Volatility and Correlation

The Perfect Hedger and the Fox
2. Auflage 2004
ISBN: 978-0-470-09139-5
Verlag: Wiley

Buch, Englisch, 864 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1645 g

Reihe: Wiley Finance Series

In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students.

The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options.

The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface.

Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.

Praise for the First Edition:

“In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.… The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.”
—Professor Ian Cooper, London Business School

“Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion…A rare combination of intellectual insight and practical common sense.”
—Anthony Neuberger, London Business School

Autoren/Hrsg.

Rebonato, Riccardo

Fachgebiete

• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Anlagen & Wertpapiere
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensfinanzen
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Unternehmensfinanzierung

Inhaltsverzeichnis

Preface xxi

0.1 Why a Second Edition? xxi

0.2 What This Book Is Not About xxiii

0.3 Structure of the Book xxiv

0.4 The New Subtitle xxiv

Acknowledgements xxvii

I Foundations 1

1 Theory and Practice of Option Modelling 3

1.1 The Role of Models in Derivatives Pricing 3

1.2 The Efficient Market Hypothesis and Why It Matters for Option Pricing 9

1.3 Market Practice 14

1.4 The Calibration Debate 17

1.5 Across-Markets Comparison of Pricing and Modelling Practices 27

1.6 Using Models 30

2 Option Replication 31

2.1 The Bedrock of Option Pricing 31

2.2 The Analytic (PDE) Approach 32

2.3 Binomial Replication 38

2.4 Justifying the Two-State Branching Procedure 65

2.5 The Nature of the Transformation between Measures: Girsanov’s Theorem 69

2.6 Switching Between the PDE, the Expectation and the Binomial Replication Approaches 73

3 The Building Blocks 75

3.1 Introduction and Plan of the Chapter 75

3.2 Definition of Market Terms 75

3.3 Hedging Forward Contracts Using Spot Quantities 77

3.4 Hedging Options: Volatility of Spot and Forward Processes 80

3.5 The Link Between Root-Mean-Squared Volatilities and the Time-Dependence of Volatility 84

3.6 Admissibility of a Series of Root-Mean-Squared Volatilities 85

3.7 Summary of the Definitions So Far 87

3.8 Hedging an Option with a Forward-Setting Strike 89

3.9 Quadratic Variation: First Approach 95

4 Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds 101

4.1 Introduction and Plan of the Chapter 101

4.2 Hedging a Plain-Vanilla Option: General Framework 102

4.3 Hedging Plain-Vanilla Options: Constant Volatility 106

4.4 Hedging Plain-Vanilla Options: Time-Dependent Volatility 116

4.5 Hedging Behaviour In Practice 121

4.6 Robustness of the Black-and-Scholes Model 127

4.7 Is the Total Variance All That Matters? 130

4.8 Hedging Plain-Vanilla Options: Mean-Reverting Real-World Drift 131

4.9 Hedging Plain-Vanilla Options: Finite Re-Hedging Intervals Again 135

5 Instantaneous and Terminal Correlation 141

5.1 Correlation, Co-Integration and Multi-Factor Models 141

5.2 The Stochastic Evolution of Imperfectly Correlated Variables 146

5.3 The Role of Terminal Correlation in the Joint Evolution of Stochastic Variables 151

5.4 Generalizing the Results 162

5.5 Moving Ahead 164

II Smiles – Equity and FX 165

6 Pricing Options in the Presence of Smiles 167

6.1 Plan of the Chapter 167

6.2 Background and Definition of the Smile 168

6.3 Hedging with a Compensated Process: Plain-Vanilla and Binary Options 169

6.4 Hedge Ratios for Plain-Vanilla Options in the Presence of Smiles 173

6.5 Smile Tale 1: ‘Sticky’ Smiles 180

6.6 Smile Tale 2: ‘Floating’ Smiles 182

6.7 When Does Risk Aversion Make a Difference? 184

7 Empirical Facts About Smiles 201

7.1 What is this Chapter About? 201

7.2 Market Information About Smiles 203

7.3 Equities 206

7.4 Interest Rates 222

7.5 FX Rates 227

7.6 Conclusions 235

8 General Features of Smile-Modelling Approaches 237

8.1 Fully-Stochastic-Volatility Models 237

8.2 Local-Volatility (Restricted-Stochastic-Volatility) Models 239

8.3 Jump–Diffusion Models 241

8.4 Variance–Gamma Models 243

8.5 Mixing Processes 243

8.6 Other Approaches 245

8.7 The Importance of the Quadratic Variation (Take 2) 246

9 The Input Data: Fitting an Exogenous Smile Surface 249

9.1 What is This Chapter About? 249

9.2 Analytic Expressions for Calls vs Process Specification 249

9.3 Direct Use of Market Prices: Pros and Cons 250

9.4 Statement of the Problem 251

9.5 Fitting Prices 252

9.6 Fitting

Über Autor(innen)

Riccardo Rebonato is Head of Group Market Risk for the Royal Bank of Scotland Group, and Head of The Royal Bank of Scotland Group Quantitative Research Centre. He is also a Visiting Lecturer at Oxford University for the Mathematical Finance Diploma and MSc. He holds Doctorates in Nuclear Engineering and Science of Materials/Solid State Physics. He sits on the Board of Directors of ISDA and on the Board of Trustees of GARP.
Prior to joining the Royal Bank of Scotland, he was Head of Complex Derivatives Trading Europe and Head of Derivatives Research at Barclays Capital (BZW), where he worked for nine years.
Before that he was a Research Fellow in Physics at Corpus Christi College, Oxford, UK. He is the author of three books, Modern Pricing of Interest-Rate Derivatives, Volatility and Correlation in Option Pricing and Interest-Rate Option Models. He has published several papers on finance in academic journals, and is on the editorial board of several journals. He is a regular speaker at conferences worldwide.