The Volatility Surface: A Practitioner's Guide (Wiley Finance)

✍ Scribed by Jim Gatheral, Nassim Nicholas Taleb

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

✦ Synopsis

A good book for its wide view of all the topics linked to the volatility trading : stochastic volatility and jumps with a quite rare study of the impact of stochastic vol over the pricing of most commons exotic products like cliquets, lookback etc... The main problem of this book are :1/ the incredible numbers of errors and typos in the proofs (typos for the two first chapters has been published by the author on the website of the Imperial College where Mr Gatheral has given lessons) 2/ the fact it's not so useful as the link between dividends and vol stochastic isn't treated at all.3/ Most of the interesting theoretical exposee are clearly uncomplete and needs further investigation. But as the author try to do a wide tour of the subject in a rather limited number of pages, this is not surprising.4/ This isn't explicit but this is of a weaker interest for stochastic volatility of underlyings other than Equities, index and funds...So finally, it's a good tour on the subject but for a lot of subjects it look likes a summary. Others books are needed. mainly the Alan Lewis book for Fourier transform's methods of pricing, the Cont/tankov on the Jumps process (see my review of this one) and the Alireza Javaheri's one for a more deeper work on THE calibration problem of stochastic volatility.

✦ 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