Modern Derivatives Pricing and Credit Exposure Analysis

This book provides a comprehensive guide for modern derivatives pricing and credit analysis. Written to provide sound theoretical detail but practical implication, it provides readers with everything they need to know to price modern financial derivatives and analyze the credit exposure of a financial instrument in today's markets.

'The authors are established practitioners with many years of quant development and implementation experience in leading financial institutions. This is well reflected in the present book, rich with useful examples and covering highly relevant topics such as (among many others) real world RFE models and backtesting, normally left out by the main-stream financial literature.'

-Fabrizio Anfuso, Head of Collateralized Exposure Modelling, Credit Suisse; Visiting Lecturer, ETH Zurich and Bocconi University Milan

"The authors have achieved a matchless combination of theoretical and most importantly, practical expertise to this book. The work is complete, insightful and exact and is suitable for all professionals dealing with XVA expert and novice alike."

-Jörg Kienitz, Director and Co-Lead Quant Unit and Adjunct Associate Professor University of Cape Town

'Modern Derivatives Pricing and Credit Exposure Analysis by Lichters, Stamm and Gallagher (with whom I have collaborated) has unique strengths. There are three chapters developing discounting from a CCP point of view, a global view and a CSA-based view. There is a fully worked out multi-asset framework based on the Linear Gaussian Model (LGM) with particular depth on inflation with both Jarrow-Yildrim and Dodgson-Kainth models. It provides a forensically detailed analysis of credit processes, mapping their limitations and highlights directions that avoid them (developed in detail from thePeng-Kou approach). The XVA coverage starts with CVA/DVA and is followed by separate chapters on FVA and KVA. The usual limitations for such a comprehensive book are present, e.g. limited treatment of smile modelling in a multi-curve setup (worth a book by itself), and limited coverage of the trade-offs in XVA between the costs of hedging risks and the (capital and modelling) costs of open risks (often forced by credit market limitations). Overall, this is a thorough and practical introduction to modern derivatives pricing."

-Chris Kenyon, front office quant; author of 10 papers in the Cutting Edge section in Risk

Autorentext
Roland Lichters has headed bank Risk and IT departments building teams, processes, pricing/risk methodologies and systems. As founding Partner of Quaternion Risk Management, responsible for R&D, he focusses besides his consulting and advisory work on the company's QuantLib-based pricing and risk analytics products, implementing the methods covered in this book. Roland holds a PhD and Diploma in Physics and lectures part-time in Financial Engineering at Trinity College Dublin.

Roland Stamm held senior positions in a number of banks' IT and Risk Management departments before joining Quaternion Risk Management as a Partner. In his banking work, he focused on market and credit risk methodology as well as the pricing and risk management of complex financial products. Roland holds a PhD in Mathematics and is co-author of the book Discounting, LIBOR, CVA and Funding (with Chris Kenyon) as well as a part-time lecturer.

Donal Gallagher is a founding Partner and Managing Director of Quaternion Risk Management and advises CFOs and CROs on the transparent pricing, risk and capital management of complex financial instruments. His research interests include default models and portfolio credit products. Donal holds a PhD from the California Institute of Technology in Applied Mathematics and lectures part time in Financial Engineering at Trinity College Dublin.

Inhalt

Contents
Preface
Acknowledgments
PART I: DISCOUNTING

1. Discounting Before the Crisis
   1.1 The Risk-Free Rate
   1.2 Pricing Linear Instruments
   1.2.1 Forward Rate Agreements
   1.2.2 Interest Rate Swaps
   1.2.3 FX Forwards
   1.2.4 Tenor Basis Swaps
   1.2.5 Cross-Currency Basis Swaps
   1.3 Curve Building
   1.4 Pricing Non-Linear Instruments
   1.4.1 Caps and Floors
   1.4.2 Swaptions
   2 What ChangedWith the Crisis
   2.1 Basis Products and Spreads
   2.1.1 Tenor Basis Swaps
   2.1.2 Cross-Currency Basis Swaps
   2.2 Collateralization
   3 Clearing House Pricing
   3.1 Introduction of Central Counterparties
   3.2 Margin Requirements
   3.3 Building the OIS Curve
   3.4 USD Specialties
   3.5 Building the Forward Projection Curves
   3.6 More USD Specialties
   3.7 Example: Implying the Par Asset Swap Spread
   3.8 Interpolation
   3.9 Pricing Non-Linear Instruments
   3.9.1 European Swaptions
   3.9.2 Bermudan Swaptions
   3.10 Not All Currencies Are Equal
   4 Global Discounting
   4.1 Collateralization In a Foreign Currency
   4.2 Non-Rebalancing Cross-Currency Swaps
   4.3 Rebalancing Cross-Currency Swaps
   4.4 Examples: Approximations of Basis Spreads
   4.4.1 Tenor Basis Spreads
   4.4.2 Flat Cross-Currency Swaps
   4.4.3 OIS Cross-Currency Basis Spread
   4.4.4 LIBOR Cross-Currency Basis Spread
   5 CSA Discounting
   5.1 ISDA Agreements and CSA Complexities
   5.2 Currency Options
   5.3 Negative Overnight Rates
   5.4 Other Assets as Collateral
   5.5 Thresholds and Asymmetries
   5.6 Some Thoughts on Initial Margin
   6 Fair Value Hedge Accounting
   6.1 Introduction
   6.2 Hedge Effectiveness
   6.3 Single-Curve Valuation
   6.4 Multi-Curve Valuation
   PART II: CREDIT AND DEBIT VALUE ADJUSTMENT
   7 Introduction
   8 Fundamentals
   8.1 Unilateral CVA
   8.2 Bilateral CVA
   9 Single Trade CVA
   9.1 Interest Rate Swap
   9.1.1 Exercise within interest periods
   9.1.2 Amortizing Swap
   9.1.3 A Simple Swap CVA Model
   9.2 Cash-Settled European Options
   9.3 FX Forward
   9.4 Cross-Currency Swap
   9.5 Rebalancing Cross-Currency Swap
   PART III: RISK FACTOR EVOLUTION
   10 A Monte Carlo Framework
   11 Interest Rates
   11.1 Linear Gauss Markov Model
   11.1.1 Multiple Curves
   11.1.2 Invariances
   11.1.3 Relation to the Hull-White model in T-Forward Measure
   11.2 Products
   11.2.1 Zero Bond Option
   11.2.2 European Swaption
   11.2.3 Bermudan Swaption with Deterministic Basis
   11.2.4 Stochastic Basis
   11.3 CSA Discounting Revisited
   11.4 Exposure Evolution Examples
   12 Foreign Exchange
   12.1 Cross-Currency LGM
   12.2 Multi-Currency LGM
   12.3 Calibration
   12.3.1 Interest Rate Processes
   12.3.2 FX Processes
   12.3.3 Correlations
   12.4 Cross-Currency Basis
   12.5 Exposure Evolution Examples
   13 Inflation
   13.1 Products
   13.2 Jarrow-Yildirim Model
   13.2.1 Calibration
   13.2.2 Foreign Currency Inflation
   13.3 Dodgson-Kainth Model
   13.3.1 Calibration
   13.3.2 Foreign Currency Inflation
   13.4 Seasonality
   13.5 Exposure Evolution Examples
   14 Equity and Commodity
   14.1 Equity
   14.2 Commodity
   15 Credit
   15.1 Market
   15.2 Gaussian Model
   15.2.1 Conclusion
   15.3 Cox-Ingersoll-Ross Model
   15.3.1 CIR without Jumps
   15.3.2 Relaxed Feller Constraint
   15.3.3 CDS Spread Distribution
   15.3.4 CIR with Jumps: JCIR
   15.3.5 JCIR Extension
   15.3.6 Examples: CDS CVA and Wrong-Way Risk
   15.3.7 Conclusion
   15.4 Black-Karasinski Model
   15.5 Peng-Kou Model
   15.5.1 Review CDS and CDS Option
   15.5.2 Compound Poisson Process
   15.5.3 Compound Polya Process
   15.5.4 Examples
   15.5.5 Conclusion
   PART IV: XVA 251
   16 Cross-Asset Scenario Generation
   16.1 Expectations and Covariances
   16.2 Path Generation
   16.3 Pseudo Random vs Low Discrepancy Sequences
   16.4 Long-Term Interest Rate Simulation
   17 Netting and Collateral
   17.1 Netting
   17.1.1 Non-netted Counterparty Exposures
   17.1.2 Netting Set Exposures
   17.1.3 Generalized Counterparty Exposures
   17.2 Collateralization
   17.2.1 Collateralized Netting Set Exposure
   17.2.2 CSA Margining
   17.2.3 Margin Settlement
   17.2.4 Interest Accrual
   17.2.5 FX Risk
   17.2.6 Collateral Choice
   18 Early Exercise and American Monte Carlo
   18.1 …