Dynamic Copula Methods in Finance

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Dynamic Copula Methods in Finance

Format:  Hardcover,

274 pages

Publisher: John Wiley & Sons Inc

Publish Date: Dec 2011

ISBN-13: 9781454907886

ISBN-10: 1454907886

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Specifications

Publisher: John Wiley & Sons Inc
Publish Date: Dec 2011
ISBN-13: 9780470683071
ISBN-10: 0470683074
Format: Hardcover
Number of Pages: 274
Shipping Weight (in pounds): 1.42
Product in Inches (L x W x H): 7.0 x 9.75 x 0.75
Walmart No.: 9780470683071

Chapter outline

Prefacep. ix
Correlation Risk in Financep. 1
Correlation Risk in Pricing and Risk Managementp. 1
Implied vs Realized Correlationp. 3
Bottom-up vs Top-down Modelsp. 4
Copula Functionsp. 4
Spatial and Temporal Dependencep. 5
Long-range Dependencep. 5
Multivariate GARCH Modelsp. 7
Copulas and Convolutionp. 8
Copula Functions: The State of the Artp. 11
Copula Functions: The Basic Recipep. 11
Market Co-movementsp. 14
Delta Hedging Multivariate Digital Productsp. 16
Linear Correlationp. 19
Rank Correlationp. 20
Multivariate Spearman's Rhop. 22
Survival Copulas and Radial Symmetryp. 23
Copula Volume and Survival Copulasp. 24
Tail Dependencep. 27
Long/Short Correlationp. 27
Families of Copulasp. 29
Elliptical Copulasp. 29
Archimedean Copulasp. 31
Kendall Functionp. 33
Exchangeabilityp. 34
Hierarchical Copulasp. 35
Conditional Probability and Factor Copulasp. 39
Copula Density and Vine Copulasp. 42
Dynamic Copulasp. 45
Conditional Copulasp. 45
Pseudo-copulasp. 46
Copula Functions and Asset Price Dynamicsp. 49
The Dynamics of Speculative Pricesp. 49
Copulas and Markov Processes: The DNO approachp. 51
The * and * Product Operatorsp. 52
Product Operators and Markov Processesp. 55
Self-similar Copulasp. 58
Simulating Markov Chains with Copulasp. 62
Time-changed Brownian Copulasp. 63
CEV Clock Brownian Copulasp. 64
VG Clock Brownian Copulasp. 65
Copulas and Martingale Processesp. 66
C-Convolutionp. 67
Markov Processes with Independent Incrementsp. 75
Markov Processes with Dependent Incrementsp. 78
Extracting Dependent Increments in Markov Processesp. 81
Martingale Processesp. 83
Multivariate Processesp. 86
Multivariate Markov Processesp. 86
Granger Causality and the Martingale Conditionp. 88
Copula-based Econometrics of Dynamic Processesp. 91
Dynamic Copula Quantile Regressionsp. 91
Copula-based Markov Processes: Non-linear Quantile Autoregressionp. 93
Copula-based Markov Processes: Semi-parametric Estimationp. 99
Copula-based Markov Processes: Non-parametric Estimationp. 108
Copula-based Markov Processes: Mixing Propertiesp. 110
Persistence and Long Memoryp. 113
C-convolution-based Markov Processes: The Likelihood Functionp. 116
Multivariate Equity Productsp. 121
Multivariate Equity Productsp. 121
European Multivariate Equity Derivativesp. 122
Path-dependent Equity Derivativesp. 125
Recursions of Running Maxima and Minimap. 126
The Memory Featurep. 130
Risk-neutral Pricing Restrictionsp. 132
Time-changed Brownian Copulasp. 133
Variance Swapsp. 135
Semi-parametric Pricing of Path-dependent Derivativesp. 136
The Multivariate Pricing Settingp. 137
H-Condition and Granger Causalityp. 137
Multivariate Pricing Recursionp. 138
Hedging Multivariate Equity Derivativesp. 141
Correlation Swapsp. 144
The Term Structure of Multivariate Equity Derivativesp. 147
Altiplanosp. 148
Everestp. 150
Spread Optionsp. 150
Multivariate Credit Productsp. 153
Credit Transfer Financep. 153
Univariate Credit Transfer Productsp. 154
Multivariate Credit Transfer Productsp. 155
Credit Information: Equity vs CDSp. 158
Structural Modelsp. 160
Univariate Model: Credit Risk as a Put Optionp. 160
Multivariate Model: Gaussian Copulap. 161
Large Portfolio Model: Vasicek Formulap. 163
Intensity-based Modelsp. 164
Univariate Model: Poisson and Cox Processesp. 165
Multivariate Model: Marshall-Olkin Copulap. 165
Homogeneous Model: Cuadras Aug Copulap. 167
Frailty Modelsp. 170
Multivariate Model: Archimedean Copulasp. 170
Large Portfolio Model: Schnbucher Formulap. 171
Granularity Adjustmentp. 171
Credit Portfolio Analysisp. 172
Semi-unsupervised Cluster Analysis: K-meansp. 172
Unsupervised Cluster Analysis: Kohonen Self-organizing Mapsp. 174
(Semi-)unsupervised Cluster Analysis: Hierarchical Correlation Modelp. 175
Dynamic Analysis of Credit Risk Portfoliosp. 176
Risk Capital Managementp. 181
A Review of Value-at-Risk and Other Measuresp. 181
Capital Aggregation and Allocationp. 185
Aggregation: C-Convolutionp. 187
Allocation: Level Curvesp. 189
Allocation with Constraintsp. 191
Risk Measurement of Managed Portfoliosp. 193
Henriksson-Merton Modelp. 195
Semi-parametric Analysis of Managed Fundsp. 200
Market-neutral Investmentsp. 201
Temporal Aggregation of Risk Measuresp. 202
The Square-root Formulap. 203
Temporal Aggregation by C-convolutionp. 203
Frontier Issuesp. 207
L'evy Copulasp. 207
Pareto Copulasp. 210
Semi-martingale Copulasp. 212
A Elements of Probabilityp. 215
Elements of Measure Theoryp. 215
Integrationp. 216
Expected Values and Momentsp. 217
The Moment-generating Function or Laplace Transformp. 218
The Characteristic Functionp. 219
Relevant Probability Distributionsp. 219
Random Vectors and Multivariate Distributionsp. 224
The Multivariate Normal Distributionp. 225
Infinite Divisibilityp. 226
Convergence of Sequences of Random Variablesp. 228
The Strong Law of Large Numbersp. 229
The Radon-Nikodym Derivativep. 229
Conditional Expectationp. 229
Elements of Stochastic Processes Theoryp. 231
Stochastic Processesp. 231
Filtrationsp. 231
Stopping Timesp. 232
Martingalesp. 233
Markov Processesp. 234
Lvy Processesp. 237
Subordinatorsp. 240
Semi-martingalesp. 240
Referencesp. 245
Extra Readingp. 251
Indexp. 259

Book description

The latest tools and techniques for pricing and risk management

This book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications. The first part of the book will briefly introduce the standard the theory of copula functions, before examining the link between copulas and Markov processes. It will then introduce new techniques to design Markov processes that are suited to represent the dynamics of market risk factors and their co-movement, providing techniques to both estimate and simulate such dynamics. The second part of the book will show readers how to apply these methods to the evaluation of pricing of multivariate derivative contracts in the equity and credit markets. It will then move on to explore the applications of joint temporal and cross-section aggregation to the problem of risk integration.

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