XVA – Credit, Funding and Capital Valuation Adjustments

Credit, Funding and Capital Valuation Adjustments

Gebonden Engels 2015 9781118556788
Verwachte levertijd ongeveer 9 werkdagen

Samenvatting

Thorough, accessible coverage of the key issues in XVA

XVA Credit, Funding and Capital Valuation Adjustments provides specialists and non–specialists alike with an up–to–date and comprehensive treatment of Credit, Debit, Funding, Capital and Margin Valuation Adjustment (CVA, DVA, FVA, KVA and MVA), including modelling frameworks as well as broader IT engineering challenges. Written by an industry expert, this book navigates you through the complexities of XVA, discussing in detail the very latest developments in valuation adjustments including the impact of regulatory capital and margin requirements arising from CCPs and bilateral initial margin.

The book presents a unified approach to modelling valuation adjustments including credit risk, funding and regulatory effects. The practical implementation of XVA models using Monte Carlo techniques is also central to the book. You′ll also find thorough coverage of how XVA sensitivities can be accurately measured, the technological challenges presented by XVA, the use of grid computing on CPU and GPU platforms, the management of data, and how the regulatory framework introduced under Basel III presents massive implications for the finance industry.

Explores how XVA models have developed in the aftermath of the credit crisis
The only text to focus on the XVA adjustments rather than the broader topic of counterparty risk.
Covers regulatory change since the credit crisis including Basel III and the impact regulation has had on the pricing of derivatives. 
Covers the very latest valuation adjustments, KVA and MVA.
The author is a regular speaker and trainer at industry events, including WBS training, Marcus Evans, ICBI, Infoline and RISK

If you′re a quantitative analyst, trader, banking manager, risk manager, finance and audit professional, academic or student looking to expand your knowledge of XVA, this book has you covered.

Specificaties

ISBN13:9781118556788
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:536

Lezersrecensies

Wees de eerste die een lezersrecensie schrijft!

Inhoudsopgave

<p>List of Tables xvii</p>
<p>List of Figures xxi</p>
<p>Acknowledgements xxv</p>
<p>CHAPTER 1 Introduction: The Valuation of Derivative Portfolios 1</p>
<p>1.1 What this book is about 1</p>
<p>1.2 Prices and Values 4</p>
<p>1.2.1 Before the Fall... 4</p>
<p>1.2.2 The Post–Crisis World... 5</p>
<p>1.3 Trade Economics in Derivative Pricing 6</p>
<p>1.3.1 The Components of a Price 6</p>
<p>1.3.2 Risk–Neutral Valuation 8</p>
<p>1.3.3 Hedging and Management Costs 11</p>
<p>1.3.4 Credit Risk: CVA/DVA 11</p>
<p>1.3.5 FVA 13</p>
<p>1.3.6 Regulatory Capital and KVA 14</p>
<p>1.4 Post–Crisis Derivative Valuation or How I Learned to Stop Worrying and Love FVA 16</p>
<p>1.4.1 The FVA Debate and the Assault on Black–Scholes–Merton 16</p>
<p>1.4.2 Different Values for Different Purposes 19</p>
<p>1.4.3 Summary: The Valuation Paradigm Shift 21</p>
<p>1.5 Reading this Book 21</p>
<p>PART ONE CVA and DVA: Counterparty Credit Risk and Credit Valuation Adjustment</p>
<p>CHAPTER 2 Introducing Counterparty Risk 25</p>
<p>2.1 Defining Counterparty Risk 25</p>
<p>2.1.1 Wrong–way and Right–way Risk 27</p>
<p>2.2 CVA and DVA: Credit Valuation Adjustment and Debit Valuation Adjustment Defined 27</p>
<p>2.3 The Default Process 28</p>
<p>2.3.1 Example Default: The Collapse of Lehman Brothers 30</p>
<p>2.4 Credit Risk Mitigants 30</p>
<p>2.4.1 Netting 30</p>
<p>2.4.2 Collateral/Security 31</p>
<p>2.4.3 Central Clearing and Margin 34</p>
<p>2.4.4 Capital 35</p>
<p>2.4.5 Break Clauses 35</p>
<p>2.4.6 Buying Protection 37</p>
<p>CHAPTER 3 CVA and DVA: Credit and Debit Valuation Adjustment Models 39</p>
<p>3.1 Introduction 39</p>
<p>3.1.1 Close–out and CVA 40</p>
<p>3.2 Unilateral CVA Model 42</p>
<p>3.2.1 Unilateral CVA by Expectation 42</p>
<p>3.2.2 Unilateral CVA by Replication 43</p>
<p>3.3 Bilateral CVA Model: CVA and DVA 48</p>
<p>3.3.1 Bilateral CVA by Expectation 48</p>
<p>3.3.2 Bilateral CVA by Replication 50</p>
<p>3.3.3 DVA and Controversy 53</p>
<p>3.4 Modelling Dependence between Counterparties 55</p>
<p>3.4.1 Gaussian Copula Model 55</p>
<p>3.4.2 Other Copula Models 56</p>
<p>3.5 Components of a CVA Calculation Engine 57</p>
<p>3.5.1 Monte Carlo Simulation 57</p>
<p>3.5.2 Trade Valuation and Approximations 57</p>
<p>3.5.3 Expected Exposure Calculation 59</p>
<p>3.5.4 Credit Integration 59</p>
<p>3.6 Counterparty Level CVA vs. Trade Level CVA 59</p>
<p>3.6.1 Incremental CVA 60</p>
<p>3.6.2 Allocated CVA 60</p>
<p>3.7 Recovery Rate/Loss–Given–Default Assumptions 63</p>
<p>CHAPTER 4 CDS and Default Probabilities 65</p>
<p>4.1 Survival Probabilities and CVA 65</p>
<p>4.2 Historical versus Implied Survival Probabilities 66</p>
<p>4.3 Credit Default Swap Valuation 67</p>
<p>4.3.1 Credit Default Swaps 67</p>
<p>4.3.2 Premium Leg 69</p>
<p>4.3.3 Protection Leg 71</p>
<p>4.3.4 CDS Value and Breakeven Spread 72</p>
<p>4.4 Bootstrapping the Survival Probability Function 72</p>
<p>4.4.1 Upfront Payments 74</p>
<p>4.4.2 Choice of Hazard Rate Function and CVA: CVA Carry 75</p>
<p>4.4.3 Calibration Problems 76</p>
<p>4.5 CDS and Capital Relief 77</p>
<p>4.6 Liquid and Illiquid Counterparties 78</p>
<p>4.6.1 Mapping to Representative CDS 79</p>
<p>4.6.2 Mapping to Baskets and Indices 80</p>
<p>4.6.3 Cross–sectional Maps 81</p>
<p>CHAPTER 5 Analytic Models for CVA and DVA 83</p>
<p>5.1 Analytic CVA Formulae 83</p>
<p>5.2 Interest Rate Swaps 84</p>
<p>5.2.1 Unilateral CVA 84</p>
<p>5.2.2 Bilateral CVA 86</p>
<p>5.3 Options: Interest Rate Caplets and Floorlets 86</p>
<p>5.4 FX Forwards 88</p>
<p>CHAPTER 6 Modelling Credit Mitigants 91</p>
<p>6.1 Credit Mitigants 91</p>
<p>6.2 Close–out Netting 91</p>
<p>6.3 Break Clauses 93</p>
<p>6.3.1 Mandatory Break Clauses 93</p>
<p>6.3.2 Optional Break Clauses 93</p>
<p>6.4 Variation Margin and CSA Agreements 97</p>
<p>6.4.1 Simple Model: Modifying the Payout Function 97</p>
<p>6.4.2 Modelling Collateral Directly 99</p>
<p>6.4.3 Lookback Method 101</p>
<p>6.4.4 Modelling Downgrade Triggers in CSA Agreements 102</p>
<p>6.5 Non–financial Security and the Default Waterfall 107</p>
<p>CHAPTER 7 Wrong–way and Right–way Risk for CVA 109</p>
<p>7.1 Introduction: Wrong–way and Right–way Risks 109</p>
<p>7.1.1 Modelling Wrong–way Risk and CVA 110</p>
<p>7.2 Distributional Models of Wrong–way/Right–way Risk 111</p>
<p>7.2.1 Simple Model: Increased Exposure 111</p>
<p>7.2.2 Copula Models 111</p>
<p>7.2.3 Linear Models and Discrete Models 114</p>
<p>7.3 A Generalised Discrete Approach to Wrong–way Risk 116</p>
<p>7.4 Stochastic Credit Models of Wrong–way/Right–way Risk 118</p>
<p>7.4.1 Sovereign Wrong–way Risk 119</p>
<p>7.5 Wrong–way/Right–way Risk and DVA 119</p>
<p>PART TWO FVA: Funding Valuation Adjustment</p>
<p>CHAPTER 8 The Discount Curve 123</p>
<p>8.1 Introduction 123</p>
<p>8.2 A Single Curve World 123</p>
<p>8.3 Curve Interpolation and Smooth Curves 126</p>
<p>8.4 Cross–currency Basis 127</p>
<p>8.5 Multi–curve and Tenor Basis 128</p>
<p>8.6 OIS and CSA Discounting 129</p>
<p>8.6.1 OIS as the Risk–free Rate 129</p>
<p>8.6.2 OIS and CSA Discounting 131</p>
<p>8.6.3 Multi–currency Collateral and the Collateral Option 134</p>
<p>8.7 Conclusions: Discounting 138</p>
<p>CHAPTER 9 Funding Costs: Funding Valuation Adjustment (FVA) 139</p>
<p>9.1 Explaining Funding Costs 139</p>
<p>9.1.1 What is FVA? 139</p>
<p>9.1.2 General Principle of Funding Costs 145</p>
<p>9.2 First Generation FVA: Discount Models 145</p>
<p>9.3 Double Counting and DVA 146</p>
<p>9.4 Second Generation FVA: Exposure Models 147</p>
<p>9.4.1 The Burgard–Kjaer Semi–Replication Model 148</p>
<p>9.5 Residual FVA and CSAs 160</p>
<p>9.6 Asymmetry 161</p>
<p>9.6.1 Case 1: Corporate vs. Bank Asymmetry 161</p>
<p>9.6.2 Case 2: Bank vs. Bank Asymmetry 162</p>
<p>9.7 Risk Neutrality, Capital and the Modigliani–Miller Theorem 162</p>
<p>9.7.1 No Market–wide Risk–neutral Measure 162</p>
<p>9.7.2 Consequences 165</p>
<p>9.7.3 The Modigliani–Miller Theorem 165</p>
<p>9.8 Wrong–way/Right–way Risk and FVA 166</p>
<p>CHAPTER 10 Other Sources of Funding Costs: CCPs and MVA 167</p>
<p>10.1 Other Sources of Funding Costs 167</p>
<p>10.1.1 Central Counterparty Funding Costs 167</p>
<p>10.1.2 Bilateral Initial Margin 170</p>
<p>10.1.3 Rating Agency Volatility Buffers and Overcollateralisation 170</p>
<p>10.1.4 Liquidity Buffers 170</p>
<p>10.2 MVA: Margin Valuation Adjustment by Replication 171</p>
<p>10.2.1 Semi–replication with no Shortfall on Default 174</p>
<p>10.3 Calculating MVA Efficiently 175</p>
<p>10.3.1 Sizing the Problem 175</p>
<p>10.3.2 Aside: Longstaff–Schwartz for Valuations and Expected Exposures 176</p>
<p>10.3.3 Calculating VaR inside a Monte Carlo 179</p>
<p>10.3.4 Case Study: Swap Portfolios 182</p>
<p>10.3.5 Adapting LSAC to VaR under Delta–Gamma Approximation 184</p>
<p>10.4 Conclusions on MVA 184</p>
<p>CHAPTER 11 The Funding Curve 187</p>
<p>11.1 Sources for the Funding Curve 187</p>
<p>11.1.1 Term Funding 188</p>
<p>11.1.2 Rolling Funding 188</p>
<p>11.2 Internal Funding Curves 188</p>
<p>11.2.1 Bank CDS Spread 188</p>
<p>11.2.2 Bank Bond Spread 189</p>
<p>11.2.3 Bank Bond–CDS Basis 189</p>
<p>11.2.4 Bank Treasury Transfer Price 190</p>
<p>11.2.5 Funding Strategy Approaches 190</p>
<p>11.3 External Funding Curves and Accounting 191</p>
<p>11.4 Multi–currency/Multi–asset Funding 192</p>
<p>PART THREE KVA: Capital Valuation Adjustment and Regulation</p>
<p>CHAPTER 12 Regulation: the Basel II and Basel III Frameworks 195</p>
<p>12.1 Introducing the Regulatory Capital Framework 195</p>
<p>12.1.1 Economic Capital 196</p>
<p>12.1.2 The Development of the Basel Framework 196</p>
<p>12.1.3 Pillar I: Capital Types and Choices 201</p>
<p>12.2 Market Risk 202</p>
<p>12.2.1 Trading Book and Banking Book 202</p>
<p>12.2.2 Standardised Method 202</p>
<p>12.2.3 Internal Model Method (IMM) 204</p>
<p>12.3 Counterparty Credit Risk 205</p>
<p>12.3.1 Weight Calculation 205</p>
<p>12.3.2 EAD Calculation 206</p>
<p>12.3.3 Internal Model Method (IMM) 208</p>
<p>12.4 CVA Capital 209</p>
<p>12.4.1 Standardised 209</p>
<p>12.4.2 Advanced 211</p>
<p>12.5 Other Sources of Regulatory Capital 213</p>
<p>12.5.1 Incremental Risk Charge (IRC) 213</p>
<p>12.5.2 Leverage Ratio 213</p>
<p>12.6 Forthcoming Regulation with Pricing Impact 214</p>
<p>12.6.1 Fundamental Review of the Trading Book 214</p>
<p>12.6.2 Revised Standardised Approach to Credit Risk 218</p>
<p>12.6.3 Bilateral Initial Margin 220</p>
<p>12.6.4 Prudent Valuation 220</p>
<p>12.6.5 EMIR and Frontloading 224</p>
<p>CHAPTER 13 KVA: Capital Valuation Adjustment 227</p>
<p>13.1 Introduction: Capital Costs in Pricing 227</p>
<p>13.1.1 Capital, Funding and Default 227</p>
<p>13.2 Extending Semi–replication to Include Capital 228</p>
<p>13.3 The Cost of Capital 232</p>
<p>13.4 KVA for Market Risk, Counterparty Credit Risk and CVA Regulatory Capital 232</p>
<p>13.4.1 Standardised Approaches 232</p>
<p>13.4.2 IMM Approaches 233</p>
<p>13.5 The Size of KVA 233</p>
<p>13.6 Conclusion: KVA 237</p>
<p>CHAPTER 14 CVA Risk Warehousing and Tax Valuation Adjustment (TVA) 239</p>
<p>14.1 Risk Warehousing XVA 239</p>
<p>14.2 Taxation 239</p>
<p>14.3 CVA Hedging and Regulatory Capital 240</p>
<p>14.4 Warehousing CVA Risk and Double Semi–Replication 240</p>
<p>CHAPTER 15 Portfolio KVA and the Leverage Ratio 247</p>
<p>15.1 The Need for a Portfolio Level Model 247</p>
<p>15.2 Portfolio Level Semi–replication 248</p>
<p>15.3 Capital Allocation 254</p>
<p>15.3.1 Market Risk 255</p>
<p>15.3.2 Counterparty Credit Risk (CCR) 255</p>
<p>15.3.3 CVA Capital 255</p>
<p>15.3.4 Leverage Ratio 256</p>
<p>15.3.5 Capital Allocation and Uniqueness 257</p>
<p>15.4 Cost of Capital to the Business 257</p>
<p>15.5 Portfolio KVA 258</p>
<p>15.6 Calculating Portfolio KVA by Regression 258</p>
<p>PART FOUR XVA Implementation</p>
<p>CHAPTER 16 Hybrid Monte Carlo Models for XVA: Building a Model for the Expected–Exposure Engine 263</p>
<p>16.1 Introduction 263</p>
<p>16.1.1 Implementing XVA 263</p>
<p>16.1.2 XVA and Monte Carlo 263</p>
<p>16.1.3 XVA and Models 264</p>
<p>16.1.4 A Roadmap to XVA Hybrid Monte Carlo 267</p>
<p>16.2 Choosing the Calibration: Historical versus Implied 268</p>
<p>16.2.1 The Case for Historical Calibration 268</p>
<p>16.2.2 The Case for Market Implied Calibration 281</p>
<p>16.3 The Choice of Interest Rate Modelling Framework 285</p>
<p>16.3.1 Interest Rate Models (for XVA) 286</p>
<p>16.3.2 The Heath–Jarrow–Morton (HJM) Framework and Models of the Short Rate 286</p>
<p>16.3.3 The Brace–Gaterak–Musiela (BGM) or Market Model Framework 305</p>
<p>16.3.4 Choice of Numeraire 313</p>
<p>16.3.5 Multi–curve: Tenor and Cross–currency Basis 314</p>
<p>16.3.6 Close–out and the Choice of Discount Curve 318</p>
<p>16.4 FX and Cross–currency Models 319</p>
<p>16.4.1 A Multi–currency Generalised Hull–White Model 320</p>
<p>16.4.2 The Triangle Rule and Options on the FX Cross 322</p>
<p>16.4.3 Models with FX Volatility Smiles 324</p>
<p>16.5 Inflation 327</p>
<p>16.5.1 The Jarrow–Yildirim Model (using Hull–White Dynamics) 327</p>
<p>16.5.2 Other Approaches 336</p>
<p>16.6 Equities 337</p>
<p>16.6.1 A Simple Log–normal Model 337</p>
<p>16.6.2 Dividends 339</p>
<p>16.6.3 Indices and Baskets 339</p>
<p>16.6.4 Managing Correlations 340</p>
<p>16.6.5 Skew: Local Volatility and Other Models 340</p>
<p>16.7 Commodities 342</p>
<p>16.7.1 Precious Metals 342</p>
<p>16.7.2 Forward–based Commodities 342</p>
<p>16.7.3 Electricity and Spark Spreads 347</p>
<p>16.8 Credit 348</p>
<p>16.8.1 A Simple Gaussian Model 349</p>
<p>16.8.2 JCIR++ 350</p>
<p>16.8.3 Other Credit Models, Wrong–way Risk Models and Credit Correlation 351</p>
<p>CHAPTER 17 Monte Carlo Implementation 353</p>
<p>17.1 Introduction 353</p>
<p>17.2 Errors in Monte Carlo 353</p>
<p>17.2.1 Discretisation Errors 354</p>
<p>17.2.2 Random Errors 357</p>
<p>17.3 Random Numbers 359</p>
<p>17.3.1 Pseudo–random Number Generators 359</p>
<p>17.3.2 Quasi–random Number Generators 364</p>
<p>17.3.3 Generating Normal Samples 369</p>
<p>17.4 Correlation 372</p>
<p>17.4.1 Correlation Matrix Regularisation 372</p>
<p>17.4.2 Inducing Correlation 373</p>
<p>17.5 Path Generation 375</p>
<p>17.5.1 Forward Induction 375</p>
<p>17.5.2 Backward Induction 375</p>
<p>CHAPTER 18 Monte Carlo Variance Reduction and Performance Enhancements 377</p>
<p>18.1 Introduction 377</p>
<p>18.2 Classic Methods 377</p>
<p>18.2.1 Antithetics 377</p>
<p>18.2.2 Control Variates 378</p>
<p>18.3 Orthogonalisation 379</p>
<p>18.4 Portfolio Compression 381</p>
<p>18.5 Conclusion: Making it Go Faster! 382</p>
<p>CHAPTER 19 Valuation Models for Use with Monte Carlo Exposure Engines 383</p>
<p>19.1 Valuation Models 383</p>
<p>19.1.1 Consistent or Inconsistent Valuation? 384</p>
<p>19.1.2 Performance Constraints 384</p>
<p>19.1.3 The Case for XVA Valuation Consistent with Trade Level Valuations 385</p>
<p>19.1.4 The Case for Consistent XVA Dynamics 386</p>
<p>19.1.5 Simulated Market Data and Valuation Model Compatibility 387</p>
<p>19.1.6 Valuation Differences as a KPI 387</p>
<p>19.1.7 Scaling 387</p>
<p>19.2 Implied Volatility Modelling 388</p>
<p>19.2.1 Deterministic Models 388</p>
<p>19.2.2 Stochastic Models 389</p>
<p>19.3 State Variable–based Valuation Techniques 389</p>
<p>19.3.1 Grid Interpolation 390</p>
<p>19.3.2 Longstaff–Schwartz 391</p>
<p>CHAPTER 20 Building the Technological Infrastructure 393</p>
<p>20.1 Introduction 393</p>
<p>20.2 System Components 393</p>
<p>20.2.1 Input Data 394</p>
<p>20.2.2 Calculation 401</p>
<p>20.2.3 Reporting 405</p>
<p>20.3 Hardware 405</p>
<p>20.3.1 CPU 406</p>
<p>20.3.2 GPU and GPGPU 406</p>
<p>20.3.3 Intel&reg; Xeon PhiTM 407</p>
<p>20.3.4 FPGA 408</p>
<p>20.3.5 Supercomputers 408</p>
<p>20.4 Software 408</p>
<p>20.4.1 Roles and Responsibilities 409</p>
<p>20.4.2 Development and Project Management Practice 410</p>
<p>20.4.3 Language Choice 415</p>
<p>20.4.4 CPU Languages 416</p>
<p>20.4.5 GPU Languages 417</p>
<p>20.4.6 Scripting and Payout Languages 418</p>
<p>20.4.7 Distributed Computing and Parallelism 418</p>
<p>20.5 Conclusion 421</p>
<p>PART FIVE Managing XVA</p>
<p>CHAPTER 21 Calculating XVA Sensitivities 425</p>
<p>21.1 XVA Sensitivities 425</p>
<p>21.1.1 Defining the Sensitivities 425</p>
<p>21.1.2 Jacobians and Hessians 426</p>
<p>21.1.3 Theta, Time Decay and Carry 427</p>
<p>21.1.4 The Explain 431</p>
<p>21.2 Finite Difference Approximation 434</p>
<p>21.2.1 Estimating Sensitivities 434</p>
<p>21.2.2 Recalibration? 435</p>
<p>21.2.3 Exercise Boundaries and Sensitivities 436</p>
<p>21.3 Pathwise Derivatives and Algorithmic Differentiation 437</p>
<p>21.3.1 Preliminaries: The Pathwise Method 438</p>
<p>21.3.2 Adjoints 440</p>
<p>21.3.3 Adjoint Algorithmic Differentiation 442</p>
<p>21.3.4 Hybrid Approaches and Longstaff–Schwartz 443</p>
<p>21.4 Scenarios and Stress Tests 445</p>
<p>CHAPTER 22 Managing XVA 447</p>
<p>22.1 Introduction 447</p>
<p>22.2 Organisational Design 448</p>
<p>22.2.1 Separate XVA Functions 448</p>
<p>22.2.2 Central XVA 451</p>
<p>22.3 XVA, Treasury and Portfolio Management 453</p>
<p>22.3.1 Treasury 453</p>
<p>22.3.2 Loan Portfolio Management 454</p>
<p>22.4 Active XVA Management 454</p>
<p>22.4.1 Market Risks 455</p>
<p>22.4.2 Counterparty Credit Risk Hedging 457</p>
<p>22.4.3 Hedging DVA? 458</p>
<p>22.4.4 Hedging FVA 459</p>
<p>22.4.5 Managing and Hedging Capital 459</p>
<p>22.4.6 Managing Collateral and MVA 460</p>
<p>22.5 Passive XVA Management 460</p>
<p>22.6 Internal Charging for XVA 460</p>
<p>22.6.1 Payment Structures 461</p>
<p>22.6.2 The Charging Process 461</p>
<p>22.7 Managing Default and Distress 462</p>
<p>PART SIX The Future</p>
<p>CHAPTER 23 The Future of Derivatives? 465</p>
<p>23.1 Reflecting on the Years of Change... 465</p>
<p>23.2 The Market in the Future 465</p>
<p>23.2.1 Products 466</p>
<p>23.2.2 CCPs, Clearing and MVA 466</p>
<p>23.2.3 Regulation, Capital and KVA 467</p>
<p>23.2.4 Computation, Automation and eTrading 467</p>
<p>23.2.5 Future Models and Future XVA 468</p>
<p>Bibliography 469</p>
<p>Index 489</p>

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