Dynamic Copula Methods in Finance (The Wiley Finance Series)

Dynamic Copula Methods in Finance......Page 3
Contents......Page 7
Preface......Page 11
1.1 Correlation Risk in Pricing and Risk Management......Page 13
1.2 Implied vs Realized Correlation......Page 15
1.4 Copula Functions......Page 16
1.6 Long-range Dependence......Page 17
1.7 Multivariate GARCH Models......Page 19
1.8 Copulas and Convolution......Page 20
2.1 Copula Functions: The Basic Recipe......Page 23
2.2 Market Co-movements......Page 26
2.3 Delta Hedging Multivariate Digital Products......Page 28
2.4 Linear Correlation......Page 31
2.5 Rank Correlation......Page 32
2.6 Multivariate Spearman’s Rho......Page 34
2.7 Survival Copulas and Radial Symmetry......Page 35
2.8 Copula Volume and Survival Copulas......Page 36
2.10 Long/Short Correlation......Page 39
2.11.1 Elliptical Copulas......Page 41
2.11.2 Archimedean Copulas......Page 43
2.12 Kendall Function......Page 45
2.13 Exchangeability......Page 46
2.14 Hierarchical Copulas......Page 47
2.15 Conditional Probability and Factor Copulas......Page 51
2.16 Copula Density and Vine Copulas......Page 54
2.17.1 Conditional Copulas......Page 57
2.17.2 Pseudo-copulas......Page 58
3.1 The Dynamics of Speculative Prices......Page 61
3.2 Copulas and Markov Processes: The DNO approach......Page 63
3.2.1 The * and   Product Operators......Page 64
3.2.2 Product Operators and Markov Processes......Page 67
3.2.3 Self-similar Copulas......Page 70
3.2.4 Simulating Markov Chains with Copulas......Page 74
3.3 Time-changed Brownian Copulas......Page 75
3.3.1 CEV Clock Brownian Copulas......Page 76
3.3.2 VG Clock Brownian Copulas......Page 77
3.4 Copulas and Martingale Processes......Page 78
3.4.1 C-Convolution......Page 79
3.4.2 Markov Processes with Independent Increments......Page 87
3.4.3 Markov Processes with Dependent Increments......Page 90
3.4.4 Extracting Dependent Increments in Markov Processes......Page 93
3.4.5 Martingale Processes......Page 95
3.5.1 Multivariate Markov Processes......Page 98
3.5.2 Granger Causality and the Martingale Condition......Page 100
4.1 Dynamic Copula Quantile Regressions......Page 103
4.2 Copula-based Markov Processes: Non-linear Quantile Autoregression......Page 105
4.3 Copula-based Markov Processes: Semi-parametric Estimation......Page 111
4.4 Copula-based Markov Processes: Non-parametric Estimation......Page 120
4.5 Copula-based Markov Processes: Mixing Properties......Page 122
4.6 Persistence and Long Memory......Page 125
4.7 C-convolution-based Markov Processes: The Likelihood Function......Page 128
5.1 Multivariate Equity Products......Page 133
5.1.1 European Multivariate Equity Derivatives......Page 134
5.1.2 Path-dependent Equity Derivatives......Page 137
5.2 Recursions of Running Maxima and Minima......Page 138
5.3 The Memory Feature......Page 142
5.4 Risk-neutral Pricing Restrictions......Page 144
5.5 Time-changed Brownian Copulas......Page 145
5.6 Variance Swaps......Page 147
5.7 Semi-parametric Pricing of Path-dependent Derivatives......Page 148
5.9 H-Condition and Granger Causality......Page 149
5.10 Multivariate Pricing Recursion......Page 150
5.11 Hedging Multivariate Equity Derivatives......Page 153
5.12 Correlation Swaps......Page 156
5.13 The Term Structure of Multivariate Equity Derivatives......Page 159
5.13.1 Altiplanos......Page 160
5.13.3 Spread Options......Page 162
6.1 Credit Transfer Finance......Page 165
6.1.1 Univariate Credit Transfer Products......Page 166
6.1.2 Multivariate Credit Transfer Products......Page 167
6.2 Credit Information: Equity vs CDS......Page 170
6.3.1 Univariate Model: Credit Risk as a Put Option......Page 172
6.3.2 Multivariate Model: Gaussian Copula......Page 173
6.3.3 Large Portfolio Model: Vasicek Formula......Page 175
6.4 Intensity-based Models......Page 176
6.4.2 Multivariate Model: Marshall–Olkin Copula......Page 177
6.4.3 Homogeneous Model: Cuadras Augé Copula......Page 179
6.5.1 Multivariate Model: Archimedean Copulas......Page 182
6.6 Granularity Adjustment......Page 183
6.7.1 Semi-unsupervised Cluster Analysis: K-means......Page 184
6.7.2 Unsupervised Cluster Analysis: Kohonen Self-organizing Maps......Page 186
6.7.3 (Semi-)unsupervised Cluster Analysis: Hierarchical Correlation Model......Page 187
6.8 Dynamic Analysis of Credit Risk Portfolios......Page 188
7.1 A Review of Value-at-Risk and Other Measures......Page 193
7.2 Capital Aggregation and Allocation......Page 197
7.2.1 Aggregation: C-Convolution......Page 199
7.2.2 Allocation: Level Curves......Page 201
7.2.3 Allocation with Constraints......Page 203
7.3 Risk Measurement of Managed Portfolios......Page 205
7.3.1 Henriksson–Merton Model......Page 207
7.3.2 Semi-parametric Analysis of Managed Funds......Page 212
7.3.3 Market-neutral Investments......Page 213
7.4 Temporal Aggregation of Risk Measures......Page 214
7.4.2 Temporal Aggregation by C-convolution......Page 215
8.1 Lévy Copulas......Page 219
8.2 Pareto Copulas......Page 222
8.3 Semi-martingale Copulas......Page 224
A.1 Elements of Measure Theory......Page 227
A.2 Integration......Page 228
A.2.1 Expected Values and Moments......Page 229
A.3 The Moment-generating Function or Laplace Transform......Page 230
A.5 Relevant Probability Distributions......Page 231
A.6 Random Vectors and Multivariate Distributions......Page 236
A.6.1 The Multivariate Normal Distribution......Page 237
A.7 Infinite Divisibility......Page 238
A.8 Convergence of Sequences of Random Variables......Page 240
A.10 Conditional Expectation......Page 241
B.1.1 Filtrations......Page 243
B.1.2 Stopping Times......Page 244
B.2 Martingales......Page 245
B.3 Markov Processes......Page 246
B.4 Lévy Processes......Page 249
B.5 Semi-martingales......Page 252
References......Page 257
Extra Reading......Page 263
Index......Page 271