The volatility surface: A practitioner's guide

✍ Scribed by Jim Gatheral, Nassim Nicholas Taleb

• Publisher: Wiley
• Year: 2006
• Tongue: English
• Leaves: 210
• Series: Wiley Finance
• Category: Library

✦ Synopsis

Praise for The Volatility Surface "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP

✦ Table of Contents

The Volatility Surface: A Practitioner's Guide......Page 6
Contents......Page 10
Figures......Page 16
Tables......Page 22
Foreword......Page 24
Preface......Page 26
HOW THIS BOOK IS ORGANIZED......Page 28
Acknowledgments......Page 30
STOCHASTIC VOLATILITY......Page 32
LOCAL VOLATILITY......Page 38
THE PROCESS......Page 46
THE HESTON SOLUTION FOR EUROPEAN OPTIONS......Page 47
DERIVATION OF THE HESTON CHARACTERISTIC FUNCTION......Page 51
SIMULATION OF THE HESTON PROCESS......Page 52
GETTING IMPLIED VOLATILITY FROM LOCAL VOLATILITIES......Page 56
LOCAL VOLATILITY IN THE HESTON MODEL......Page 62
IMPLIED VOLATILITY IN THE HESTON MODEL......Page 64
THE SPX IMPLIED VOLATILITY SURFACE......Page 67
LOCAL VARIANCE IN THE HESTON-NANDI MODEL......Page 74
A NUMERICAL EXAMPLE......Page 75
DISCUSSION OF RESULTS......Page 80
WHY JUMPS ARE NEEDED......Page 81
JUMP DIFFUSION......Page 83
CHARACTERISTIC FUNCTION METHODS......Page 87
STOCHASTIC VOLATILITY PLUS JUMPS......Page 96
MERTON’S MODEL OF DEFAULT......Page 105
CAPITAL STRUCTURE ARBITRAGE......Page 108
LOCAL AND IMPLIED VOLATILITY IN THE JUMP-TO-RUIN MODEL......Page 110
THE EFFECT OF DEFAULT RISK ON OPTION PRICES......Page 113
THE CREDITGRADES MODEL......Page 115
SHORT EXPIRATIONS......Page 118
THE MEDVEDEV-SCAILLET RESULT......Page 120
INCLUDING JUMPS......Page 124
LONG EXPIRATIONS: FOUQUE, PAPANICOLAOU, AND SIRCAR......Page 126
SMALL VOLATILITY OF VOLATILITY: LEWIS......Page 127
EXTREME STRIKES: ROGER LEE......Page 128
ASYMPTOTICS IN SUMMARY......Page 131
DYNAMICS OF THE VOLATILITY SKEW UNDER STOCHASTIC VOLATILITY......Page 132
DYNAMICS OF THE VOLATILITY SKEW UNDER LOCAL VOLATILITY......Page 133
DIGITAL OPTIONS AND DIGITAL CLIQUETS......Page 134
DEFINITIONS......Page 138
LIMITING CASES......Page 139
THE REFLECTION PRINCIPLE......Page 140
THE LOOKBACK HEDGING ARGUMENT......Page 143
PUT-CALL SYMMETRY......Page 144
QUASISTATIC HEDGING AND QUALITATIVE VALUATION......Page 145
ADJUSTING FOR DISCRETE MONITORING......Page 148
SOME APPLICATIONS OF BARRIER OPTIONS......Page 151
CONCLUSION......Page 152
LOCALLY CAPPED GLOBALLY FLOORED CLIQUET......Page 153
REVERSE CLIQUET......Page 156
NAPOLEON......Page 158
SPANNING GENERALIZED EUROPEAN PAYOFFS......Page 164
VARIANCE AND VOLATILITY SWAPS......Page 167
VALUING VOLATILITY DERIVATIVES......Page 177
LISTED QUADRATIC-VARIATION BASED SECURITIES......Page 187
SUMMARY......Page 192
Postscript......Page 193
Bibliography......Page 194
Index......Page 200