One of the key features of the first and second editions of this book was the accompanying spreadsheets that were prepared to allow the reader to gain some simple insight into some of the quantitative aspects discussed. Many of these examples have been used for training courses and have therefore evolved to be quite intuitive and user-friendly. The spreadsheets can be downloaded freely from Jon Gregory's website, www.cvacentral.com, under the counterparty risk section. New examples may be added over time.

Spreadsheet 4.1  LCR example.

Spreadsheet 4.2  NSFR example.

Spreadsheet 6.1  Compression example.

Spreadsheet 7.1  Margin calculation including thresholds and initial margins.

Spreadsheet 9.1  Initial margin calculation of an interest rate swap using historical simulation.

Spreadsheet 9.2  Example ISDA SIMM™ calculations.

Spreadsheet 10.1  Illustration of Auction Incentive Pool (AIP) calculation.

Spreadsheet 10.2  Illustration of variation margin gains haircutting (VMGH) and selective tear-up approaches to loss allocation.

Spreadsheet 11.1  Simple exposure metric calculation.

Spreadsheet 11.2  EPE and PFE for a normal distribution.

Spreadsheet 11.3  Simple example of a cross-currency swap profile.

Spreadsheet 11.4  Simple calculation of the exposure of a CDS.

Spreadsheet 11.5  Simple two transaction example of netting effects.

Spreadsheet 11.6  Impact of variation and initial margin on exposure and funding.

Spreadsheet 12.1  Calculating risk-neutral default probabilities.

Spreadsheet 12.2  Example cross-sectional methodology for credit spreads.

Spreadsheet 13.1  Implementation of SA-CCR.

Spreadsheet 13.2  Calculation of ‘alpha’ factor.

Spreadsheet 13.3  EPE and EEPE example.

Spreadsheet 13.4  Comparison of capital costs across different methodologies.

Spreadsheet 15.1  Semianalytical calculation of the exposure for a swap.

Spreadsheet 15.2  Example marginal exposure calculation.

Spreadsheet 15.3  Simple simulation of an interest rate swap exposure.

Spreadsheet 15.4  Simple margin simulation based on portfolio value.

Spreadsheet 15.5  One-factor Hull-White model for exposure for interest rate products.

Spreadsheet 15.6  Illustration of the impact of netting.

Spreadsheet 15.7  Marginal EPEs.

Spreadsheet 15.8  Notional resetting cross-currency swap.

Spreadsheet 15.9  Quantifying the impact of margin on exposure.

Spreadsheet 16.1  ColVA calculation.

Spreadsheet 17.1  Direct CVA calculation for an interest rate swap.

Spreadsheet 17.2  Path-wise CVA calculation for an interest rate swap.

Spreadsheet 17.3  CVA and DVA calculations.

Spreadsheet 17.4  Incremental CVA and DVA calculations.

Spreadsheet 17.5  Marginal CVA and DVA calculations.

Spreadsheet 17.6  Simple wrong-way risk example.

Spreadsheet 17.7  Direct simulation of wrong-way risk for an interest rate swap.

Spreadsheet 17.8  Exposure distribution using a Gaussian copula approach.

Spreadsheet 18.1  Symmetric FVA calculation compared to discounting approach.

Spreadsheet 18.2  Asymmetric FVA calculation.

Spreadsheet 18.3  FVA Allocation.

Spreadsheet 19.1  KVA calculation for interest rate swap.

The following is a list of Appendices that contain additional mathematical detail. These Appendices can be downloaded freely from www.cvacentral.com.

Appendix 7A Exposure and time period scaling

Appendix 11A Exposure metrics for a normal distribution

Appendix 11B Forward and swap exposure profiles

Appendix 11C Approximate cross-currency profile

Appendix 11D Simple aggregation example for a normal distribution

Appendix 12A Risk-neutral default probability calculation

Appendix 13A Large homogenous pool approximation for credit losses

Appendix 13B Standardised CVA capital formula

Appendix 15A Swaption analogy and the EPE of an interest rate swap

Appendix 15B Marginal EPE

Appendix 15C Collateralised EPE approx.

Appendix 15D Simple initial margin calculation

Appendix 16A ColVA formula

Appendix 17A CVA formula derivation

Appendix 17B CVA as a running spread

Appendix 17C CVA approx. via EPE

Appendix 17D Bilateral CVA formula (CVA and DVA)

Appendix 17E Incremental CVA

Appendix 17F Wrong-way risk and CVA

Appendix 17G CVA for a CDS contract

Appendix 18A FVA formula and discounting

Appendix 19A KVA calculation

Appendix 21A Beta hedging

The first edition of this book was published about a decade ago in the aftermath of a global financial crisis and focused on the importance of counterparty credit. Since then, the area of counterparty credit risk has broadened to consider the importance of related aspects such as collateral, funding, capital, and initial margin. This area has continued to see rapid change due to regulation, accounting standards, and evolving market practice. As previously, this is much more than a new edition because most of the content has been rewritten and expanded significantly.

I hope this book can be used as a comprehensive and relatively non-mathematical reference for the subject we now generally refer to as xVA. There are other mathematical books on this subject and the book by Andrew Green (Green 2015) is recommended as a comprehensive quantitative guide to the subject.

As with previous editions, I have saved space by putting mathematical appendices together with accompanying spreadsheets on my personal website at www.cvacentral.com. Since many do not study this material in depth, this has proved to be a reasonable compromise for most readers. There is also a list of errata that can be found on this website.

I have also made use of numerous survey results and I am grateful to Solum Financial and Deloitte for allowing me to reproduce these. I am also grateful to IBM and IHS Markit who have provided calculation examples in previous editions, some of which are used here. These will all be mentioned in the text.

Finally, I would like to thank the following people for feedback on this and earlier editions of the book: Manuel Ballester, Teimuraz Barbakadze, Ronnie Barnes, Raymond Cheng, Vladimir Cheremisin, Michael Clayton, Andrew Cooke, Christian Crispoldi, Daniel Dickler, Wei-Ming Feng, Julia Fernald, Leonard Fichte, Piero Foscari, Teddy Fredaigues, Sayoko Fujisawa, Naoyuki Fujita, Shota Fukamizu, Dimitrios Giannoulis, Glen Gibson, Sergej Goriatchev, Arthur Guerin, Kazuhisa Hirota, Kale Kakhiani, Toshiyuki Kitano, Henry Kwon, Edvin Lundstrom, David Mengle, Richard Morrin, Ivan Pomarico, Yufi Pak, Hans-Werner Pfaff, Francesco Ivan Pomarico, Erik van Raaij, Kei Sagami, Guilherme Sanches, Neil Schofield, Andreas Schwaderlapp, Florent Serre, Masum Shaikh, Ana Sousa, Salvatore Stefanelli, Richard Stratford, Carlos Sterling, Norikazu Takei, Hidetoshi Tanimura, Todd Tauzer, Satoshi Terakado, Nick Vause, Frederic Vrins, Nana Yamada, and Valter Yoshida.

Jon Gregory
December 2019

Jon Gregory is an independent expert specialising in counterparty risk and xVA related projects. He has worked on many aspects of credit risk and derivatives in his career, being previously with Barclays Capital, BNP Paribas, and Citigroup. He is a senior advisor for Solum Financial Derivatives Advisory. He is also a faculty member for London Financial Studies and the Certificate of Quantitative Finance. He currently serves on the Academic Advisory Board of IHS Markit and is a Managing Editor of the journal Quantitative Finance.

Jon has a PhD from Cambridge University.

In 2007, a global financial crisis (GFC) started which eventually became more severe and long-lasting than could have ever been anticipated. Along the way, there were major casualties such as the bankruptcy of the investment bank Lehman Brothers. Governments around the world had to bailout other financial institutions such as American International Group (AIG) in the US and the Royal Bank of Scotland in the UK.

The GFC caused a major focus on counterparty credit risk (CCR) which is the credit risk in relation to derivative products. A derivative trade is a contractual relationship that may be in force from a few days to several decades. During the lifetime of the contract, the two counterparties have claims against each other such as in the form of cash flows that evolve as a function of underlying assets and market conditions. Derivatives transactions create CCR due to the risk of insolvency of one party. This CCR in turn creates systemic risk due to derivatives trading volume being dominated by a relatively small number of large derivatives counterparties (‘dealers’) that are then key nodes of the financial system.

Post-GFC, participants in the derivatives market became more aware of CCR and its quantification via credit value adjustment (CVA). They also started to create more value adjustments, or xVAs, in order to quantify other costs such as funding, collateral, and capital. Derivatives pricing used to be focused on so-called ‘exotics’ with the majority of simple or vanilla derivatives thought to be relatively straightforward to deal with. However, the birth of xVA has changed this and even the most simple derivatives may have complex pricing and valuation issues arising from xVA.

Regulation has also enhanced the need to consider xVA (or XVA). Increasing capital requirements, constraints on funding, liquidity, and leverage together with a clearing mandate and bilateral margin requirements all make derivatives trading more expensive and complex. However, derivatives are still fundamentally important: for example, without them end users would have to use less effective hedges, which would create income statement volatility. The International Swaps and Derivatives Association (ISDA 2014b) reports that 85% of end users said that derivatives were very important or important to their risk management strategy and 79% said they planned to increase or maintain their use of over-the-counter (OTC) derivatives.

Chapters 25Chapters 610Chapters 1115Chapters 1620Chapter 21

The online Appendices and Spreadsheets provide more detail on various xVA calculations. This book is a relatively non-mathematical treatment of xVA. For a more mathematically-rigorous text for quantitative researchers, Andrew Green's book (Green 2015) is strongly recommended.