STOCHASTIC VOLATILITY AND JUMP PROCESSES
1 Financial Time Series and Their Characteristics 1 11 Asset Returns, 2 12 Distributional Properties of Returns, 6 13 Processes Considered, 17 2 Linear Time Series Analysis and Its Applications 22 21 Stationarity, 23 22 Correlation and Autocorrelation Function, 23 23 White Noise and Linear Time Series, 26 24 Simple Autoregressive Models, 28 25 Simple Moving-Average Models, 42 26 Simple ARMA Models, 48 27 Unit-Root Nonstationarity, 56 28 Seasonal Models, 61 29 Regression Models with Time Series Errors, 66 210 Long-Memory Models, 72 Appendix A Some SCA Commands, 74 3 Conditional Heteroscedastic Models 79 31 Characteristics of Volatility, 80 32 Structure of a Model, 81 33 The ARCH Model, 82 34 The GARCH Model, 93 35 The Integrated GARCH Model, 100 36 The GARCH-M Model, 101 37 The Exponential GARCH Model, 102 38 The CHARMA Model, 107 39 Random Coefficient Autoregressive Models, 109 310 The Stochastic Volatility Model, 110 311 The Long-Memory Stochastic Volatility Model, 110 312 An Alternative Approach, 112 313 Application, 114 314 Kurtosis of GARCH Models, 118 Appendix A Some RATS Programs for Estimating Volatility Models, 120 4 Nonlinear Models and Their Applications 126 41 Nonlinear Models, 128 42 Nonlinearity Tests, 152 43 Modeling, 161 44 Forecasting, 161 45 Application, 164 Appendix A Some RATS Programs for Nonlinear Volatility Models, 168 Appendix B S-Plus Commands for Neural Network, 169 5 High-Frequency Data Analysis and Market Microstructure 175 51 Nonsynchronous Trading, 176 52 Bid-Ask Spread, 179 53 Empirical Characteristics of Transactions Data, 181 54 Models for Price Changes, 187 55 Duration Models, 194 56 Nonlinear Duration Models, 206 57 Bivariate Models for Price Change and Duration, 207 Appendix A Review of Some Probability Distributions, 212 Appendix B Hazard Function, 215 Appendix C Some RATS Programs for Duration Models, 216 6 Continuous-Time Models and Their Applications 221 61 Options, 222 62 Some Continuous-Time Stochastic Processes, 222 63 Ito’s Lemma, 226 64 Distributions of Stock Prices and Log Returns, 231 65 Derivation of Black–Scholes Differential Equation, 232 66 Black–Scholes Pricing Formulas, 234 67 An Extension of Ito’s Lemma, 240 68 Stochastic Integral, 242 69 Jump Diffusion Models, 244 610 Estimation of Continuous-Time Models, 251 Appendix A Integration of Black–Scholes Formula, 251 Appendix B Approximation to Standard Normal Probability, 253 7 Extreme Values, Quantile Estimation, and Value at Risk 256 71 Value at Risk, 256 72 RiskMetrics, 259 73 An Econometric Approach to VaR Calculation, 262 74 Quantile Estimation, 267 75 Extreme Value Theory, 270 76 An Extreme Value Approach to VaR, 279 77 A New Approach Based on the Extreme Value Theory, 284 8 Multivariate Time Series Analysis and Its Applications 299 81 Weak Stationarity and Cross-Correlation Matrixes, 300 82 Vector Autoregressive Models, 309 83 Vector Moving-Average Models, 318 84 Vector ARMA Models, 322 85 Unit-Root Nonstationarity and Co-Integration, 328 86 Threshold Co-Integration and Arbitrage, 332 87 Principal Component Analysis, 335 88 Factor Analysis, 341 Appendix A Review of Vectors and Matrixes, 348 Appendix B Multivariate Normal Distributions, 353 9 Multivariate Volatility Models and Their Applications 357 91 Reparameterization, 358 92 GARCH Models for Bivariate Returns, 363 93 Higher Dimensional Volatility Models, 376 94 Factor-Volatility Models, 383 95 Application, 385 96 Multivariate t Distribution, 387 Appendix A Some Remarks on Estimation, 388 10 Markov Chain Monte Carlo Methods with Applications 395 101 Markov Chain Simulation, 396 102 Gibbs Sampling, 397 103 Bayesian Inference, 399 104 Alternative Algorithms, 403 105 Linear Regression with Time-Series Errors, 406 106 Missing Values and Outliers, 410 107 Stochastic Volatility Models, 418 108 Markov Switching Models, 429 109 Forecasting, 438 1010 Other Applications, 441