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by Sébastien Bossu, Peter Carr
Advanced Equity Derivatives: Volatility and Correlation
Cover
Series Page
Title Page
Copyright
Dedication
Foreword
Preface
Acknowledgments
Chapter 1: Exotic Derivatives
1.1 Single-Asset Exotics
1.2 Multi-Asset Exotics
1.3 Structured Products
References
Problems
Chapter 2: The Implied Volatility Surface
2.1 The Implied Volatility Smile and Its Consequences
2.2 Interpolation and Extrapolation
2.3 Implied Volatility Surface Properties
2.4 Implied Volatility Surface Models
References and Bibliography
Problems
Chapter 3: Implied Distributions
3.1 Butterfly Spreads and the Implied Distribution
3.2 European Payoff Pricing and Replication
3.3 Pricing Methods for European Payoffs
3.4 Greeks
References
Problems
Chapter 4: Local Volatility and Beyond
4.1 Local Volatility Trees
4.2 Local Volatility in Continuous Time
4.3 Calculating Local Volatilities
4.4 Stochastic Volatility
References
Problems
Chapter 5: Volatility Derivatives
5.1 Volatility Trading
5.2 Variance Swaps
5.3 Realized Volatility Derivatives
5.4 Implied Volatility Derivatives
Problems
Chapter 6: Introducing Correlation
6.1 Measuring Correlation
6.2 Correlation Matrices
6.3 Correlation Average
6.4 Black-Scholes with Constant Correlation
6.5 Local Volatility with Constant Correlation
References
Problems
Chapter 7: Correlation Trading
7.1 Dispersion Trading
7.2 Correlation Swaps
Problems
Chapter 8: Local Correlation
8.1 The Implied Correlation Smile and Its Consequences
8.2 Local Volatility with Local Correlation
8.3 Dynamic Local Correlation Models
8.4 Limitations
References
Problems
Chapter 9: Stochastic Correlation
9.1 Stochastic Single Correlation
9.2 Stochastic Average Correlation
9.3 Stochastic Correlation Matrix
References
Problems
Appendix 9.A: Sufficient Condition for Lower Bound Unattainability
Appendix 9.B: Necessary Condition for Upper Bound Unattainability
Appendix A: Probability Review
A.1 Standard Probability Theory
A.2 Random Variables, Distribution, and Independence
A.3 Conditioning
A.4 Random Processes and Stochastic Calculus
Appendix B: Linear Algebra Review
B.1 Euclidean Spaces
B.2 Square Matrix Decompositions
Solutions Manual
Chapter 1: Exotic Derivatives
Chapter 2: The Implied Volatility Surface
Chapter 3: Implied Distributions
Chapter 4: Local Volatility and Beyond
Chapter 5: Volatility Derivatives
Chapter 6: Introducing Correlation
Chapter 8: Local Correlation
Chapter 9: Stochastic Correlation
Author's Note
About the Author
Index
End User License Agreement
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End User License Agreement
Index
A
Asian options
Attainable boundaries
Attracting boundaries
Autocallable options
Average correlation
B
Barrier options
Basket options
Basket variance
Best-of options
Binomial trees
Black-Scholes model
with constant correlation
and volatility trading
B-O model
Boortz's Common Factor Model
Breeden-Litzenberger formula
Brownian motion
Butterfly spreads
and Dupire's equation
no arbitrage condition
C
Calendar spreads
Capital Guaranteed Performance Note
Carr-Wu model.
See
LNV model
Cauchy-Schwarz inequality
Change of measure
Change of numeraire
Chicago Board Options Exchange (CBOE)
Cholesky decomposition
Cliquet options
Common factor model
Conditioning
Constant correlation
Black-Scholes model with
local volatility with (LVCC)
Correlation.
See also
Local correlation; Stochastic correlation; Dispersion trading
average correlation
Black-Scholes with constant correlation
continuously monitored
correlation matrices
correlation proxy
correlation swaps
historical
implied
measuring
trading
Cross-sectional dispersion
Cubic spline interpolation
D
Daily volatility rule
De Finetti formula (fifth property of Euclidean metric)
Delta
delta hedging
and implied volatility smile
sticky-delta rule
Digital options
Dispersion trading
cross-sectional dispersion
vanilla dispersion trades
variance dispersion trades
Dollar gamma
Dupire's equation
Dynamic correlation models
E
Eigenvalues
Equity correlation matrix
Equity-linked notes
Euclidean metric (fifth property of)
Euclidean spaces
Euler-Maruyama discretization
European payoff pricing and replication
Exotic derivatives
Asian options
barrier options
basket options
cliquet options
digital options
forward start options
lookback options
multi-asset options
quanto options
ratchet options
spread options
structured products
worst-of/best-of options
Extrapolation
F
Feller condition
Fifth property of Euclidean metric
Filtered probability space
Fischer-Wright model.
See also
Jacobi process
Forward start options
Forward variance
G
Gamma.
See also
Dollar gamma
Generalized variance swaps
Geometric basket call
Girsanov theorem
Gram-Schmidt's orthonormalization process
Greeks.
See also
Delta; Gamma
Gurrieri's model
H
Hedge ratios
Hedging.
See also
Overhedging
correlation swaps
delta-hedging
with local volatility
variance swaps
Hedging theory (of stochastic volatility models)
Heston model
Historical correlation
Historical volatility
I
Implied correlation
Implied distributions
butterfly spreads and
European payoff pricing and replication
and exotic pricing
Greeks
and overhedging
problems
references
solutions
Implied volatility
local volatility from
market- vs. model-implied
Implied volatility derivatives
VIX futures
VIX options
Implied volatility smile
Implied volatility surface
Gurrieri's model
indirect models
interpolation and extrapolation
LNV model
properties
SABR model
SVI model
Independence
Interpolation
Ito-Doeblin theorem
J
Jacobi process
Jensen's inequality
Joint distribution
Jumps
K
Knock-in/knock-out option
Kolmogorov equation
L
Law of the unconscious statistician
LNV model
Local correlation
dynamic models
implied correlation smile
local volatility model with (LVLC)
Local volatility
and binomial trees
calculating
connection with stochastic volatility
Dupire's equation
hedging with
from implied volatility
with local correlation (LVLC)
model with constant correlation (LVCC)
pricing
Log-Normal Variance (LNV) model
Lookback options
LVCC model
LVLC model
M
Market capitalization weights
Market price of volatility risk
Market-implied volatility
Matrices:
correlation
square matrix decompostion
Milstein's discretization method
Model-implied volatility
Monte Carlo simulations
Multi-asset options
N
No butterfly spread arbitrage condition
No call or put spread arbitrage condition
Non-attracting boundaries
Nontradable average correlation
Normalized liquidity rule
O
Orthogonality
Overhedging
P
Parseval's identity
Path-dependent payoff
Pearson's correlation coefficient
Perfect hedging with puts and calls
Probability space
Probability theory
Q
Quanto options
R
Radon-Nikodym derivative
Random processes
Random variables
Ratchet options
Rayleigh quotient
Realized variance
Realized volatility
derivatives
Reverse Convertible Note
S
SABR model
Siegel's paradox
Spectral decomposition
Spread options
Square matrix decompositions
Sticky-strike rule
Sticky-delta rule
Sticky-moneyness rule
Stochastic Alpha, Beta, Rho (SABR) model
Stochastic calculus
Stochastic correlation
average (
see also
Average correlation)
correlation matrices
stochastic single correlation
Stochastic volatility.
See also
Stochastic volatility-inspired (SVI) model
connection with local volatility
and forward start options
hedging theory
and jumps
Monte Carlo simulations
problems
Stochastic volatility-inspired (SVI) model
Structured products
SVI model
T
Toy model
Tradable average correlation
U
Unattainability
V
Vanilla dispersion trades
Vanilla options
Variance dispersion trades
Variance futures
Variance swaps
forward variance
hedging and pricing
market
payoffs
variance futures
Vega notional
VIX.
See also
Volatility Index (VIX)
Volatility derivatives
implied
realized
variance swaps
volatility trading
Volatility Index (VIX)
VIX futures
VIX options
Volatility trading
Volga
W
Wiener process
Worst-of options
Worst-of-put pricing
Wright-Fisher process
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