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

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