The Volatility Surface A Practitioner's Guide,9780471792512

The Volatility Surface A Practitioner's Guide

by ;
Edition: 1st
ISBN13: 9780471792512
ISBN10: 0471792519
Format: Hardcover
Pub. Date: 2006-09-11
Publisher(s): Wiley
  • Free Shipping Icon

    Free Shipping On Orders Over $35

    Your order must be $35 or more to qualify for free economy shipping. Marketplace items, eBooks and apparel do not qualify towards the $35 purchase minimum.

  • eCampus.com Device Compatibility Matrix

    Click the device icon to install or view instructions

    Apple iOS | iPad, iPhone, iPod
    Apple iOS | iPad, iPhone, iPod
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Windows 10 / 8 / 7 / Vista / XP
    Windows 10 / 8 / 7 / Vista / XP
    Mac OS X | **iMac / Macbook
    Mac OS X | **iMac / Macbook
    Enjoy offline reading with these devices
    Apple Devices
    Android Devices
    Windows Devices
    Mac Devices
    iPad, iPhone, iPod
    Our reader is compatible
     
     
     
    Android 2.2 +
     
    Our reader is compatible
     
     
    Kindle Fire
     
    Our reader is compatible
     
     
    Windows
    10 / 8 / 7 / Vista / XP
     
     
    Our reader is compatible
     
    Mac
     
     
     
    Our reader is compatible
List Price: $70.00

Buy New

Usually Ships in 8 - 10 Business Days.
$69.93
Add to Cart

Rent Book

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:1825 Days access
Downloadable:Lifetime Access
$52.80
*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.
$52.80*
Add to Cart

Used Book

We're Sorry
Sold Out

Buy from our Marketplace starting at $44.87

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

"Written by a practitioner for practitioners, The Volatility Surface 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."--BOOK JACKET.

Author Biography

JIM GATHERAL is a Managing Director at Merrill Lynch and also an Adjunct Professor at the Courant Institute of Mathematical Sciences, New York University.Dr. Gatheral obtained a PhD in theoretical physics from Cambridge Universityin 1983. Since then, he has been involved in all of the major derivative product areasas a bookrunner, risk manager, and quantitative analyst in London, Tokyo, and New York. From 1997 to 2005, Dr. Gatheral headed the Equity Quantitative Analytics group at Merrill Lynch. His current research focus is equity market microstructure and algorithmic trading.

Table of Contents

List of Figures xiii
List of Tables xix
Foreword xxi
Preface xxiii
Acknowledgments xxvii
CHAPTER 1 Stochastic Volatility and Local Volatility 1(14)
Stochastic Volatility
1(6)
Derivation of the Valuation Equation
4(3)
Local Volatility
7(8)
History
7(1)
A Brief Review of Dupire's Work
8(1)
Derivation of the Dupire Equation
9(2)
Local Volatility in Terms of Implied Volatility
11(2)
Special Case: No Skew
13(1)
Local Variance as a Conditional Expectation of Instantaneous Variance
13(2)
CHAPTER 2 The Heston Model 15(10)
The Process
15(1)
The Heston Solution for European Options
16(4)
A Digression: The Complex Logarithm in the Integration (2.13)
19(1)
Derivation of the Heston Characteristic Function
20(1)
Simulation of the Heston Process
21(4)
Milstein Discretization
22(1)
Sampling from the Exact Transition Law
23(1)
Why the Heston Model Is so Popular
24(1)
CHAPTER 3 The Implied Volatility Surface 25(18)
Getting Implied Volatility from Local Volatilities
25(6)
Model Calibration
25(1)
Understanding Implied Volatility
26(5)
Local Volatility in the Heston Model
31(2)
Ansatz
32(1)
Implied Volatility in the Heston Model
33(3)
The Term Structure of Black-Scholes Implied Volatility in the Heston Model
34(1)
The Black-Scholes Implied Volatility Skew in the Heston Model
35(1)
The SPX Implied Volatility Surface
36(7)
Another Digression: The SVI Parameterization
37(3)
A Heston Fit to the Data
40(2)
Final Remarks on SV Models and Fitting the Volatility Surface
42(1)
CHAPTER 4 The Heston-Nandi Model 43(7)
Local Variance in the Heston-Nandi Model
43(1)
A Numerical Example
44(5)
The Heston-Nandi Density
45(1)
Computation of Local Volatilities
45(1)
Computation of Implied volatilities
46(3)
Discussion of Results
49(1)
CHAPTER 5 Adding Jumps 50(24)
Why Jumps are Needed
50(2)
Jump Diffusion
52(4)
Derivation of the Valuation Equation
52(2)
Uncertain Jump Size
54(2)
Characteristic Function Methods
56(9)
Lévy Processes
56(1)
Examples of Characteristic Functions for Specific Processes
57(1)
Computing Option Prices from the Characteristic Function
58(1)
Proof of (5.6)
58(2)
Computing Implied Volatility
60(1)
Computing the At-the-Money Volatility Skew
60(1)
How Jumps Impact the Volatility Skew
61(4)
Stochastic Volatility Plus Jumps
65(9)
Stochastic Volatility Plus Jumps in the Underlying Only (SVJ)
65(1)
Some Empirical Fits to the SPX Volatility Surface
66(2)
Stochastic Volatility with Simultaneous Jumps in Stock Price and Volatility (SVJJ)
68(3)
SVJ Fit to the September 15, 2005, SPX Option Data
71(2)
Why the SVJ Model Wins
73(1)
CHAPTER 6 Modeling Default Risk 74(13)
Merton's Model of Default
74(3)
Intuition
75(1)
Implications for the Volatility Skew
76(1)
Capital Structure Arbitrage
77(2)
Put-Call Parity
77(1)
The Arbitrage
78(1)
Local and Implied Volatility in the Jump-to-Ruin Model
79(3)
The Effect of Default Risk on Option Prices
82(2)
The CreditGrades Model
84(3)
Model Setup
84(1)
Survival Probability
85(1)
Equity Volatility
86(1)
Model Calibration
86(1)
CHAPTER 7 Volatility Surface Asymptotics 87(14)
Short Expirations
87(2)
The Medvedev-Scaillet Result
89(4)
The SABR Model
91(2)
Including Jumps
93(2)
Corollaries
94(1)
Long Expirations: Fouque, Papanicolaou, and Sircar
95(1)
Small Volatility of Volatility: Lewis
96(1)
Extreme Strikes: Roger Lee
97(3)
Example: Black-Scholes
99(1)
Stochastic Volatility Models
99(1)
Asymptotics in Summary
100(1)
CHAPTER 8 Dynamics of the Volatility Surface 101(6)
Dynamics of the Volatility Skew under Stochastic Volatility
101(1)
Dynamics of the Volatility Skew under Local Volatility
102(1)
Stochastic Implied Volatility Models
103(1)
Digital Options and Digital Cliquets
103(4)
Valuing Digital Options
104(1)
Digital Cliquets
104(3)
CHAPTER 9 Barrier Options 107(15)
Definitions
107(1)
Limiting Cases
108(1)
Limit Orders
108(1)
European Capped Calls
109(1)
The Reflection Principle
109(3)
The Lookback Hedging Argument
112(1)
One-Touch Options Again
113(1)
Put-Call Symmetry
113(1)
QuasiStatic Hedging and Qualitative Valuation
114(3)
Out-of-the-Money Barrier Options
114(1)
One-Touch Options
115(1)
Live-Out Options
116(1)
Lookback Options
117(1)
Adjusting for Discrete Monitoring
117(3)
Discretely Monitored Lookback Options
119(1)
Parisian Options
120(1)
Some Applications of Barrier Options
120(1)
Ladders
120(1)
Ranges
120(1)
Conclusion
121(1)
CHAPTER 10 Exotic Cliquets 122
Locally Capped Globally Floored Cliquet
122(3)
Valuation under Heston and Local Volatility Assumptions
123(1)
Performance
124(1)
Reverse Cliquet
125(2)
Valuation under Heston and Local Volatility Assumptions
126(1)
Performance
127(1)
Napoleon
127(6)
Valuation under Heston and Local Volatility Assumptions
128(2)
Performance
130(1)
Investor Motivation
130(1)
More on Napoleons
131(2)
CHAPTER 11 Volatility Derivatives 133(29)
Spanning Generalized European Payoffs
133(3)
Example: European Options
134(1)
Example: Amortizing Options
135(1)
The Log Contract
135(1)
Variance and Volatility Swaps
136(10)
Variance Swaps
137(1)
Variance Swaps in the Heston Model
138(1)
Dependence on Skew and Curvature
138(2)
The Effect of Jumps
140(3)
Volatility Swaps
143(1)
Convexity Adjustment in the Heston Model
144(2)
Valuing Volatility Derivatives
146(10)
Fair Value of the Power Payoff
146(1)
The Laplace Transform of Quadratic Variation under Zero Correlation
147(2)
The Fair Value of Volatility under Zero Correlation
149(2)
A Simple Lognormal Model
151(3)
Options on Volatility: More on Model Independence
154(2)
Listed Quadratic-Variation Based Securities
156(5)
The VIX Index
156(2)
VXB Futures
158(2)
Knock-on Benefits
160(1)
Summary
161(1)
Postscript 162(1)
Bibliography 163(6)
Index 169

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.