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Volatility and Correlation. The Perfect Hedger and the Fox. 2nd Edition. The Wiley Finance Series

  • ID: 2216677
  • Book
  • 864 Pages
  • John Wiley and Sons Ltd
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The new edition of
Volatility and Correlation has been thoroughly updated and expanded with over 80% new or reworked material, reflecting the changes and developments that have taken place in the field. The new and updated material includes: empirical and theoretical analysis of the smile dynamics; examination of the perfect–replication model in relation to exotic options; treatment of additional important models, namely, Variance Gamma, displaced diffusion, CEV, stochastic volatility for interest–rate smiles and equity/FX options; questioning of the informational efficiency of markets in commonly–used calibration and hedging practices.

The book is split into four sections. Part I deals with a deterministic–volatility Black world (no smiles), and sets out the author′s ′philosophical′ approach to option pricing. Part II deals with smiles in the equity and FX worlds. Beginning with a review of relevant empirical information about smiles, this part 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 process–based model, and can directly prescribe the dynamics of the smile surface. Part III focuses on interest rates, and part IV extends the setting used for the deterministic–volatility LIBOR market model in order to account for interest–rate smiles in a financially–motivated and computationally–tractable manner. In this final part the author deals, in increasing levels of complexity, with CEV processes, with diffusive stochastic volatility and with Markov–chain processes.

Covering FX, equity and interest–rate products, Volatility and Correlation is a blend of theoretical and practical material and is designed for traders, risk managers, financial professionals and students.

The second edition is even more comprehensive than the first, and ideally suited to quantitatively oriented traders and risk managers. Rebonato has a knack for distilling the essence from a wide range of complex option pricing models. Darrell Duffie, Stanford University, USA

The author has greatly extended the first edition of this book, whose main merit remains its courage to deal with relevant issues for practitioners. Rather than concentrating on fictional problems stemming from the need to give financial ground to one s favourite theories, the author moves from problems posed by the market. At times a colloquial stance is privileged over mathematical rigor and formalism, allowing a larger public to benefit from this book. Damiano Brigo, Head of Credit Models, Banca IMI, author of Interest Rate Models: Theory and Practice.

This book is about equity, FX and interest–rate option pricing at its best. It combines rigorous theory with practical knowledge of markets and models. Riccardo Rebonato uses his technical mastery to make the theory clear, and his wealth of experience to give insights into applications. Whatever your level of knowledge of these markets, you will learn from him. Ian Cooper, Professor of Finance, London Business School

In this book, Riccardo Rebonato discloses his invaluable expertise, shedding light over the gloomy path of modern model selection for pricing and hedging derivatives. Both practitioners and academics will benefit from his teachings and advice. Fabio Mercurio, Head of Financial Models, Banca IMI, Milan, Italy

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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

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Riccardo Rebonato
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