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.
Table of Contents
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
Indifference Valuation Model
Pure Counterparty Risk
Valuation and Hedging
Bilateral Counterparty Risk under Funding Constraints
Martingale Pricing Approach
Reduced-Form BSDE Modeling
A Reduced-Form TVA BSDE Approach to Counterparty Risk under Funding Constraints
Pre-Default BSDE Modeling
The Four Wings of the TVA
Dynamic Copula Models
Dynamic Gaussian Copula Model
Clean Valuation and Hedging of Credit Derivatives
Model of Default Times
Clean Pricing, Calibration and Hedging
CVA Pricing and Hedging
CVA Computations for one CDS in the Common-Shock Model
Common-Shock Model with Deterministic Intensities
Numerical Results with Deterministic Intensities
Common-Shock Model with Stochastic Intensities
CVA Computations for Credit Portfolios in the Common-Shock Model
Portfolio of CDS
Rating Triggers and Credit Migrations
Credit Value Adjustment and Collateralization under Rating Triggers
Markov Copula Approach for Rating-Based Pricing
A Unified Perspective
Marked Default Time Reduced-Form Modeling
Dynamic Gaussian Copula TVA Model
Dynamic Marshall-Olkin Copula TVA Model
Stochastic Analysis Prerequisites
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
Consistent Markov Processes
Stéphane Crépey, Tomasz R. Bielecki, Damiano Brigo
"… a fresh take on mitigation of counterparty risk … [the book] gives a ground-up approach for analysis and managing of risks associated with non-payment of promised cash flows due to the default by a party in an over-the-counter derivative transaction. It should be of value to researchers, graduate students, financial quants, managers in banks, CVA desks, and members of supervisory bodies."
—hedgeweek.com, July 2014
"The landscape of the rates and credit markets has changed so drastically since the 2008 crisis that older textbooks are barely relevant and, from an analytic perspective, appropriate methods have to be rethought from scratch. The present volume is one of the best contributions in this direction, featuring a clear description of the various ‘value adjustments,’ new models for portfolio credit risk, a unified analytic framework based on BSDEs, and detailed treatment of numerical methods."
—Mark Davis, Imperial College London
"Understanding the subtle interconnections between credit and funding is key to a modern valuation of derivatives. This timely contribution, written by world-class academics who are also well-recognized experts in the field, offers a rigorous and comprehensive treatment of the main theories underpinning the new valuation principles. Numerical examples are also provided to help the reader grasp key concepts and ideas of the advanced models and techniques here presented. Overall, an excellent textbook. Brigo’s dialogue is the icing on the cake."
—Fabio Mercurio, Head of Derivatives Research, Bloomberg LP
"A big hooray for this book on CVA, DVA, FVA/LVA, RVA, TVA, and other three letter acronyms (TLA!)."
—Peter Carr, PhD, Managing Director, Morgan Stanley, and Executive Director, NYU Courant Master of Science Program in Mathematics in Finance