Counterparty Risk and Funding A Tale of Two Puzzles

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.

Financial Landscape A Galilean Dialogue on Counterparty Risk, CVA, DVA, Multiple Curves, Collateral, and Funding To the Discerning Reader The First Day The Second Day The Third Day The Fourth Day The Whys of the LOIS Financial Setup Indifference Valuation Model LOIS Formula Numerical Study Model-Free DevelopmentsPure Counterparty Risk Cash Flows Valuation and Hedging CSA Specifications Bilateral Counterparty Risk under Funding Constraints Introduction Market Model Trading Strategies Martingale Pricing Approach TVA Example Reduced-Form BSDE Modeling A Reduced-Form TVA BSDE Approach to Counterparty Risk under Funding Constraints Introduction Pre-Default BSDE Modeling Markov Case The Four Wings of the TVA Introduction TVA Representations CSA Specifications Clean Valuations TVA Computations Dynamic Copula Models Dynamic Gaussian Copula Model Introduction Model Clean Valuation and Hedging of Credit Derivatives Counterparty Risk Common-Shock Model Introduction Model of Default Times Clean Pricing, Calibration and Hedging Numerical Results CVA Pricing and Hedging CVA Computations for one CDS in the Common-Shock Model Introduction Generalities Common-Shock Model with Deterministic Intensities Numerical Results with Deterministic Intensities Common-Shock Model with Stochastic Intensities Numerics CVA Computations for Credit Portfolios in the Common-Shock Model Portfolio of CDS CDO Tranches Further Developments Rating Triggers and Credit Migrations Introduction Credit Value Adjustment and Collateralization under Rating Triggers Markov Copula Approach for Rating-Based Pricing Applications A Unified PerspectiveIntroduction Marked Default Time Reduced-Form Modeling Dynamic Gaussian Copula TVA Model Dynamic Marshall-Olkin Copula TVA Model Mathematical Appendix Stochastic Analysis Prerequisites Stochastic Integration Itô Processes Jump-Diffusions Feynman-Kac Formula Backward Stochastic Differential Equations Measure Changes and Random Intensity of Jumps Reduction of Filtration and Hazard Intensity Pre-Default Credit Risk Modeling Markov Consistency and Markov Copulas Introduction Consistent Markov Processes Markov Copulas Examples Index

Stéphane Crépey, Tomasz R. Bielecki, Damiano Brigo