ding and Capital Valuation Adjustments
XVA: Credit, Funding and Capital Valuation Adjustments
ANDREW GREEN
This edition first published 2016
© 2016 John Wiley & Sons Ltd
Registered office
John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.
Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.
Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with the respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
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
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.
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
