XVA. Green Andrew

ding and Capital Valuation Adjustments

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      XVA: Credit, Funding and Capital Valuation Adjustments

      ANDREW GREEN

      This edition first published 2016

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      Library of Congress Cataloging-in-Publication Data

      Green, Andrew,

      XVA: credit, funding and capital valuation adjustments / Andrew Green.

      pages cm. – (The wiley finance series)

      Includes bibliographical references and index.

      ISBN 978-1-118-55678-8 (hardback) – ISBN 978-1-118-55675-7 (ebk) – ISBN 978-1-118-55676-4 (ebk) – ISBN 978-1-119-16123-3 (ebk) 1. Finance. 2. Derivative securities. I. Title.

      HG173.G744 2015

      332.64′57–dc23

      2015019353

      A catalogue record for this book is available from the British Library.

      ISBN 978-1-118-55678-8 (hardback) ISBN 978-1-118-55675-7 (ebk)

      ISBN 978-1-118-55676-4 (ebk) ISBN 978-1-119-16123-3 (obk)

      Cover Design: Wiley

      Cover Image: ©iStock/Tuomas Kujansuu

For Simone

      Acknowledgements

      I would like to thank both Dr Chris Dennis and Dr Chris Kenyon for kindly agreeing to review this book prior to publication and for their work on a number of research topics that are contained within this book. Any errors or omissions are my own, however.

      I would also like to thank the many colleagues and peers from both market and academia with whom I have had useful discussions on quantitative finance over many years. This includes colleagues from my current and past employers but also includes a great many others.

      I owe a debt of gratitude to my many teachers over a number of years, but perhaps most of all to my DPhil supervisor, Professor James Binney, whose own publications inspired me ultimately to write my own book.

      Finally I would like to thank friends and family for putting up with my absence during the writing process.

      CHAPTER 1

      Introduction: The Valuation of Derivative Portfolios

      Price is what you pay. Value is what you get.

– Warren BuffettAmerican business magnate, investor and philanthropist (1930–)

      1.1 What this book is about

      This book is about XVA or Valuation Adjustments, the valuation of the credit, funding and regulatory capital requirements embedded in derivative contracts. It introduces Credit Valuation Adjustment (CVA) and Debit Valuation Adjustment (DVA) to account for credit risk, Funding Valuation Adjustment (FVA) for the impact of funding costs including Margin Valuation Adjustment (MVA) for the funding cost associated with initial margin, Capital Valuation Adjustment (KVA) for the impact of Regulatory Capital and Tax Valuation Adjustment (TVA) for the impact of taxation on profits and losses. The book provides detailed descriptions of models to calculate the valuation adjustments and the technical infrastructure required to calculate them efficiently. However, more fundamentally this book is about the valuation and pricing of derivative contracts. The reality is that credit, funding and capital concerns are very far from minor adjustments to the value of a single derivative contract or portfolio of derivatives. The treatment of CVA, DVA, FVA, MVA, KVA and TVA as adjustments reflects the historical development of derivative models and typical bank organisational design rather than the economic reality that places credit, funding and capital costs at the centre of accurate pricing and valuation of derivatives.

      Since the seminal papers by Fischer Black and Myron Scholes and Robert C. Merton published in 1973, derivative pricing and valuation has been centred in the Black-Scholes-Merton framework complete with its simplifying assumptions:

      • Arbitrage opportunities do not exist.

      • Any amount of money can be borrowed or lent at the risk-free rate which is constant and accrues continuously in time.

      • Any amount of stock can be bought or sold including short selling with no restrictions.

      • There are no transaction taxes or margin requirements.

      • The underlying asset pays no dividend.

      • The asset price is a continuous function with no jumps.

      • The underlying asset has a constant volatility.

      • Neither counterparty to the transaction is at risk of default.

      • The market is complete, that is there are no unhedgeable risks.

      It could also be argued that there are additional implicit assumptions underlying the Black-Scholes-Merton framework:

      • No capital requirement or costs associated with regulatory requirements such as liquidity buffers

      • No price impact of trading

      • The Modigliani-Millar theorem on the separation of funding and investment decisions applies to derivatives (Modigliani and Miller, 1958).

      However, even in the mid-1970s it was clear that these assumptions were there to simplify the problem of option pricing and were not a reflection of reality. Subsequently, a number of authors sought to relax these assumptions:

      • Constant interest rates – Merton (1973)

      • No dividends – Merton (1973)

      • No transaction costs – Ingersoll (1976)

      •