Crépey / Bielecki / Brigo Counterparty Risk and Funding

A Tale of Two Puzzles
1. Auflage 2016
ISBN: 978-1-4987-8570-9
Verlag: CRC Press
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 388 Seiten

Reihe: Chapman and Hall/CRC Financial Mathematics Series

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.

Zielgruppe

Financial practitioners including quants and managers; researchers in financial mathematics and financial engineering; graduate students in finance, risk modeling, or applied math.

Autoren/Hrsg.

Crépey, Stéphane

Bielecki, Tomasz R.

Brigo, Damiano

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines

Inhaltsverzeichnis

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 Developments
Pure 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 Perspective
Introduction
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