Оглавление
Green Andrew. XVA
Acknowledgements
CHAPTER 1. Introduction: The Valuation of Derivative Portfolios
1.1 What this book is about
1.2 Prices and Values
1.2.1 Before the Fall…
1.2.2 The Post-Crisis World…
1.3 Trade Economics in Derivative Pricing
1.3.1 The Components of a Price
1.3.2 Risk-Neutral Valuation
1.3.3 Hedging and Management Costs
1.3.4 Credit Risk: CVA/DVA
1.3.5 FVA
1.3.6 Regulatory Capital and KVA
1.4 Post-Crisis Derivative Valuation or How I Learned to Stop Worrying and Love FVA
1.4.1 The FVA Debate and the Assault on Black-Scholes-Merton
1.4.2 Different Values for Different Purposes
1.4.3 Summary: The Valuation Paradigm Shift
1.5 Reading this Book
PART One. CVA and DVA: Counterparty Credit Risk and Credit Valuation Adjustment
CHAPTER 2. Introducing Counterparty Risk
2.1 Defining Counterparty Risk
2.1.1 Wrong-way and Right-way Risk
2.2 CVA and DVA: Credit Valuation Adjustment and Debit Valuation Adjustment Defined
2.3 The Default Process
2.3.1 Example Default: The Collapse of Lehman Brothers
2.4 Credit Risk Mitigants
2.4.1 Netting
2.4.2 Collateral/Security
2.4.3 Central Clearing and Margin
2.4.4 Capital
2.4.5 Break Clauses
2.4.6 Buying Protection
CHAPTER 3. CVA and DVA: Credit and Debit Valuation Adjustment Models
3.1 Introduction
3.1.1 Close-out and CVA
3.2 Unilateral CVA Model
3.2.1 Unilateral CVA by Expectation
3.2.2 Unilateral CVA by Replication
3.3 Bilateral CVA Model: CVA and DVA
3.3.1 Bilateral CVA by Expectation
3.3.2 Bilateral CVA by Replication
3.3.3 DVA and Controversy
3.4 Modelling Dependence between Counterparties
3.4.1 Gaussian Copula Model
3.4.2 Other Copula Models
3.5 Components of a CVA Calculation Engine
3.5.1 Monte Carlo Simulation
3.5.2 Trade Valuation and Approximations
3.5.3 Expected Exposure Calculation
3.5.4 Credit Integration
3.6 Counterparty Level CVA vs. Trade Level CVA
3.6.1 Incremental CVA
3.6.2 Allocated CVA
3.7 Recovery Rate/Loss-Given-Default Assumptions
CHAPTER 4. CDS and Default Probabilities
4.1 Survival Probabilities and CVA
4.2 Historical versus Implied Survival Probabilities
4.3 Credit Default Swap Valuation
4.3.1 Credit Default Swaps
4.3.2 Premium Leg
4.3.3 Protection Leg
4.3.4 CDS Value and Breakeven Spread
4.4 Bootstrapping the Survival Probability Function
4.4.1 Upfront Payments
4.4.2 Choice of Hazard Rate Function and CVA: CVA Carry
4.4.3 Calibration Problems
4.5 CDS and Capital Relief
4.6 Liquid and Illiquid Counterparties
4.6.1 Mapping to Representative CDS
4.6.2 Mapping to Baskets and Indices
4.6.3 Cross-sectional Maps
CHAPTER 5. Analytic Models for CVA and DVA
5.1 Analytic CVA Formulae
5.2 Interest Rate Swaps
5.2.1 Unilateral CVA
5.2.2 Bilateral CVA
5.3 Options: Interest Rate Caplets and Floorlets
5.4 FX Forwards
CHAPTER 6. Modelling Credit Mitigants
6.1 Credit Mitigants
6.2 Close-out Netting
6.3 Break Clauses
6.3.1 Mandatory Break Clauses
6.3.2 Optional Break Clauses
6.4 Variation Margin and CSA Agreements
6.4.1 Simple Model: Modifying the Payout Function
6.4.2 Modelling Collateral Directly
6.4.3 Lookback Method
6.4.4 Modelling Downgrade Triggers in CSA Agreements
6.5 Non-financial Security and the Default Waterfall
CHAPTER 7. Wrong-way and Right-way Risk for CVA
7.1 Introduction: Wrong-way and Right-way Risks
7.1.1 Modelling Wrong-way Risk and CVA
7.2 Distributional Models of Wrong-way/ Right-way Risk
7.2.1 Simple Model: Increased Exposure
7.2.2 Copula Models
7.2.3 Linear Models and Discrete Models
7.3 A Generalised Discrete Approach to Wrong-Way Risk
7.4 Stochastic Credit Models of Wrong-way/Right-way Risk
7.4.1 Sovereign Wrong-way Risk
7.5 Wrong-way/Right-way Risk and DVA
PART Two. FVA: Funding Valuation Adjustment
CHAPTER 8. The Discount Curve
8.1 Introduction
8.2 A Single Curve World
8.3 Curve Interpolation and Smooth Curves
8.4 Cross-currency Basis
8.5 Multi-curve and Tenor Basis
8.6 OIS and CSA Discounting
8.6.1 OIS as the Risk-free Rate
8.6.2 OIS and CSA Discounting
8.6.3 Multi-currency Collateral and the Collateral Option
8.7 Conclusions: Discounting
CHAPTER 9. Funding Costs: Funding Valuation Adjustment (FVA)
9.1 Explaining Funding Costs
9.1.1 What is FVA?
9.1.2 General Principle of Funding Costs
9.2 First Generation FVA: Discount Models
9.3 Double Counting and DVA
9.4 Second Generation FVA: Exposure Models
9.4.1 The Burgard-Kjaer Semi-Replication Model
9.5 Residual FVA and CSAs
9.6 Asymmetry
9.6.1 Case 1: Corporate vs. Bank Asymmetry
9.6.2 Case 2: Bank vs. Bank Asymmetry
9.7 Risk Neutrality, Capital and the Modigliani-Miller Theorem
9.7.1 No Market-wide Risk-neutral Measure
9.7.2 Consequences
9.7.3 The Modigliani-Miller Theorem
9.8 Wrong-way/Right-way Risk and FVA
CHAPTER 10. Other Sources of Funding Costs: CCPs and MVA
10.1 Other Sources of Funding Costs
10.1.1 Central Counterparty Funding Costs
10.1.2 Bilateral Initial Margin
10.1.3 Rating Agency Volatility Buffers and Overcollateralisation
10.1.4 Liquidity Buffers
10.2 MVA: Margin Valuation Adjustment by Replication
10.2.1 Semi-replication with no Shortfall on Default
10.3 Calculating MVA Efficiently
10.3.1 Sizing the Problem
10.3.2 Aside: Longstaff-Schwartz for Valuations and Expected Exposures
10.3.3 Calculating VaR inside a Monte Carlo
10.3.4 Case Study: Swap Portfolios
10.3.5 Adapting LSAC to VaR under Delta-Gamma Approximation
10.4 Conclusions on MVA
CHAPTER 11. The Funding Curve
11.1 Sources for the Funding Curve
11.1.1 Term Funding
11.1.2 Rolling Funding
11.2 Internal Funding Curves
11.2.1 Bank CDS Spread
11.2.2 Bank Bond Spread
11.2.3 Bank Bond-CDS Basis
11.2.4 Bank Treasury Transfer Price
11.2.5 Funding Strategy Approaches
11.3 External Funding Curves and Accounting
11.4 Multi-currency/Multi-asset Funding
PART Three. KVA: Capital Valuation Adjustment and Regulation
CHAPTER 12. Regulation: the Basel II and Basel III Frameworks
12.1 Introducing the Regulatory Capital Framework
12.1.1 Economic Capital
12.1.2 The Development of the Basel Framework
12.1.3 Pillar I: Capital Types and Choices
12.2 Market Risk
12.2.1 Trading Book and Banking Book
12.2.2 Standardised Method
12.2.3 Internal Model Method (IMM)
12.3 Counterparty Credit Risk
12.3.1 Weight Calculation
12.3.2 EAD Calculation
12.3.3 Internal Model Method (IMM)
12.4 CVA Capital
12.4.1 Standardised
12.4.2 Advanced
12.5 Other Sources of Regulatory Capital
12.5.1 Incremental Risk Charge (IRC)
12.5.2 Leverage Ratio
12.6 Forthcoming Regulation with Pricing Impact
12.6.1 Fundamental Review of the Trading Book
12.6.2 Revised Standardised Approach to Credit Risk
12.6.3 Bilateral Initial Margin
12.6.4 Prudent Valuation
12.6.5 EMIR and Frontloading
CHAPTER 13. KVA: Capital Valuation Adjustment
13.1 Introduction: Capital Costs in Pricing
13.1.1 Capital, Funding and Default
13.2 Extending Semi-replication to Include Capital
13.3 The Cost of Capital
13.4 KVA for Market Risk, Counterparty Credit Risk and CVA Regulatory Capital
13.4.1 Standardised Approaches
13.4.2 IMM Approaches
13.5 The Size of KVA
13.6 Conclusion: KVA
CHAPTER 14. CVA Risk Warehousing and Tax Valuation Adjustment (TVA)
14.1 Risk Warehousing XVA
14.2 Taxation
14.3 CVA Hedging and Regulatory Capital
14.4 Warehousing CVA Risk and Double Semi-Replication
CHAPTER 15. Portfolio KVA and the Leverage Ratio
15.1 The Need for a Portfolio Level Model
15.2 Portfolio Level Semi-replication
15.3 Capital Allocation
15.3.1 Market Risk
15.3.2 Counterparty Credit Risk (CCR)
15.3.3 CVA Capital
15.3.4 Leverage Ratio
15.3.5 Capital Allocation and Uniqueness
15.4 Cost of Capital to the Business
15.5 Portfolio KVA
15.6 Calculating Portfolio KVA by Regression
PART Four. XVA Implementation
CHAPTER 16. Hybrid Monte Carlo Models for XVA: Building a Model for the Expected-Exposure Engine
16.1 Introduction
16.1.1 Implementing XVA
16.1.2 XVA and Monte Carlo
16.1.3 XVA and Models
16.1.4 A Roadmap to XVA Hybrid Monte Carlo
16.2 Choosing the Calibration: Historical versus Implied
16.2.1 The Case for Historical Calibration
16.2.2 The Case for Market Implied Calibration
16.3 The Choice of Interest Rate Modelling Framework
16.3.1 Interest Rate Models (for XVA)
16.3.2 The Heath-Jarrow-Morton (HJM) Framework and Models of the Short Rate
16.3.3 The Brace-Gaterak-Musiela (BGM) or Market Model Framework
16.3.4 Choice of Numeraire
16.3.5 Multi-curve: Tenor and Cross-currency Basis
16.3.6 Close-out and the Choice of Discount Curve
16.4 FX and Cross-currency Models
16.4.1 A Multi-currency Generalised Hull-White Model
16.4.2 The Triangle Rule and Options on the FX Cross
16.4.3 Models with FX Volatility Smiles
16.5 Inflation
16.5.1 The Jarrow-Yildirim Model (using Hull-White Dynamics)
16.5.2 Other Approaches
16.6 Equities
16.6.1 A Simple Log-normal Model
16.6.2 Dividends
16.6.3 Indices and Baskets
16.6.4 Managing Correlations
16.6.5 Skew: Local Volatility and Other Models
16.7 Commodities
16.7.1 Precious Metals
16.7.2 Forward-based Commodities
16.7.3 Electricity and Spark Spreads
16.8 Credit
16.8.1 A Simple Gaussian Model
16.8.2 JCIR++
16.8.3 Other Credit Models, Wrong-way Risk Models and Credit Correlation
CHAPTER 17. Monte Carlo Implementation
17.1 Introduction
17.2 Errors in Monte Carlo
17.2.1 Discretisation Errors
17.2.2 Random Errors
17.3 Random Numbers
17.3.1 Pseudo-random Number Generators
17.3.2 Quasi-random Number Generators
17.3.3 Generating Normal Samples
17.4 Correlation
17.4.1 Correlation Matrix Regularisation
17.4.2 Inducing Correlation
17.5 Path Generation
17.5.1 Forward Induction
17.5.2 Backward Induction
CHAPTER 18. Monte Carlo Variance Reduction and Performance Enhancements
18.1 Introduction
18.2 Classic Methods
18.2.1 Antithetics
18.2.2 Control Variates
18.3 Orthogonalisation
18.4 Portfolio Compression
18.5 Conclusion: Making it Go Faster!
CHAPTER 19. Valuation Models for Use with Monte Carlo Exposure Engines
19.1 Valuation Models
19.1.1 Consistent or Inconsistent Valuation?
19.1.2 Performance Constraints
19.1.3 The Case for XVA Valuation Consistent with Trade Level Valuations
19.1.4 The Case for Consistent XVA Dynamics
19.1.5 Simulated Market Data and Valuation Model Compatibility
19.1.6 Valuation Differences as a KPI
19.1.7 Scaling
19.2 Implied Volatility Modelling
19.2.1 Deterministic Models
19.2.2 Stochastic Models
19.3 State Variable-based Valuation Techniques
19.3.1 Grid Interpolation
19.3.2 Longstaff-Schwartz
CHAPTER 20. Building the Technological Infrastructure
20.1 Introduction
20.2 System Components
20.2.1 Input Data
20.2.2 Calculation
20.2.3 Reporting
20.3 Hardware
20.3.1 CPU
20.3.2 GPU and GPGPU
20.3.3 Intel® Xeon Phi™
20.3.4 FPGA
20.3.5 Supercomputers
20.4 Software
20.4.1 Roles and Responsibilities
20.4.2 Development and Project Management Practice
20.4.3 Language Choice
20.4.4 CPU Languages
20.4.5 GPU Languages
20.4.6 Scripting and Payout Languages
20.4.7 Distributed Computing and Parallelism
20.5 Conclusion
PART Five. Managing XVA
CHAPTER 21. Calculating XVA Sensitivities
21.1 XVA Sensitivities
21.1.1 Defining the Sensitivities
21.1.2 Jacobians and Hessians
21.1.3 Theta, Time Decay and Carry
21.1.4 The Explain
21.2 Finite Difference Approximation
21.2.1 Estimating Sensitivities
21.2.2 Recalibration?
21.2.3 Exercise Boundaries and Sensitivities
21.3 Pathwise Derivatives and Algorithmic Differentiation
21.3.1 Preliminaries: The Pathwise Method
21.3.2 Adjoints
21.3.3 Adjoint Algorithmic Differentiation
21.3.4 Hybrid Approaches and Longstaff-Schwartz
21.4 Scenarios and Stress Tests
CHAPTER 22. Managing XVA
22.1 Introduction
22.2 Organisational Design
22.2.1 Separate XVA Functions
22.2.2 Central XVA
22.3 XVA, Treasury and Portfolio Management
22.3.1 Treasury
22.3.2 Loan Portfolio Management
22.4 Active XVA Management
22.4.1 Market Risks
22.4.2 Counterparty Credit Risk Hedging
22.4.3 Hedging DVA?
22.4.4 Hedging FVA
22.4.5 Managing and Hedging Capital
22.4.6 Managing Collateral and MVA
22.5 Passive XVA Management
22.6 Internal Charging for XVA
22.6.1 Payment Structures
22.6.2 The Charging Process
22.7 Managing Default and Distress
PART Six. The Future
CHAPTER 23. The Future of Derivatives?
23.1 Reflecting on the Years of Change…
23.2 The Market in the Future
23.2.1 Products
23.2.2 CCPs, Clearing and MVA
23.2.3 Regulation, Capital and KVA
23.2.4 Computation, Automation and eTrading
23.2.5 Future Models and Future XVA
Bibliography
Index
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