT1P Model 57

3.1.7 A Case Study with AT1P: Lehman Brothers Default History 58

3.1.8 Comments 60

3.1.9 SBTV Model 61

3.1.10 A Case Study with SBTV: Lehman Brothers Default History 62

3.1.11 Comments 64

3.2 Firm Value Models: Hints at the Multiname Picture 64

3.3 Reduced Form (Intensity) Models 65

3.3.1 CDS Calibration and Intensity Models 66

3.3.2 A Simpler Formula for Calibrating Intensity to a Single CDS 70

3.3.3 Stochastic Intensity: The CIR Family 72

3.3.4 The Cox-Ingersoll-Ross Model (CIR) Short-Rate Model for r 72

3.3.5 Time-Inhomogeneous Case: CIR++ Model 74

3.3.6 Stochastic Diffusion Intensity is Not Enough: Adding Jumps. The JCIR(++) Model 75

3.3.7 The Jump-Diffusion CIR Model (JCIR) 76

3.3.8 Market Incompleteness and Default Unpredictability 78

3.3.9 Further Models 78

3.4 Intensity Models: The Multiname Picture 78

3.4.1 Choice of Variables for the Dependence Structure 78

3.4.2 Firm Value Models? 80

3.4.3 Copula Functions 80

3.4.4 Copula Calibration, CDOs and Criticism of Copula Functions 86

PART II PRICING COUNTERPARTY RISK: UNILATERAL CVA

4 Unilateral CVA and Netting for Interest Rate Products 89

4.1 First Steps towards a CVA Pricing Formula 89

4.1.1 Symmetry versus Asymmetry 90

4.1.2 Modelling the Counterparty Default Process 91

4.2 The Probabilistic Framework 92

4.3 The General Pricing Formula for Unilateral Counterparty Risk 94

4.4 Interest Rate Swap (IRS) Portfolios 97

4.4.1 Counterparty Risk in Single IRS 97

4.4.2 Counterparty Risk in an IRS Portfolio with Netting 100

4.4.3 The Drift Freezing Approximation 102

4.4.4 The Three-Moments Matching Technique 104

4.5 Numerical Tests 106

4.5.1 Case A: IRS with Co-Terminal Payment Dates 106

4.5.2 Case B: IRS with Co-Starting Resetting Date 108

4.5.3 Case C: IRS with First Positive, Then Negative Flow 108

4.5.4 Case D: IRS with First Negative, Then Positive Flows 109

4.5.5 Case E: IRS with First Alternate Flows 113

4.6 Conclusions 120

5 Wrong Way Risk (WWR) for Interest Rates 121

5.1 Modelling Assumptions 122

5.1.1 G2++ Interest Rate Model 122

5.1.2 CIR++ Stochastic Intensity Model 123

5.1.3 CIR++ Model: CDS Calibration 124

5.1.4 Interest Rate/Credit Spread Correlation 126

5.1.5 Adding Jumps to the Credit Spread 126

5.2 Numerical Methods 127

5.2.1 Discretization Scheme 128

5.2.2 Simulating Intensity Jumps 128

5.2.3 American Monte Carlo (Pallavicini 200...

Produktinformationen

Titel: Counterparty Credit Risk, Collateral and Funding
Untertitel: With Pricing Cases For All Asset Classes
Autor:
EAN: 9780470662496
ISBN: 978-0-470-66249-6
Digitaler Kopierschutz: Adobe-DRM
Format: E-Book (pdf)
Herausgeber: Wiley
Genre: Betriebswirtschaft
Anzahl Seiten: 464
Veröffentlichung: 07.03.2013
Jahr: 2013
Untertitel: Englisch
Dateigrösse: 17.7 MB