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Volatility and Correlation: The Perfect Hedger and the Fox, 2nd Edition

Volatility and Correlation: The Perfect Hedger and the Fox, 2nd Edition

Riccardo Rebonato

ISBN: 978-1-118-67353-9

Apr 2013

864 pages


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

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

2 Option Replication 31

3 The Building Blocks 75

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

5 Instantaneous and Terminal Correlation 141

II Smiles – Equity and FX 165

6 Pricing Options in the Presence of Smiles 167

7 Empirical Facts About Smiles 201

8 General Features of Smile-Modelling Approaches 237

9 The Input Data: Fitting an Exogenous Smile Surface 249

10 Quadratic Variation and Smiles 293

11 Local-Volatility Models: the Derman-and-Kani Approach 319

12 Extracting the Local Volatility from Option Prices 345

13 Stochastic-Volatility Processes 389

14 Jump–Diffusion Processes 439

15 Variance–Gamma 511

16 Displaced Diffusions and Generalizations 529

17 No-Arbitrage Restrictions on the Dynamics of Smile Surfaces 563

III Interest Rates – Deterministic Volatilities 601

18 Mean Reversion in Interest-Rate Models 603

19 Volatility and Correlation in the LIBOR Market Model 625

20 Calibration Strategies for the LIBOR Market Model 639

21 Specifying the Instantaneous Volatility of Forward Rates 667

22 Specifying the Instantaneous Correlation Among Forward Rates 687

IV Interest Rates – Smiles 701

23 How to Model Interest-Rate Smiles 703

24 (CEV) Processes in the Context of the LMM 729

25 Stochastic-Volatility Extensions of the LMM 751

26 The Dynamics of the Swaption Matrix 765

27 Stochastic-Volatility Extension of the LMM: Two-Regime Instantaneous Volatility 783

Bibliography 805

Index 813