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## Book Description

Solve the DVA/FVA Overlap Issue and Effectively Manage Portfolio Credit Risk

Counterparty Risk and Funding: A Tale of Two Puzzles explains how to study risk embedded in financial transactions between the bank and its counterparty. The authors provide an analytical basis for the quantitative methodology of dynamic valuation, mitigation, and hedging of bilateral counterparty risk on over-the-counter (OTC) derivative contracts under funding constraints. They explore credit, debt, funding, liquidity, and rating valuation adjustment (CVA, DVA, FVA, LVA, and RVA) as well as replacement cost (RC), wrong-way risk, multiple funding curves, and collateral.

The first part of the book assesses today’s financial landscape, including the current multi-curve reality of financial markets. In mathematical but model-free terms, the second part describes all the basic elements of the pricing and hedging framework. Taking a more practical slant, the third part introduces a reduced-form modeling approach in which the risk of default of the two parties only shows up through their default intensities. The fourth part addresses counterparty risk on credit derivatives through dynamic copula models. In the fifth part, the authors present a credit migrations model that allows you to account for rating-dependent credit support annex (CSA) clauses. They also touch on nonlinear FVA computations in credit portfolio models. The final part covers classical tools from stochastic analysis and gives a brief introduction to the theory of Markov copulas.

The credit crisis and ongoing European sovereign debt crisis have shown the importance of the proper assessment and management of counterparty risk. This book focuses on the interaction and possible overlap between DVA and FVA terms. It also explores the particularly challenging issue of counterparty risk in portfolio credit modeling. Primarily for researchers and graduate students in financial mathematics, the book is also suitable for financial quants, managers in banks, CVA desks, and members of supervisory bodies.

1. Preliminaries
2. Preface
3. Part I Financial Landscape
1. Chapter 1 A Galilean Dialogue on Counterparty Risk, CVA, DVA, Multiple Curves, Collateral and Funding
1. 1.1 To the Discerning Reader
2. 1.2 The First Day
3. 1.3 The Second Day
4. 1.4 The Third Day
5. 1.5 The Fourth Day
2. Chapter 2 The Whys of the LOIS
1. 2.1 Financial Setup
2. 2.2 Indifference Valuation Model
3. 2.3 LOIS Formula
4. 2.4 Numerical Study
5. Conclusion
4. Part II Model-Free Developments
1. Chapter 3 Pure Counterparty Risk
1. 3.1 Cash Flows
2. 3.2 Valuation and Hedging
1. 3.2.1 Valuation of the Contract
2. 3.2.2 Valuation of Counterparty Risk
3. 3.2.3 Exposure at Default
4. 3.2.4 TVA and CVA/DVA/RC
5. 3.2.5 Dynamic Hedging of Counterparty Risk
3. 3.3 CSA Specifications
2. Chapter 4 Bilateral Counterparty Risk under Funding Constraints
1. 4.1 Introduction
2. 4.2 Market Model
4. 4.4 Martingale Pricing Approach
5. 4.5 TVA
1. 4.5.1 Clean Price
2. 4.5.2 CSA Close-Out Cash-Flow
3. 4.5.3 TVA Representation
6. 4.6 Example
1. 4.6.1 Setup
2. 4.6.2 Analysis of a Solution
3. 4.6.3 Comparison with the Results of Burgard and Kjaer
5. Part III Reduced-Form BSDE Modeling
1. Chapter 5 A Reduced-Form TVA BSDE Approach to Counterparty Risk under Funding Constraints
1. 5.1 Introduction
2. 5.2 Pre-Default BSDE Modeling
3. 5.3 Markov Case
1. 5.3.1 Factor Process
2. 5.3.2 Min-Variance Hedging of Market Risk
3. 5.3.3 Min-Variance Hedging Constrained to Perfect Hedging of Jump-to-Default Risk
4. 5.3.4 Unilateral or Bilateral in the End?
2. Chapter 6 The Four Wings of the TVA
1. 6.1 Introduction
2. 6.2 TVA Representations
1. 6.2.1 Setup
2. 6.2.2 BSDEs
3. 6.2.3 CVA, DVA, LVA and RC
3. 6.3 CSA Specifications
4. 6.4 Clean Valuations
1. 6.4.1 Products
2. 6.4.2 Gaussian Vasicek Short Rate Model
3. 6.4.3 Lévy Hull-White Short Rate Model
4. 6.4.4 Numerics
5. 6.5 TVA Computations
6. Conclusion
6. Part IV Dynamic Copula Models
1. Chapter 7 Dynamic Gaussian Copula Model
1. 7.1 Introduction
2. 7.2 Model
1. 7.2.1 Gaussian Distributions
2. 7.2.2 Model of Default Times
3. 7.2.3 Fundamental Martingales
3. 7.3 Clean Valuation and Hedging of Credit Derivatives
4. 7.4 Counterparty Risk
1. 7.4.1 Numerics
2. Chapter 8 Common-Shock Model
1. 8.1 Introduction
2. 8.2 Model of Default Times
1. 8.2.1 Conditional Joint Survival Function
2. 8.2.2 Itô-Markov Formula
3. 8.2.3 Intensity Structure
3. 8.3 Clean Pricing, Calibration and Hedging
1. 8.3.1 Pricing Equations
2. 8.3.2 Min-Variance Hedging
3. 8.3.3 Convolution Recursion Pricing Schemes
4. 8.3.4 Random Recoveries
4. 8.4 Numerical Results
5. 8.5 CVA Pricing and Hedging
3. Chapter 9 CVA Computations for One CDS in the Common-Shock Model
1. 9.1 Introduction
2. 9.2 Generalities
1. 9.2.1 Specification-Free Results in a Common-Shock Setup
3. 9.3 Common-Shock Model with Deterministic Intensities
1. 9.3.1 Implementation
4. 9.4 Numerical Results with Deterministic Intensities
5. 9.5 Common-Shock Model with Stochastic Intensities
1. 9.5.1 CIR++ Intensities
2. 9.5.2 Extended CIR Intensities
6. 9.6 Numerics
7. Conclusions
4. Chapter 10 CVA Computations for Credit Portfolios in the Common-Shock Model
1. 10.1 Portfolio of CDS
2. 10.2 CDO Tranches
7. Part V Further Developments
1. Chapter 11 Rating Triggers and Credit Migrations
1. 11.1 Introduction
2. 11.2 Credit Value Adjustment and Collateralization under Rating Triggers
3. 11.3 Markov Copula Approach for Rating-Based Pricing
4. 11.4 Applications
2. Chapter 12 A Unified Perspective
1. 12.1 Introduction
2. 12.2 Marked Default Time Reduced-Form Modeling
3. 12.3 Dynamic Gaussian Copula TVA Model
4. 12.4 Dynamic Marshall-Olkin Copula TVA Model
5. Conclusion
8. Part VI Mathematical Appendix
1. Chapter 13 Stochastic Analysis Prerequisites
1. Setup
2. 13.1 Stochastic Integration
3. 13.2 Itô Processes
1. 13.2.1 Finite Variation Jumps
2. 13.2.2 General Case
4. 13.3 Jump-Diffusions
5. 13.4 Feynman-Kac Formula
6. 13.5 Backward Stochastic Differential Equations
7. 13.6 Measure Changes and Random Intensity of Jumps
8. 13.7 Reduction of Filtration and Hazard Intensity Pre-Default Credit Risk Modeling
2. Chapter 14 Markov Consistency and Markov Copulas
1. 14.1 Introduction
2. 14.2 Consistent Markov Processes
3. 14.3 Markov Copulas
4. 14.4 Examples
1. 14.4.1 Diffusions
2. 14.4.2 Jump-Diffusions
3. 14.4.3 Diffusion Modulated Markov Jump Processes.
9. Bibliography