Applied Quantitative Finance

Preface......Page 15
Contributors......Page 19
Frequently Used Notation......Page 21
Value at Risk......Page 23
The Practical Need......Page 25
Statistical Modeling for VaR......Page 26
VaR Approximations......Page 28
Pros and Cons of Delta-Gamma Approximations......Page 29
General Properties of Delta-Gamma-Normal Models......Page 30
Derivation......Page 34
Properties......Page 37
Error Analysis......Page 38
Tail Behavior......Page 42
Inversion of the cdf minus the Gaussian Approximation......Page 43
Monte-Carlo Sampling Method......Page 46
Partial Monte-Carlo with Importance Sampling......Page 50
XploRe Examples......Page 52
Applications of Copulas for the Calculation of Value-at-Risk......Page 57
Definition......Page 58
Examples of Copulas......Page 59
Further Important Properties of Copulas......Page 61
Selecting the Marginal Distributions......Page 62
Estimating the Copula Parameters......Page 63
Generating Scenarios - Monte Carlo Value-at-Risk......Page 65
Examples......Page 67
Results......Page 69
Risk Categories -- a Definition of Terms......Page 73
Descriptive Statistics of Yield Spread Time Series......Page 75
Data Analysis with XploRe......Page 76
Discussion of Results......Page 79
Historical Simulation and Value at Risk......Page 85
Risk Factor: Full Yield......Page 86
Risk Factor: Benchmark......Page 89
Risk Factor: Spread over Benchmark Yield......Page 90
Simultaneous Simulation......Page 91
VaR Estimation and Backtesting with XploRe......Page 92
P-P Plots......Page 95
Q-Q Plots......Page 96
Discussion of Simulation Results......Page 97
Risk Factor: Full Yield......Page 99
Risk Factor: Spread over Benchmark Yield......Page 100
Conservative Approach......Page 101
Simultaneous Simulation......Page 102
XploRe for Internal Risk Models......Page 103
Credit Risk......Page 107
Rating Migrations......Page 109
From Credit Events to Migration Counts......Page 110
Estimating Rating Transition Probabilities......Page 111
Dependent Migrations......Page 112
Computation and Quantlets......Page 115
Aggregation over Periods......Page 116
Are the Transition Probabilities Stationary?......Page 117
Computation and Quantlets......Page 119
Examples with Graphical Presentation......Page 120
Time Homogeneous Markov Chain......Page 123
Bootstrapping Markov Chains......Page 124
Computation and Quantlets......Page 126
Portfolio Migration......Page 128
Introduction......Page 133
Construction of portfolio credit risk models......Page 135
Dependence modelling......Page 136
Factor modelling......Page 137
Copula modelling......Page 139
Random sample generation......Page 141
Portfolio results......Page 142
Implied Volatility......Page 147
The Analysis of Implied Volatilities......Page 149
Introduction......Page 150
Calculating the Implied Volatility......Page 151
Surface smoothing......Page 153
Data description......Page 156
PCA of ATM Implied Volatilities......Page 158
Common PCA of the Implied Volatility Surface......Page 159
How Precise Are Price Distributions Predicted by IBT?......Page 167
Implied Binomial Trees......Page 168
The Derman and Kani (D & K) algorithm......Page 169
Compensation......Page 173
Barle and Cakici (B & C) algorithm......Page 175
Simulation using Derman and Kani algorithm......Page 176
Simulation using Barle and Cakici algorithm......Page 178
Comparison with Monte-Carlo Simulation......Page 180
Example -- Analysis of DAX data......Page 184
Introduction......Page 193
Extracting the SPD using Call-Options......Page 195
Black-Scholes SPD......Page 197
Estimating the call pricing function......Page 198
Further dimension reduction......Page 199
Local Polynomial Estimation......Page 203
Data......Page 205
SPD, delta and gamma......Page 207
Bootstrap confidence bands......Page 209
Comparison to Implied Binomial Trees......Page 212
Introduction......Page 219
Application to DAX Data......Page 220
Estimation of the Historical SPD......Page 222
The Estimation Method......Page 223
Application to DAX Data......Page 224
Comparison of Implied and Historical SPD......Page 227
Skewness Trades......Page 229
Performance......Page 232
Kurtosis Trades......Page 234
Performance......Page 236
A Word of Caution......Page 238
Econometrics......Page 241
Introduction......Page 243
Model specifications......Page 244
Estimation of the BEKK-model......Page 246
Data description......Page 247
Estimating bivariate GARCH......Page 248
Estimating the (co)variance processes......Page 251
Forecasting exchange rate densities......Page 254
Statistical Process Control......Page 259
Control Charts......Page 260
Chart characteristics......Page 265
Average Run Length and Critical Values......Page 269
Probability Mass and Cumulative Distribution Function......Page 270
Comparison with existing methods......Page 272
Two-sided CUSUM and Crosier......Page 273
Real data example -- monitoring CAPM......Page 275
Introduction......Page 281
Discrete Time Approximation of a Diffusion......Page 282
Hypothesis Testing......Page 283
Kernel Estimator......Page 285
Introduction into Empirical Likelihood......Page 286
Empirical Likelihood for Time Series Data......Page 287
Goodness-of-Fit Statistic......Page 290
Goodness-of-Fit test......Page 294
Application......Page 296
Simulation Study and Illustration......Page 298
Appendix......Page 301
Introduction......Page 305
The Price Function......Page 306
State Space Form......Page 307
Kalman Filtering given all parameters......Page 308
Filtering and state smoothing......Page 309
Maximum likelihood estimation of the parameters......Page 310
The Data......Page 311
Setting the system matrices......Page 315
Kalman filter and maximized log likelihood......Page 317
Diagnostic checking with standardized residuals......Page 320
Calculating the Kalman smoother......Page 322
Procedure equivalence......Page 324
Smoothed constant state variables......Page 326
Introduction......Page 331
Hurst and Rescaled Range Analysis......Page 332
Stationary Long Memory Processes......Page 334
Fractional Brownian Motion and Noise......Page 335
Data Analysis......Page 337
Trading the Negative Persistence......Page 340
Intervals of homogeneity......Page 345
The adaptive estimator......Page 348
A small simulation study......Page 349
Estimating the coefficients of an exchange rate basket......Page 351
The Thai Baht basket......Page 353
Estimation results......Page 357
Estimating the volatility of financial time series......Page 360
The standard approach......Page 361
Modeling volatility via power transformation......Page 362
Adaptive estimation under local time-homogeneity......Page 363
Technical appendix......Page 366
Introduction to simulation techniques......Page 371
Pricing path independent European options on one underlying......Page 372
Pricing path dependent European options on one underlying......Page 376
Pricing options on multiple underlyings......Page 377
Error bounds......Page 378
Construction of the Halton sequence......Page 379
Experimental results......Page 381
Pricing options with simulation techniques - a guideline......Page 383
Integration of the payoff function in the simulation framework......Page 384
Restrictions for the payoff functions......Page 387
Nonparametric Estimators of GARCH Processes......Page 389
Deconvolution density and regression estimates......Page 391
Nonparametric ARMA Estimates......Page 392
Nonparametric GARCH Estimates......Page 401
Introduction......Page 407
Client/Server based Statistical Computing......Page 408
Why Spreadsheets?......Page 409
Using MD*ReX......Page 410
Applications......Page 412
Value at Risk Calculations with Copulas......Page 413
Implied Volatility Measures......Page 415
Index......Page 417