Volatility Surface A Practitioner's Guide

ISBN-10: 0471792519

ISBN-13: 9780471792512

Edition: 2006

List price: $70.00 Buy it from $32.09
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Description:

A detailed look at the volatility surface The volatility surface, formed from implied volatilities of all strikes and expirations, moves around. This randomness needs to be explicitly modeled for the effective pricing, trading, and risk management of equity derivatives. Focusing on equity derivatives, author Jim Gatheral examines why options are priced as they are and, starting from a powerful representation of implied volatility in terms of a weighted average of realized volatilities, explores the implications of various popular models for pricing. Along the way he also discusses default risk models, capital structure arbitrage, quadratic variation-based payoffs, VIX futures contracts, and much more. Throughout The Volatility Surface, specific examples are considered to make theory come to life for practitioners. Jim Gatheral, PhD (New York, NY) has been Managing Director, Head of Global Quantitative Analytics at Merrill Lynch since 1995. He is an Adjunct Professor at the Courant Institute of Mathematical Sciences at New York University and is a frequent speaker at derivatives conferences around the world.
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Book details

List price: $70.00
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/11/2006
Binding: Hardcover
Pages: 208
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 0.264
Language: English

Nassim Nicholas Taleb was born in 1960 in Amioun, Lebanon. He is a researcher, essayist, trader, epistemologist, and former practitioner of mathematical finance. Taleb received his bachelors and masters degree in science from the University of Paris. He holds an MBA from the Wharton School at the University of Pennsylvania, and a Ph.D. in Management Science from the University of Paris- Dauphine. Taleb began his financial mathematics career in several of New York City's Wall Street firms before becoming a scholar in the epistemology of chance events, randomness, and the unknown. Taleb's book, Fooled by Randomness, was translated into 23 languages. His book, The Black Swan, was translated into 27 languages and spent several months on the New York Times Bestseller list. Taleb is a Distinguished Professor of Risk Engineering at Polytechnic Institute of New York University and visiting professor of Marketing (Cognitive Science) at London Business School. Taleb has also taught at the University of Massachusetts in Amherst, Courant Institute of New York University, and the Wharton Business School Financial Institutions Center.

List of Figures
List of Tables
Foreword
Preface
Acknowledgments
Stochastic Volatility and Local Volatility
Stochastic Volatility
Derivation of the Valuation Equation
Local Volatility
History
A Brief Review of Dupire's Work
Derivation of the Dupire Equation
Local Volatility in Terms of Implied Volatility
Special Case: No Skew
Local Variance as a Conditional Expectation of Instantaneous Variance
The Heston Model
The Process
The Heston Solution for European Options
A Digression: The Complex Logarithm in the Integration (2.13)
Derivation of the Heston Characteristic Function
Simulation of the Heston Process
Milstein Discretization
Sampling from the Exact Transition Law
Why the Heston Model Is so Popular
The Implied Volatility Surface
Getting Implied Volatility from Local Volatilities
Model Calibration
Understanding Implied Volatility
Local Volatility in the Heston Model
Ansatz
Implied Volatility in the Heston Model
The Term Structure of Black-Scholes Implied Volatility in the Heston Model
The Black-Scholes Implied Volatility Skew in the Heston Model
The SPX Implied Volatility Surface
Another Digression: The SVI Parameterization
A Heston Fit to the Data
Final Remarks on SV Models and Fitting the Volatility Surface
The Heston-Nandi Model
Local Variance in the Heston-Nandi Model
A Numerical Example
The Heston-Nandi Density
Computation of Local Volatilities
Computation of Implied Volatilities
Discussion of Results
Adding Jumps
Why Jumps are Needed
Jump Diffusion
Derivation of the Valuation Equation
Uncertain Jump Size
Characteristic Function Methods
L'evy Processes
Examples of Characteristic Functions for Specific Processes
Computing Option Prices from the Characteristic Function
Proof of (5.6)
Computing Implied Volatility
Computing the At-the-Money Volatility Skew
How Jumps Impact the Volatility Skew
Stochastic Volatility Plus Jumps
Stochastic Volatility Plus Jumps in the Underlying Only (SVJ)
Some Empirical Fits to the SPX Volatility Surface
Stochastic Volatility with Simultaneous Jumps in Stock Price and Volatility (SVJJ)
SVJ Fit to the September 15, 2005, SPX Option Data
Why the SVJ Model Wins
Modeling Default Risk
Merton's Model of Default
Intuition
Implications for the Volatility Skew
Capital Structure Arbitrage
Put-Call Parity
The Arbitrage
Local and Implied Volatility in the Jump-to-Ruin Model
The Effect of Default Risk on Option Prices
The CreditGrades Model
Model Setup
Survival Probability
Equity Volatility
Model Calibration
Volatility Surface Asymptotics
Short Expirations
The Medvedev-Scaillet Result
The SABR Model
Including Jumps
Corollaries
Long Expirations: Fouque, Papanicolaou, and Sircar
Small Volatility of Volatility: Lewis
Extreme Strikes: Roger Lee
Example: Black-Scholes
Stochastic Volatility Models
Asymptotics in Summary
Dynamics of the Volatility Surface
Dynamics of the Volatility Skew under Stochastic Volatility
Dynamics of the Volatility Skew under Local Volatility
Stochastic Implied Volatility Models
Digital Options and Digital Cliq
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