Details

Counterparty Credit Risk, Collateral and Funding

With Pricing Cases For All Asset Classes
The Wiley Finance Series 1. Aufl.

von: Damiano Brigo, Massimo Morini, Andrea Pallavicini
69,99 €
Verlag:	Wiley
Format:	PDF
Veröffentl.:	07.03.2013
ISBN/EAN:	9780470662496
Sprache:	englisch
Anzahl Seiten:	464

In den Warenkorb

Als Gutschein

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

Titelbeschreibung

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.

Inhaltsverzeichnis

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 2006) 128 5.2.4 Callable Payoffs 128 5.3 Results and Discussion 129 5.3.1 WWR in Single IRS 129 5.3.2 WWR in an IRS Portfolio with Netting 129 5.3.3 WWR in European Swaptions 130 5.3.4 WWR in Bermudan Swaptions 130 5.3.5 WWR in CMS Spread Options 132 5.4 Contingent CDS (CCDS) 132 5.5 Results Interpretation and Conclusions 133 6 Unilateral CVA for Commodities with WWR 135 6.1 Oil Swaps and Counterparty Risk 135 6.2 Modelling Assumptions 137 6.2.1 Commodity Model 137 6.2.2 CIR++ Stochastic-Intensity Model 139 6.3 Forward versus Futures Prices 140 6.3.1 CVA for Commodity Forwards without WWR 141 6.3.2 CVA for Commodity Forwards with WWR 142 6.4 Swaps and Counterparty Risk 142 6.5 UCVA for Commodity Swaps 144 6.5.1 Counterparty Risk from the Payer’s Perspective: The Airline Computes Counterparty Risk 145 6.5.2 Counterparty Risk from the Receiver’s Perspective: The Bank Computes Counterparty Risk 148 6.6 Inadequacy of Basel’s WWR Multipliers 148 6.7 Conclusions 151 7 Unilateral CVA for Credit with WWR 153 7.1 Introduction to CDSs with Counterparty Risk 153 7.1.1 The Structure of the Chapter 155 7.2 Modelling Assumptions 155 7.2.1 CIR++ Stochastic-Intensity Model 156 7.2.2 CIR++ Model: CDS Calibration 157 7.3 CDS Options Embedded in CVA Pricing 158 7.4 UCVA for Credit Default Swaps: A Case Study 160 7.4.1 Changing the Copula Parameters 160 7.4.2 Changing the Market Parameters 164 7.5 Conclusions 164 8 Unilateral CVA for Equity with WWR 167 8.1 Counterparty Risk for Equity Without a Full Hybrid Model 167 8.1.1 Calibrating AT1P to the Counterparty’s CDS Data 168 8.1.2 Counterparty Risk in Equity Return Swaps (ERS) 169 8.2 Counterparty Risk with a Hybrid Credit-Equity Structural Model 172 8.2.1 The Credit Model 172 8.2.2 The Equity Model 174 8.2.3 From Barrier Options to Equity Pricing 176 8.2.4 Equity and Equity Options 179 8.3 Model Calibration and Empirical Results 180 8.3.1 BP and FIAT in 2009 181 8.3.2 Uncertainty in Market Expectations 186 8.3.3 Further Results: FIAT in 2008 and BP in 2010 188 8.4 Counterparty Risk and Wrong Way Risk 191 8.4.1 Deterministic Default Barrier 193 8.4.2 Uncertainty on the Default Barrier 198 9 Unilateral CVA for FX 205 9.1 Pricing with Two Currencies: Foundations 206 9.2 Unilateral CVA for a Fixed-Fixed CCS 210 9.2.1 Approximating the Volatility of Cross Currency Swap Rates 216 9.2.2 Parameterization of the FX Correlation 218 9.3 Unilateral CVA for Cross Currency Swaps with Floating Legs 224 9.4 Why a Cross Currency Basis? 226 9.4.1 The Approach of Fujii, Shimada and Takahashi (2010) 227 9.4.2 Collateral Rates versus Risk-Free Rates 228 9.4.3 Consequences of Perfect Collateralization 229 9.5 CVA for CCS in Practice 230 9.5.1 Changing the CCS Moneyness 234 9.5.2 Changing the Volatility 235 9.5.3 Changing the FX Correlations 235 9.6 Novations and the Cost of Liquidity 237 9.6.1 A Synthetic Contingent CDS: The Novation 238 9.6.2 Extending the Approach to the Valuation of Liquidity 241 9.7 Conclusions 243 PART III ADVANCED CREDIT AND FUNDING RISK PRICING 10 New Generation Counterparty and Funding Risk Pricing 247 10.1 Introducing the Advanced Part of the Book 247 10.2 What We Have Seen Before: Unilateral CVA 249 10.2.1 Approximation: Default Bucketing and Independence 250 10.3 Unilateral Debit Valuation Adjustment (UDVA) 250 10.4 Bilateral Risk and DVA 251 10.5 Undesirable Features of DVA 253 10.5.1 Profiting From Own Deteriorating Credit Quality 253 10.5.2 DVA Hedging? 253 10.5.3 DVA: Accounting versus Capital Requirements 254 10.5.4 DVA: Summary and Debate on Realism 255 10.6 Close-Out: Risk-Free or Replacement? 256 10.7 Can We Neglect the First-to-Default Time? 257 10.7.1 A Simplified Formula without First-to-Default: The Case of an Equity Forward 258 10.8 Payoff Risk 258 10.9 Collateralization, Gap Risk and Re-Hypothecation 259 10.10 Funding Costs 262 10.11 Restructuring Counterparty Risk 263 10.11.1 CVA Volatility: The Wrong Way 263 10.11.2 Floating Margin Lending 264 10.11.3 Global Valuation 265 10.12 Conclusions 266 11 A First Attack on Funding Cost Modelling 269 11.1 The Problem 269 11.2 A Closer Look at Funding and Discounting 271 11.3 The Approach Proposed by Morini and Prampolini (2010) 272 11.3.1 The Borrower’s Case 273 11.3.2 The Lender’s Case 274 11.3.3 The Controversial Role of DVA: The Borrower 275 11.3.4 The Controversial Role of DVA: The Lender 276 11.3.5 Discussion 277 11.4 What Next on Funding? 278 12 Bilateral CVA–DVA and Interest Rate Products 279 12.1 Arbitrage-Free Valuation of Bilateral Counterparty Risk 281 12.1.1 Symmetry versus Asymmetry 285 12.1.2 Worsening of Credit Quality and Positive Mark-to-Market 285 12.2 Modelling Assumptions 286 12.2.1 G2++ Interest Rate Model 286 12.2.2 CIR++ Stochastic Intensity Model 288 12.2.3 Realistic Market Data Set for CDS Options 289 12.3 Numerical Methods 290 12.4 Results and Discussion 291 12.4.1 Bilateral VA in Single IRS 292 12.4.2 Bilateral VA in an IRS Portfolio with Netting 296 12.4.3 Bilateral VA in Exotic Interest Rate Products 301 12.5 Conclusions 302 13 Collateral, Netting, Close-Out and Re-Hypothecation 305 13.1 Trading Under the ISDA Master Agreement 306 13.1.1 Mathematical Setup and CBVA Definition 306 13.1.2 Collateral Delay and Dispute Resolutions 308 13.1.3 Close-Out Netting Rules 308 13.1.4 Collateral Re-Hypothecation 309 13.2 Bilateral CVA Formula under Collateralization 310 13.2.1 Collecting CVA Contributions 310 13.2.2 CBVA General Formula 312 13.2.3 CCVA and CDVA Definitions 312 13.3 Close-Out Amount Evaluation 313 13.4 Special Cases of Collateral-Inclusive Bilateral Credit Valuation Adjustment 314 13.5 Example of Collateralization Schemes 315 13.5.1 Perfect Collateralization 315 13.5.2 Collateralization Through Margining 316 13.6 Conclusions 316 14 Close-Out and Contagion with Examples of a Simple Payoff 319 14.1 Introduction to Close-Out Modelling and Earlier Work 319 14.1.1 Close-Out Modelling: Context 319 14.1.2 Legal Documentation on Close-Out 320 14.1.3 Literature 320 14.1.4 Risk-Free versus Replacement Close-Out: Practical Consequences 321 14.2 Classical Unilateral and Bilateral Valuation Adjustments 322 14.3 Bilateral Adjustment and Close-Out: Risk-Free or Replacement? 323 14.4 A Quantitative Analysis and a Numerical Example 323 14.4.1 Contagion Issues 326 14.5 Conclusions 329 15 Bilateral Collateralized CVA and DVA for Rates and Credit 331 15.1 CBVA for Interest Rate Swaps 332 15.1.1 Changing the Margining Frequency 332 15.1.2 Inspecting the Exposure Profiles 334 15.1.3 A Case Where Re-Hypothecation is Worse than No Collateral at All 335 15.1.4 Changing the Correlation Parameters 336 15.1.5 Changing the Credit Spread Volatility 337 15.2 Modelling Credit Contagion 340 15.2.1 The CDS Price Process 340 15.2.2 Calculation of Survival Probability 341 15.2.3 Modelling Default-Time Dependence 344 15.3 CBVA for Credit Default Swaps 345 15.3.1 Changing the Copula Parameters 345 15.3.2 Inspecting the Contagion Risk 347 15.3.3 Changing the CDS Moneyness 347 15.4 Conclusions 349 16 Including Margining Costs in Collateralized Contracts 351 16.1 Trading Under the ISDA Master Agreement 352 16.1.1 Collateral Accrual Rates 352 16.1.2 Collateral Management and Margining Costs 353 16.2 CBVA General Formula with Margining Costs 355 16.2.1 Perfect Collateralization 356 16.2.2 Futures Contracts 357 16.3 Changing the Collateralization Currency 357 16.3.1 Margining Cost in Foreign Currency 357 16.3.2 Settlement Liquidity Risk 358 16.3.3 Gap Risk in Single-Currency Contracts with Foreign-Currency Collaterals 359 16.4 Conclusions 359 17 Funding Valuation Adjustment (FVA)? 361 17.1 Dealing with Costs of Funding 361 17.1.1 Central Clearing, CCPs and this Book 362 17.1.2 High Level Features 362 17.1.3 Single-Deal (Micro) vs. Homogeneous (Macro) Funding Models 363 17.1.4 Previous Literature on Funding and Collateral 364 17.1.5 Including FVA along with Credit and Debit Valuation Adjustment 365 17.1.6 FVA is not DVA 365 17.2 Collateral- and Funding-Inclusive Bilateral Valuation Adjusted Price 366 17.3 Funding Risk and Liquidity Policies 367 17.3.1 Funding, Hedging and Collateralization 367 17.3.2 Liquidity Policies 368 17.4 CBVA Pricing Equation with Funding Costs (CFBVA) 372 17.4.1 Iterative Solution of the CFBVA Pricing Equation 373 17.4.2 Funding Derivative Contracts in a Diffusion Setting 374 17.4.3 Implementing Hedging Strategies via Derivative Markets 377 17.5 Detailed Examples 378 17.5.1 Funding with Collateral 378 17.5.2 Collateralized Contracts Priced by a CCP 379 17.5.3 Dealing with Own Credit Risk: FVA and DVA 380 17.5.4 Deriving Earlier Results on FVA and DVA 381 17.6 Conclusions: FVA and Beyond 382 18 Non-Standard Asset Classes: Longevity Risk 385 18.1 Introduction to Longevity Markets 385 18.1.1 The Longevity Swap Market 385 18.1.2 Longevity Swaps: Collateral and Credit Risk 386 18.1.3 Indexed Longevity Swaps 390 18.1.4 Endogenous Credit Collateral and Funding-Inclusive Swap Rates 390 18.2 Longevity Swaps: The Payoff P391 18.3 Mark-to-Market for Longevity Swaps 394 18.4 Counterparty and Own Default Risk, Collateral and Funding 397 18.5 An Example of Modelling Specification from Biffis et al. (2011) 401 18.6 Discussion of the Results in Biffis et al. (2011) 404 19 Conclusions and Further Work 409 19.1 A Final Dialogue: Models, Regulations, CVA/DVA, Funding and More 409 Bibliography 415 Index 423

Autorenportrait

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.

Back cover copy

"This impressive book covers an important and highly complex area of quantitative finance dealing with counterparty credit risk. It covers many vital topics and demonstrates in great detail how to compute Credit, Debt, and Funding Value Adjustments. Written by some of the best experts in the field, it provides important insights in its subject matter, which will be of great value for practitioners, academics, and regulators." —Alexander Lipton, Co-Head of Global Quantitative Group at Bank of America Merrill Lynch and Honorary Professor at Imperial College "This book could rightly be called The Encyclopaedia of Credit Value Adjustments, although it is both more detailed and more pleasantly readable than an encyclopaedia. It is the one-stop CVA (and more) reference for practitioners and academics alike." (This endorsement is a personal opinion and does not represent the view of the Financial Services Authority) —Dirk Tasche, Technical Specialist, Risk Specialists Division, Financial Services Authority "There are many books in Finance. This one is different. It focuses on CVA (Credit Valuation Adjustment), a topic related to counterparty risk. The first chapter alone is worth the price of the book. This chapter is an 'extended dialogue,' where Brigo uses a question and answer format to teach, in an entertaining manner, a lot of the fundamental ideas, as well as the jargon with its alphabet-city innumerable acronyms, of modern financial mathematics, both as it is practiced in industry and in academia. His approach is creative and original; it could be acted out by two performers in front of a live audience. The book is urgently needed at a time when credit risk has emerged as the issue of the times." —Professor Philip Protter, Professor of Statistics, Statistics Department, Columbia University