Interest Rate Derivatives Explained: Volume 1: Products and Markets

By J. Kienitz

Aimed at practitioners who need to understand the current fixed income markets and learn the techniques necessary to master the fundamentals, this book provides a thorough but concise description of fixed income markets, looking at the business, products and structures and advanced modeling of interest rate instruments.

• Language: English
• Publisher: Palgrave Macmillan
• Release date: Dec 5, 2014
• ISBN: 9781137360076

Book preview

Interest Rate Derivatives Explained

Volume 1: Products and Markets

Jörg Kienitz

© Jörg Kienitz 2014

All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission.

No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6–10 Kirby Street, London EC1N 8TS.

Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages.

The author has asserted his right to be identified as the author of this work in accordance with the Copyright, Designs and Patents Act 1988.

First published 2014 by

PALGRAVE MACMILLAN

Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS.

Palgrave Macmillan in the US is a division of St Martin’s Press LLC, 175 Fifth Avenue, New York, NY 10010.

Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world.

Palgrave® and Macmillan® are registered trademarks in the United States, the United Kingdom, Europe and other countries

ISBN: 978–1–137–36006–9

This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin.

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

A catalog record for this book is available from the Library of Congress.

To Amberley, Beatrice and Benoît

Contents

List of Figures

List of Tables

Introduction   Goals of this Book and Global overview

I.1 Introduction and management summary

I.2 Short overview

I.3 Use of the book

I.4 Credits

Part I   Markets and Linear Products

1 Clearing, Collateral, Pricing

1.1 Introduction and objectives

1.2 Netting and collateral

1.3 Clearing

1.3.1 What is central clearing?

1.3.2 Clearing members

1.3.3 Resume

1.4 Counterparty credit risk

1.5 General pricing theory

1.5.1 Numeraire

1.6 Reading list

2 Rates

2.1 Introduction and objectives

2.2 Daycount, rolling and other conventions

2.2.1 Daycount

2.3 Rates

2.3.1 Roll conventions – business dates

2.3.2 Discount factors

2.3.3 Forward rates

2.3.4 Other rates

2.3.5 Interest rate curves

2.4 Reading list

3 Markets and Products – Deposits, Bonds, Futures, Repo

3.1 Introduction and objectives

3.2 Deposits

3.2.1 Market quotes

3.3 Futures

3.4 Bonds

3.4.1 Bond math

3.4.2 Par rate

3.4.3 Yield to maturity

3.4.4 Bond risk measures

3.5 Repos

3.6 Market quotes

3.7 Reading list

4 Markets and Products – FRAs and Swaps

4.1 Introduction and objectives

4.2 FRAs

4.2.1 FRA math

4.2.2 FRA quotes

4.3 Swaps

4.3.1 Fixed against float interest rate swap

4.3.2 Swap quotes

4.3.3 In arrears swaps

4.4 Float against float interest rate swaps

4.4.1 Money market basis swaps

4.4.2 Constant maturity swaps (CMS)

4.4.3 Other type of swaps

4.5 Reading list

5 Using Curves

5.1 Introduction and objectives

5.2 Interpolation methods

5.2.1 Constant interpolation

5.2.2 Linear interpolation

5.2.3 Cubic spline interpolation

5.2.4 Which method to use and how?

5.3 Curve construction

5.3.1 Bootstrapping

5.3.2 Curve construction – optimization

5.4 Risk measures

5.4.1 Risk measures 1D

5.4.2 Risk measures nD

5.4.3 Forward buckets

5.5 Interpolation in two and three dimensions

5.6 Example: cap and floor volatilities

5.7 Reading list

Part II   Markets and Non-Linear Products

6 Options I

6.1 Introduction and objectives

6.2 Market conventions

6.2.1 Black model

6.2.2 Normal model

6.2.3 Displaced diffusion model – shifted black model

6.3 Caps and floors

6.3.1 Cap/Floor math

6.3.2 Cap/Floor quotes

6.4 Swaptions

6.4.1 Swaption math

6.4.2 Swaption quotes

6.4.3 The swaption smile/skew

6.5 Transforming volatility

6.5.1 Transforming caplet volatilities

6.5.2 Transforming swaption volatilities

6.5.3 Examples

6.6 Bond options

6.7 Reading list

7 Options II

7.1 Introduction and objectives

7.2 CMS caps and floors

7.2.1 CMS math

7.2.2 CMS quotes

7.3 CMS spread options

7.3.1 CMS spread option math

7.3.2 CMS spread option quotes

7.4 Reading list

Part III   Counterparty Credit Risk Adjustments

8 Adjustments

8.1 Introduction and objectives

8.2 The credit value adjustment (CVA)

8.3 Bilateral CVA (BCVA) and debit value adjustment (DVA)

8.4 The funding value adjustment (FVA)

8.5 CVA, DVA, FVA – what to do?

8.5.1 Example

8.6 Reading list

Bibliography

Index

List of Figures

List of Tables

Introduction

Goals of this Book and Global Overview

I.1   Introduction and management summary

A: We have written an exposition on interest rates. This comes in two volumes.

R: Hhm!

A: The first volume is on the products, on markets, the infrastructure and curves.

R: Hhm!

A: We consider the new practice after the beginning of the financial crisis! And we do not only write down formulas but we have many examples and explain the stuff from the scratch! This includes many working Excel sheets.

R: Oh, that sounds really interesting to me since I want to get a grip on this stuff. And fast!

A: That is exactly what we provide. You get an overview of how curves are built nowadays and get a nice overview of collateralization and CSA as well as the adjustments CVA, DVA and FVA.

R: So this seems rather practical and ready to use.

A: Exactly, you can also play around with numbers, prices and risk figures since everything is illustrated on accompanying spreadsheets. So, you wish to understand a CMS Cap, just play around and study what happens when you move the curve, flatten the implied volatility, etc...

R: I see. This is why a new book on interest rates has been written!

A: Yes, we know that there are several books on the topic. Some of the most prominent figures in Quantitative Finance have contributed to this subject. But the volumes are very complete and, thus, make up several hundred pages. They have all the very details and the exact math.

R: You mean you guys are not exact?

A: No, no, this is not what I mean. But take the CMS again. If you really want to deeply understand what is going on you have to go through the whole mathematics and apply change-of-measure, calculate expectations, use de-integration formulas, and so forth. We give you the final result and we provide you with a spreadsheet with all the stuff implemented so that you can play around and study the example to get a feeling for what happens. The formulas we provide are (hopefully) exact but we do not give the derivation and explain all the underlying concepts from stochastic analysis.

R: That is nice but if I have built up the intuition and want to dig deeper into the subject...

A: Then, you can consult the reading list at the end of each chapter to find further sources of information.

R: That sounds promising! I am starting now! And this is all covered in a book of 160 pages? That is quite ambitious!

A: Honestly, we give an outline of the current market practice and you can handle a lot of products and learn about the new regulated markets. But, of course, we cannot cover every detail and every convention. But we included references for further reading. Also this volume does not cover volatility modeling or term structure models which are necessary to set up volatility surfaces and price exotic options. This is covered in the second volume of the Interest Rate Explained series. Again, this also gives an overview and you will be quite well prepared if you worked through the book but details about the numerical implementation cannot be handled in an introductory text of less than 200 pages.

I.2   Short overview

The interest rate market has undergone a significant change after the beginning of the crisis in August 2007. Figure I.1 is a road map of the crisis. Several paradigms from the markets were violated after August 2007. Expecially that a big bank cannot go bankrupt. This is reflected for instance in the money market basis spreads, the cross currency basis spread or the ECB rates corridor.

Figure I.1 shows the basis spreads reflecting the fact that standard short term deposit rate is not risk free. In fact credit and liquidity risk are immanent in the rates. The longer the tenor of the rates the higher the risks. The basis, or money market basis to be precise, is the spread of the short term money market rate with respect to the corresponding rate calculated from overnight index quotes. With regard to Figure I.1 we see that in August 2007 when BNP Paribas froze funds, the bankruptcy of Lehman in 2008 as well as the Greek crisis led to significant