Volatility and Correlation

The Perfect Hedger and the Fox

By: Riccardo Rebonato

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Product code: 20143
ISBN: 0470091398
864 pages
Format: Hb
Published by: John Wiley & Sons, 2004, 2nd edition

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Volatility and Correlation - front page cover image

Description of Volatility and Correlation

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.

Volatility and Correlation - Chapter headings

Why a Second Edition
What This Book Is Not About
The New Sub-Title

I: Foundations

1. Theory and Practice of Option Modelling
2. Option Replication
3. The Building Blocks
4. Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds
5. Instantaneous and Terminal Correlation

II: Smiles - Equity and FX

6. Pricing Options in the Presence of Smiles
7. Empirical Facts about Smiles
8. General Features of Smile-Modelling Approaches
9. The Input Data: Fitting an Exogenous Smile Surface
10. Quadratic Variation and Smiles
11. Local-Volatility Models: the Derman-and-Kani Approach
12. Extracting the Local Volatility from Option Prices
13. Stochastic-Volatility Processes
14. Jump-Diffusion Processes
15. Variance-Gamma
16 Displaced Diffusions and Generalizations
17 No-Arbitrage Restrictions on the Dynamics of Smile Surfaces

III: Interest Rates - Deterministic Volatilities

18. Mean Reversion in Interest-Rate Models
19. Volatility and Correlation in the LIBOR Market Model
20. Calibration Strategies for the LIBOR Market Model
21. Specifying the Instantaneous Volatility of Forward Rates
22. Specifying the Instantaneous Correlation Among Forward Rates

IV:Interest Rates - Smiles

23. How To Model Interest-Rate Smiles
24. Constant-Elasticity-of-Variance (CEV) Processes in the Context of the LMM
25. Stochastic-Volatility Extensions of the LIBOR Market Model
26. The Dynamics of the Swaption Matrix
27. Stochastic-Volatility Extension of the LMM: Two-Regime Instantaneous Volatility

Authobiography of Riccardo Rebonato

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.