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