Modern Derivatives. Pricing and Credit. Exposure Anatysis. Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest!
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1 Modern Derivatives Pricing and Credit Exposure Anatysis Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest!ng Roland Lichters, Roland Stamm, Donal Gallagher
2 Contents List of Figures ListofTables Preface Acknowledgements List ofabbreviations and Symbols xiv xxii xxv xxix xxx Parti Discounting 1 1 Discounting Before the Crisis The risk-free rate Pacing linear Instruments Forward rate agreements Interest rate swaps FXforwards Tenor basis swaps Cross-currency basis swaps Curve building Pricing non-linear instruments Caps and floors Swaptions 11 2 What Changed with the Crisis Basis products and spreads Tenor basis swaps Cross-currency basis swaps Collateralization 17 3 Clearing House Pricing Introduction of central counterparties Margin requirements Building the OIS curve USD specialities Building the forward protection curves More USD specialities Example: implying the par asset swap spread 27 vii
3 viii Contents 3.8 Interpolation Pricing non-linear instruments European swaptions Bermudan swaptions Not all currencies are equal 33 4 Global Discounting Collateralization in a foreign currency Non-rebalancing cross-currency swaps Rebalancing cross-currency swaps Examples: approximations of basis spreads Tenor basis spreads Fiat cross-currency swaps OIS cross-currency basis spread LIBOR cross-currency basis spread 43 5 CSA Discounting ISDA agreements and CSA complexities Currency options Negative overnight rates Other assets as collateral Thresholds and asymmetries Some thoughts on initial margin 51 6 Fair Value Hedge Accounting in a Multi-Curve World Introduction Hedge effectiveness Single-curve valuation Multi-curve valuation 59 Part II Credit and Debit Value Adjustment 67 7 Introduction 69 8 Fundamentals Unilateral CVA Bilateral CVA 76 9 Single Trade CVA Interest rate swap Exercise within interest periods Amortizing swap A simple swap CVA model Cash-settled European options FX forward Cross-currency swap Rebalancing cross-currency swap 101
4 Contents j ix Part III Risk Factor Evolution 10 Introduction - A Monte Carlo Framework 11 Interest Rates 11.1 Linear Gauss Markov model Multiple curves Invariances Relation to the Hull-White model in T-forward measure 11.2 Products Zero bond option European swaption Bermudan swaption with deterministic basis Stochastic basis 11.3 CSA discounting revisited 11.4 Exposure evolution examples 12 Foreign Exchange 12.1 Cross-currency LGM 12.2 Multi-currency LGM 12.3 Calibration Interest rate processes FX processes Correlations 12.4 Cross-currency basis 12.5 Exposure evolution examples 13 Inflation 13.1 Products 13.2 Jarrow-Yildirim model Calibration Foreign currency inflation 13.3 Dodgson-Kainth model Calibration Foreign currency inflation 13.4 Seasonality 13.5 Exposure evolution examples 14 Equity and Commodity 14.1 Equity 14.2 Commodity 15 Credit 15.1 Market 15.2 Gaussian model Conclusion
5 x Contents 15.3 Cox-Ingersoll-Ross model CIR without jumps Relaxed feller constraint CDS spread distribution CIRwith jumps: JCIR JCIR extension Examples: CDS CVA and wrong-way risk Conclusion Black-Karasinski model Peng-Kou model Review CDS and CDS option Compound Poisson process Compound Polya process Examples Conclusion 233 Part IV XVA Cross-Asset Scenario Generation Expectations and covariances Path generation Pseudo-random vs low discrepancy sequences Long-term interest rate Simulation Netting and Collateral Netting Non-netted counterparty exposures Netting set exposures Generalized counterparty exposures Collateralization Collateralized netting set exposure CSAmargining Margin settlement Interest accrual FXrisk Collateral choice Early Exercise and American Monte Carlo American Monte Carlo Utilizing American Monte Carlo for CVA CVA Risk and Algorithmic Differentiation Algorithmic differentiation AD basics 276
6 Contents j xi 19.3 AD examples Vanilla swap and interest rate sensitivities European swaptions with deltas and vega cube Further applications of AD FVA A simple definition of FVA DVA = FBA? The role of the spreads The expectation approach The semi-replication approach CSA pricing revisited MVA Outlook KVA KVA by semi-replication Calculation of KVA Risk-warehousing and TVA 308 Part V Credit Risk Introduction Fundamentals Portfolio credit models Independent defaults Static default correlation modelling Dynamic default correlation modelling Industry portfolio credit models Pricing Portfolio Credit Products Introduction Synthetic portfolio credit derivatives Nth-to-default basket Synthetic collateralized debt Obligation Synthetic CDO Cashflow structures Introduction Cashflow CDO structures Overall pricing framework Pricing formulas Example results Test deal 347
7 xii [ Contents Testresults Discussion ofresults Credit Risk and Basel Capital for Derivatives Introduction Potential future exposure Real-world measure Traditional approach Adjusted risk-neutral approach Joint measure model approach Standardized approach, CEM and SA-CCR Current standardized approach: CEM New standardized approach: SA-CCR Basel internal model approach Capital requirements for centrally cleared derivatives CVA capital charge The Standard approach The IMM approach Mitigation of the CVA capital charge Exemptions Backtesting Introduction Backtest model framework Example: Anderson-Darling test REE backtesting Creating the sample distance and sampling distribution Example I: Risk-neutral LGM Example II: Risk-neutral LGM with drift adjustment Portfolio backtesting Outlook 390 Part VI Appendix 393 A The Change ofnumeraire Toolkit 395 B The Feynman-Kac Connection 398 C The Black76 Formula 400 C.l The Standard Black76 formula 400 C.2 The normal Black76 formula 401 D Hull-White Model 403 D.l Summary 403 D.2 Bank account and forward measure 407 D.3 Cross-currency Hull-White model 410
8 Contents J xiii E Linear Gauss Markov Model 423 E.l One Factor 423 E.2 Two factors 426 E.3 Cross-currency LGM 430 F Dodgson-Kainth Model 433 F.l Domestic currency inflation 433 F.2 Foreign currency inflation 435 G CIR Model with Jumps 441 H CDS and CDS Option: Filtration Switching and the PK Model 446 Bibliography 450 Index 457
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