Credit Correlation: Theory and Practice

Description

This book provides an advanced guide to correlation modelling for credit portfolios, providing both theoretical underpinnings and practical implementation guidance. The book picks up where pre-crisis credit books left off, offering guidance for quants on the latest tools and techniques for credit portfolio modelling in the presence of CVA (Credit Value Adjustments). Written at an advanced level, it assumes that readers are familiar with the fundamentals of credit modelling covered, for example, in the market leading books by Schonbucher (2003) and O’Kane (2008). Coverage will include the latest default correlation approaches; correlation modelling in the ‘Marshall-Olkin’ contagion framework, in the context of CVA; numerical implementation; and pricing, calibration and risk challenges. The explosive growth of credit derivatives markets in the early-to-mid 000’s was bought to a close by the 2007 financial crisis, where these instruments were held largely to blame for the economic downturn. However, in the wake of increased regulation across all financial instruments and the challenge of buying and selling bonds in large amounts, credit derivatives have once again been found to be the answer and the market has grown significantly. Written by a practitioner for practitioners, this book will also interest researchers in mathematical finance who want to understand how things happen and work ‘on the floor’. Building the reader’s knowledge from the ground up, and with numerous real life examples used throughout, this book will prove a popular reference for anyone with a mathematical mind interested credit markets. Youssef Elouerkhaoui is a Managing Director and the Global Head of Credit Quantitative Analysis at Citi. His group supports all modelling and product development activities for Credit Markets. This includes: Flow, Correlation, Options and Exotics, CDOs and Emerging Markets. He also supports CVA, Funding and Regulatory Capital for Credit Markets. Prior to this, he was a Director in the Fixed Income Derivatives Quantitative Research Group at UBS, where he was in charge of model development for Structured Credit. Before joining UBS, Youssef was a Quantitative Research Analyst at Credit Lyonnais Supporting the Interest Rates Exotics business. He has also worked as a Senior Consultant in the Risk Analytics and Research Group at Ernst & Young. He is a graduate of Ecole Centrale Paris and he holds a PhD in Mathematics from Paris-Dauphine University. Youssef is author to numerous professional and academic research articles in mathematical finance for both professional and academic journals, contributed to the book ‘Credit Correlation: Life After Copluas’ (Lipton and Rennie) and is a regular speaker at all the major quantitative finance conferences, including Risk’s Quant Europe, ICBI’s Global Derivatives, and WBSs Fixed Income Conference. Front Matter ....Pages i-xxiv Introduction and Context (Youssef Elouerkhaoui)....Pages 1-22 Front Matter ....Pages 23-23 Mathematical Fundamentals (Youssef Elouerkhaoui)....Pages 25-52 Expectations in the Enlarged Filtration (Youssef Elouerkhaoui)....Pages 53-57 Copulas and Conditional Jump Diffusions (Youssef Elouerkhaoui)....Pages 59-93 Front Matter ....Pages 95-95 Correlation Demystified: A General Overview (Youssef Elouerkhaoui)....Pages 97-138 Correlation Skew: A Black-Scholes Approach (Youssef Elouerkhaoui)....Pages 139-149 An Introduction to the Marshall-Olkin Copula (Youssef Elouerkhaoui)....Pages 151-179 Numerical Tools: Basket Expansions (Youssef Elouerkhaoui)....Pages 181-194 Static Replication (Youssef Elouerkhaoui)....Pages 195-202 The Homogeneous Transformation (Youssef Elouerkhaoui)....Pages 203-214 The Asymptotic Homogeneous Expansion (Youssef Elouerkhaoui)....Pages 215-222 The Asymptotic Expansion (Youssef Elouerkhaoui)....Pages 223-229 CDO-Squared: Correlation of Correlation (Youssef Elouerkhaoui)....Pages 231-260 Second Generation Models: From Flat to Correlation Skew (Youssef Elouerkhaoui)....Pages 261-283 Third Generation Models: From Static to Dynamic Models (Youssef Elouerkhaoui)....Pages 285-314 Front Matter ....Pages 315-315 Pricing Path-Dependent Credit Products (Youssef Elouerkhaoui)....Pages 317-339 Hedging in Incomplete Markets (Youssef Elouerkhaoui)....Pages 341-362 Min-Variance Hedging with Carry (Youssef Elouerkhaoui)....Pages 363-379 Correlation Calibration with Stochastic Recovery (Youssef Elouerkhaoui)....Pages 381-409 Front Matter ....Pages 411-411 New Frontiers in Credit Modelling: The CVA Challenge (Youssef Elouerkhaoui)....Pages 413-446 Back Matter ....Pages 447-456