Statistical models and methods for financial markets:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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New York, NY
Springer
2008
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| Series: | Springer texts in statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 354 S. graph. Darst. |
| ISBN: | 9780387778266 |
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MARC
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| 245 | 1 | 0 | |a Statistical models and methods for financial markets |c Tze Leung Lai ; Haipeng Xing |
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| 300 | |a XX, 354 S. |b graph. Darst. | ||
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| 650 | 7 | |a Processos estocásticos |2 larpcal | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Finance |x Statistical methods | |
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| adam_text | Contents
Preface........................................................ vii
Part I Basic Statistical Methods and Financial Applications
1 Linear Regression Models ................................. 3
1.1 Ordinary least squares (OLS) ............................ 4
1.1.1 Residuals and their sum of squares .................. 4
1.1.2 Properties of projection matrices.................... 5
1.1.3 Properties of nonnegative definite matrices ........... 6
1.1.4 Statistical properties of OLS estimates............... 7
1.2 Statistical inference...................................... 8
1.2.1 Confidence intervals............................... 8
1.2.2 ANOVA (analysis of variance) tests.................. 10
1.3 Variable selection........................................ 12
1.3.1 Test-based and other variable selection criteria........ 12
1.3.2 Stepwise variable selection.......................... 15
1.4 Regression diagnostics ................................... 16
1.4.1 Analysis of residuals............................... 17
1.4.2 Influence diagnostics............................... 18
1.5 Extension to stochastic regressors ......................... 19
1.5.1 Minimum-variance linear predictors.................. 19
1.5.2 Futures markets and hedging with futures contracts ... 20
1.5.3 Inference in the case of stochastic regressors.......... 21
1.6 Bootstrapping in regression............................... 22
1.6.1 The plug-in principle and bootstrap resampling....... 22
1.6.2 Bootstrapping regression models .................... 24
1.6.3 Bootstrap confidence intervals....................... 25
1.7 Generalized least squares................................. 25
Contents
1.8 Implementation and illustration........................... 26
Exercises ................................................... 32
Multivariate Analysis and Likelihood Inference............ 37
2.1 Joint distribution of random variables...................... 38
2.1.1 Change of variables................................ 39
2.1.2 Mean and covariance matrix........................ 39
2.2 Principal component analysis (PCA)....................... 41
2.2.1 Basic definitions................................... 41
2.2.2 Properties of principal components.................. 42
2.2.3 An example: PCA of U.S. Treasury-LIBOR
swap rates........................................ 44
2.3 Multivariate normal distribution........................... 48
2.3.1 Definition and density function...................... 48
2.3.2 Marginal and conditional distributions............... 50
2.3.3 Orthogonality and independence, with applications
to regression...................................... 50
2.3.4 Sample covariance matrix and Wishart distribution .... 52
2.4 Likelihood inference ..................................... 55
2.4.1 Method of maximum likelihood ..................... 55
2.4.2 Asymptotic inference .............................. 58
2.4.3 Parametric bootstrap.............................. 59
Exercises ................................................... 60
Basic Investment Models and Their Statistical Analysis ... 63
3.1 Asset returns ........................................... 64
3.1.1 Definitions ....................................... 64
3.1.2 Statistical models for asset prices and returns......... 66
3.2 Markowitz s portfolio theory.............................. 67
3.2.1 Portfolio weights.................................. 67
3.2.2 Geometry of efficient sets........................... 68
3.2.3 Computation of efficient portfolios................... 69
3.2.4 Estimation of fi and £ and an example.............. 71
3.3 Capital asset pricing model (CAPM)....................... 72
3.3.1 The model........................................ 72
3.3.2 Investment implications............................ 77
3.3.3 Estimation and testing............................. 77
3.3.4 Empirical studies of CAPM......................... 79
3.4 Multifactor pricing models................................ 81
3.4.1 Arbitrage pricing theory............................ 81
3.4.2 Factor analysis.................................... 82
3.4.3 The PCA approach................................ 85
3.4.4 The Fama-French three-factor model................. 86
Contents xv
3.5 Applications of resampling to portfolio management ......... 87
3.5.1 Michaud s resampled efficient frontier................ 87
3.5.2 Bootstrap estimates of performance.................. 88
Exercises ................................................... 89
Parametric Models and Bayesian Methods................. 93
4.1 Maximum likelihood and generalized linear models........... 94
4.1.1 Numerical methods for computing MLE.............. 94
4.1.2 Generalized linear models .......................... 95
4.2 Nonlinear regression models............................... 97
4.2.1 The Gauss-Newton algorithm....................... 98
4.2.2 Statistical inference................................100
4.2.3 Implementation and an example.....................101
4.3 Bayesian inference.......................................103
4.3.1 Prior and posterior distributions ....................103
4.3.2 Bayes procedures..................................104
4.3.3 Bayes estimators of multivariate normal mean
and covariance matrix .............................105
4.3.4 Bayes estimators in Gaussian regression models.......107
4.3.5 Empirical Bayes and shrinkage estimators............108
4.4 Investment applications of shrinkage estimators and
Bayesian methods.......................................109
4.4.1 Shrinkage estimators of /x and £ for the plug-in
efficient frontier...................................110
4.4.2 An alternative Bayesian approach...................Ill
Exercises ...................................................113
Time Series Modeling and Forecasting.....................115
5.1 Stationary time series analysis............................115
5.1.1 Weak stationarity.................................115
5.1.2 Tests of independence..............................117
5.1.3 Wold decomposition and MA, AR, and ARMA models . 119
5.1.4 Forecasting in ARMA models.......................121
5.1.5 Parameter estimation and order determination........122
5.2 Analysis of nonstationary time series.......................123
5.2.1 Detrending.......................................123
5.2.2 An empirical example..............................124
5.2.3 Transformation and differencing.....................128
5.2.4 Unit-root nonstationarity and ARIMA models........129
5.3 Linear state-space models and Kalman filtering..............130
5.3.1 Recursive formulas for P(|t_1,xt|(_1, and xt|t.........131
5.3.2 Dynamic linear models and time-varying betas
in CAPM ........................................133
xvi Contents
Exercises ...................................................135
6 Dynamic Models of Asser Returns and Their Volatilities . . 139
6.1 Stylized facts on time series of asset returns.................140
6.2 Moving average estimators of time-varying volatilities........144
6.3 Conditional heteroskedastic models........................146
6.3.1 The ARCH model.................................146
6.3.2 The GARCH model ...............................147
6.3.3 The integrated GARCH model......................152
6.3.4 The exponential GARCH model.....................152
6.4 The ARMA-GARCH and ARMA-EGARCH models .........155
6.4.1 Forecasting future returns and volatilities.............156
6.4.2 Implementation and illustration.....................156
Exercises ...................................................157
Part II Advanced Topics in Quantitative Finance
7 Nonparametric Regression and Substantive-Empirical
Modeling..................................................163
7.1 Regression functions and minimum-variance prediction.......164
7.2 Univariate predictors.....................................165
7.2.1 Running-mean/running-line smoothers and local
polynomial regression..............................165
7.2.2 Kernel smoothers..................................166
7.2.3 Regression splines.................................166
7.2.4 Smoothing cubic splines............................169
7.3 Selection of smoothing parameter..........................170
7.3.1 The bias-variance trade-off.........................170
7.3.2 Cross-validation...................................171
7.4 Multivariate predictors...................................172
7.4.1 Tensor product basis and multivariate adaptive
regression splines..................................172
7.4.2 Additive regression models .........................173
7.4.3 Projection pursuit regression........................174
7.4.4 Neural networks...................................174
7.5 A modeling approach that combines domain knowledge with
nonparametric regression.................................176
7.5.1 Penalized spline models and estimation of
forward rates .....................................177
7.5.2 A semiparametric penalized spline model for the
forward rate curve of corporate debt.................178
Exercises ...................................................179
Contents xvii
Option Pricing and Market Data..........................181
8.1 Option prices and pricing theory ..........................182
8.1.1 Options data and put-call parity....................182
8.1.2 The Black-Scholes formulas for European options......183
8.1.3 Optimal stopping and American options..............187
8.2 Implied volatility........................................188
8.3 Alternatives to and modifications of the Black-Scholes model
and pricing theory.......................................192
8.3.1 The implied volatility function (IVF) model ..........192
8.3.2 The constant elasticity of variance (CEV) model ......192
8.3.3 The stochastic volatility (SV) model.................193
8.3.4 Nonparametric methods............................194
8.3.5 A combined substantive-empirical approach...........195
Exercises ...................................................197
Advanced Multivariate and Time Series Methods
in Financial Econometrics .................................199
9.1 Canonical correlation analysis.............................200
9.1.1 Cross-covariance and correlation matrices.............200
9.1.2 Canonical correlations .............................201
9.2 Multivariate regression analysis ...........................203
9.2.1 Least squares estimates in multivariate regression .....203
9.2.2 Reduced-rank regression............................203
9.3 Modified Cholesky decomposition and high-dimensional
covariance matrices......................................205
9.4 Multivariate time series..................................206
9.4.1 Stationarity and cross-correlation....................206
9.4.2 Dimension reduction via PCA.......................206
9.4.3 Linear regression with stochastic regressors...........207
9.4.4 Unit-root tests....................................211
9.4.5 Cointegrated VAR.................................213
9.5 Long-memory models and regime
switching/structural change...............................217
9.5.1 Long memory in integrated models..................217
9.5.2 Change-point AR-GARCH models...................219
9.5.3 Regime-switching models...........................224
9.6 Stochastic volatility and multivariate volatility models .......225
9.6.1 Stochastic volatility models.........................225
9.6.2 Multivariate volatility models.......................228
9.7 Generalized method of moments (GMM) ...................229
9.7.1 Instrumental variables for linear relationships.........229
9.7.2 Generalized moment restrictions and
GMM estimation..................................231
xviii Contents
9.7.3 An example: Comparison of different short-term
interest rate models................................233
Exercises ...................................................234
10 Interest Rate Markets.....................................239
10.1 Elements of interest rate markets..........................240
10.1.1 Bank account (money market account)
and short rates....................................241
10.1.2 Zero-coupon bonds and spot rates...................241
10.1.3 Forward rates.....................................244
10.1.4 Swap rates and interest rate swaps ..................245
10.1.5 Caps, floors, and swaptions.........................247
10.2 Yield curve estimation...................................247
10.2.1 Nonparametric regression using spline
basis functions....................................248
10.2.2 Parametric models.................................248
10.3 Multivariate time series of bond yields and other
interest rates............................................252
10.4 Stochastic interest rates and short-rate models..............255
10.4.1 Vasicek, Cox-Ingersoll-Ross, and Hull-White models .. . 258
10.4.2 Bond option prices ................................259
10.4.3 Black-Karasinski model............................260
10.4.4 Multifactor affine yield models......................261
10.5 Stochastic forward rate dynamics and pricing of LIBOR and
swap rate derivatives.....................................261
10.5.1 Standard market formulas based on Black s model
of forward prices..................................262
10.5.2 Arbitrage-free pricing: martingales and numeraires.....263
10.5.3 LIBOR and swap market models....................264
10.5.4 The HJM models of the instantaneous forward rate .... 266
10.6 Parameter estimation and model selection..................267
10.6.1 Calibrating interest rate models in the
financial industry..................................267
10.6.2 Econometric approach to fitting
term-structure models .............................270
10.6.3 Volatility smiles and a substantive-empirical approach.. 271
Exercises ...................................................272
11 Statistical Trading Strategies..............................275
11.1 Technical analysis, trading strategies,
and data-snooping checks.................................277
11.1.1 Technical analysis.................................277
11.1.2 Momentum and contrarian strategies ................279
Contents xix
11.1.3 Pairs trading strategies.............................279
11.1.4 Empirical testing of the profitability
of trading strategies ...............................282
11.1.5 Value investing and knowledge-based
trading strategies..................................285
11.2 High-frequency data, market microstructure, and associated
trading strategies........................................286
11.2.1 Institutional background and stylized facts about
transaction data...................................287
11.2.2 Bid-ask bounce and nonsynchronous trading models . . . 291
11.2.3 Modeling time intervals between trades ..............292
11.2.4 Inference on underlying price process ................297
11.2.5 Real-time trading systems..........................299
11.3 Transaction costs and dynamic trading.....................300
11.3.1 Estimation and analysis of transaction costs..........300
11.3.2 Heterogeneous trading objectives and strategies.......300
11.3.3 Multiperiod trading and dynamic strategies...........301
Exercises ...................................................302
12 Statistical Methods in Risk Management..................305
12.1 Financial risks and measures of market risk.................306
12.1.1 Types of financial risks.............................306
12.1.2 Internal models for capital requirements..............307
12.1.3 Vail and other measures of market risk ..............307
12.2 Statistical models for Vail and ES.........................309
12.2.1 The Gaussian convention and the ^-modification.......309
12.2.2 Applications of PCA and an example................310
12.2.3 Time series models................................311
12.2.4 Backtesting VaR models ...........................311
12.3 Measuring risk for nonlinear portfolios.....................312
12.3.1 Local valuation via Taylor expansions................312
12.3.2 Full valuation via Monte Carlo......................314
12.3.3 Multivariate copula functions.......................314
12.3.4 Variance reduction techniques.......................316
12.4 Stress testing and extreme value theory ....................318
12.4.1 Stress testing.....................................318
12.4.2 Extraordinary losses and extreme value theory........318
12.4.3 Scenario analysis and Monte Carlo simulations........321
Exercises ...................................................321
xx Contents
Appendix A. Martingale Theory and Central Limit Theorems . 325
Appendix B. Limit Theorems for Stationary Processes.........331
Appendix C. Limit Theorems Underlying Unit-Root Tests
and Cointegration.........................................333
References.....................................................337
Index..........................................................349
|
| adam_txt |
Contents
Preface. vii
Part I Basic Statistical Methods and Financial Applications
1 Linear Regression Models . 3
1.1 Ordinary least squares (OLS) . 4
1.1.1 Residuals and their sum of squares . 4
1.1.2 Properties of projection matrices. 5
1.1.3 Properties of nonnegative definite matrices . 6
1.1.4 Statistical properties of OLS estimates. 7
1.2 Statistical inference. 8
1.2.1 Confidence intervals. 8
1.2.2 ANOVA (analysis of variance) tests. 10
1.3 Variable selection. 12
1.3.1 Test-based and other variable selection criteria. 12
1.3.2 Stepwise variable selection. 15
1.4 Regression diagnostics . 16
1.4.1 Analysis of residuals. 17
1.4.2 Influence diagnostics. 18
1.5 Extension to stochastic regressors . 19
1.5.1 Minimum-variance linear predictors. 19
1.5.2 Futures markets and hedging with futures contracts . 20
1.5.3 Inference in the case of stochastic regressors. 21
1.6 Bootstrapping in regression. 22
1.6.1 The plug-in principle and bootstrap resampling. 22
1.6.2 Bootstrapping regression models . 24
1.6.3 Bootstrap confidence intervals. 25
1.7 Generalized least squares. 25
Contents
1.8 Implementation and illustration. 26
Exercises . 32
Multivariate Analysis and Likelihood Inference. 37
2.1 Joint distribution of random variables. 38
2.1.1 Change of variables. 39
2.1.2 Mean and covariance matrix. 39
2.2 Principal component analysis (PCA). 41
2.2.1 Basic definitions. 41
2.2.2 Properties of principal components. 42
2.2.3 An example: PCA of U.S. Treasury-LIBOR
swap rates. 44
2.3 Multivariate normal distribution. 48
2.3.1 Definition and density function. 48
2.3.2 Marginal and conditional distributions. 50
2.3.3 Orthogonality and independence, with applications
to regression. 50
2.3.4 Sample covariance matrix and Wishart distribution . 52
2.4 Likelihood inference . 55
2.4.1 Method of maximum likelihood . 55
2.4.2 Asymptotic inference . 58
2.4.3 Parametric bootstrap. 59
Exercises . 60
Basic Investment Models and Their Statistical Analysis . 63
3.1 Asset returns . 64
3.1.1 Definitions . 64
3.1.2 Statistical models for asset prices and returns. 66
3.2 Markowitz's portfolio theory. 67
3.2.1 Portfolio weights. 67
3.2.2 Geometry of efficient sets. 68
3.2.3 Computation of efficient portfolios. 69
3.2.4 Estimation of fi and £ and an example. 71
3.3 Capital asset pricing model (CAPM). 72
3.3.1 The model. 72
3.3.2 Investment implications. 77
3.3.3 Estimation and testing. 77
3.3.4 Empirical studies of CAPM. 79
3.4 Multifactor pricing models. 81
3.4.1 Arbitrage pricing theory. 81
3.4.2 Factor analysis. 82
3.4.3 The PCA approach. 85
3.4.4 The Fama-French three-factor model. 86
Contents xv
3.5 Applications of resampling to portfolio management . 87
3.5.1 Michaud's resampled efficient frontier. 87
3.5.2 Bootstrap estimates of performance. 88
Exercises . 89
Parametric Models and Bayesian Methods. 93
4.1 Maximum likelihood and generalized linear models. 94
4.1.1 Numerical methods for computing MLE. 94
4.1.2 Generalized linear models . 95
4.2 Nonlinear regression models. 97
4.2.1 The Gauss-Newton algorithm. 98
4.2.2 Statistical inference.100
4.2.3 Implementation and an example.101
4.3 Bayesian inference.103
4.3.1 Prior and posterior distributions .103
4.3.2 Bayes procedures.104
4.3.3 Bayes estimators of multivariate normal mean
and covariance matrix .105
4.3.4 Bayes estimators in Gaussian regression models.107
4.3.5 Empirical Bayes and shrinkage estimators.108
4.4 Investment applications of shrinkage estimators and
Bayesian methods.109
4.4.1 Shrinkage estimators of /x and £ for the plug-in
efficient frontier.110
4.4.2 An alternative Bayesian approach.Ill
Exercises .113
Time Series Modeling and Forecasting.115
5.1 Stationary time series analysis.115
5.1.1 Weak stationarity.115
5.1.2 Tests of independence.117
5.1.3 Wold decomposition and MA, AR, and ARMA models . 119
5.1.4 Forecasting in ARMA models.121
5.1.5 Parameter estimation and order determination.122
5.2 Analysis of nonstationary time series.123
5.2.1 Detrending.123
5.2.2 An empirical example.124
5.2.3 Transformation and differencing.128
5.2.4 Unit-root nonstationarity and ARIMA models.129
5.3 Linear state-space models and Kalman filtering.130
5.3.1 Recursive formulas for P(|t_1,xt|(_1, and xt|t.131
5.3.2 Dynamic linear models and time-varying betas
in CAPM .133
xvi Contents
Exercises .135
6 Dynamic Models of Asser Returns and Their Volatilities . . 139
6.1 Stylized facts on time series of asset returns.140
6.2 Moving average estimators of time-varying volatilities.144
6.3 Conditional heteroskedastic models.146
6.3.1 The ARCH model.146
6.3.2 The GARCH model .147
6.3.3 The integrated GARCH model.152
6.3.4 The exponential GARCH model.152
6.4 The ARMA-GARCH and ARMA-EGARCH models .155
6.4.1 Forecasting future returns and volatilities.156
6.4.2 Implementation and illustration.156
Exercises .157
Part II Advanced Topics in Quantitative Finance
7 Nonparametric Regression and Substantive-Empirical
Modeling.163
7.1 Regression functions and minimum-variance prediction.164
7.2 Univariate predictors.165
7.2.1 Running-mean/running-line smoothers and local
polynomial regression.165
7.2.2 Kernel smoothers.166
7.2.3 Regression splines.166
7.2.4 Smoothing cubic splines.169
7.3 Selection of smoothing parameter.170
7.3.1 The bias-variance trade-off.170
7.3.2 Cross-validation.171
7.4 Multivariate predictors.172
7.4.1 Tensor product basis and multivariate adaptive
regression splines.172
7.4.2 Additive regression models .173
7.4.3 Projection pursuit regression.174
7.4.4 Neural networks.174
7.5 A modeling approach that combines domain knowledge with
nonparametric regression.176
7.5.1 Penalized spline models and estimation of
forward rates .177
7.5.2 A semiparametric penalized spline model for the
forward rate curve of corporate debt.178
Exercises .179
Contents xvii
Option Pricing and Market Data.181
8.1 Option prices and pricing theory .182
8.1.1 Options data and put-call parity.182
8.1.2 The Black-Scholes formulas for European options.183
8.1.3 Optimal stopping and American options.187
8.2 Implied volatility.188
8.3 Alternatives to and modifications of the Black-Scholes model
and pricing theory.192
8.3.1 The implied volatility function (IVF) model .192
8.3.2 The constant elasticity of variance (CEV) model .192
8.3.3 The stochastic volatility (SV) model.193
8.3.4 Nonparametric methods.194
8.3.5 A combined substantive-empirical approach.195
Exercises .197
Advanced Multivariate and Time Series Methods
in Financial Econometrics .199
9.1 Canonical correlation analysis.200
9.1.1 Cross-covariance and correlation matrices.200
9.1.2 Canonical correlations .201
9.2 Multivariate regression analysis .203
9.2.1 Least squares estimates in multivariate regression .203
9.2.2 Reduced-rank regression.203
9.3 Modified Cholesky decomposition and high-dimensional
covariance matrices.205
9.4 Multivariate time series.206
9.4.1 Stationarity and cross-correlation.206
9.4.2 Dimension reduction via PCA.206
9.4.3 Linear regression with stochastic regressors.207
9.4.4 Unit-root tests.211
9.4.5 Cointegrated VAR.213
9.5 Long-memory models and regime
switching/structural change.217
9.5.1 Long memory in integrated models.217
9.5.2 Change-point AR-GARCH models.219
9.5.3 Regime-switching models.224
9.6 Stochastic volatility and multivariate volatility models .225
9.6.1 Stochastic volatility models.225
9.6.2 Multivariate volatility models.228
9.7 Generalized method of moments (GMM) .229
9.7.1 Instrumental variables for linear relationships.229
9.7.2 Generalized moment restrictions and
GMM estimation.231
xviii Contents
9.7.3 An example: Comparison of different short-term
interest rate models.233
Exercises .234
10 Interest Rate Markets.239
10.1 Elements of interest rate markets.240
10.1.1 Bank account (money market account)
and short rates.241
10.1.2 Zero-coupon bonds and spot rates.241
10.1.3 Forward rates.244
10.1.4 Swap rates and interest rate swaps .245
10.1.5 Caps, floors, and swaptions.247
10.2 Yield curve estimation.247
10.2.1 Nonparametric regression using spline
basis functions.248
10.2.2 Parametric models.248
10.3 Multivariate time series of bond yields and other
interest rates.252
10.4 Stochastic interest rates and short-rate models.255
10.4.1 Vasicek, Cox-Ingersoll-Ross, and Hull-White models . . 258
10.4.2 Bond option prices .259
10.4.3 Black-Karasinski model.260
10.4.4 Multifactor affine yield models.261
10.5 Stochastic forward rate dynamics and pricing of LIBOR and
swap rate derivatives.261
10.5.1 Standard market formulas based on Black's model
of forward prices.262
10.5.2 Arbitrage-free pricing: martingales and numeraires.263
10.5.3 LIBOR and swap market models.264
10.5.4 The HJM models of the instantaneous forward rate . 266
10.6 Parameter estimation and model selection.267
10.6.1 Calibrating interest rate models in the
financial industry.267
10.6.2 Econometric approach to fitting
term-structure models .270
10.6.3 Volatility smiles and a substantive-empirical approach. 271
Exercises .272
11 Statistical Trading Strategies.275
11.1 Technical analysis, trading strategies,
and data-snooping checks.277
11.1.1 Technical analysis.277
11.1.2 Momentum and contrarian strategies .279
Contents xix
11.1.3 Pairs trading strategies.279
11.1.4 Empirical testing of the profitability
of trading strategies .282
11.1.5 Value investing and knowledge-based
trading strategies.285
11.2 High-frequency data, market microstructure, and associated
trading strategies.286
11.2.1 Institutional background and stylized facts about
transaction data.287
11.2.2 Bid-ask bounce and nonsynchronous trading models . . . 291
11.2.3 Modeling time intervals between trades .292
11.2.4 Inference on underlying price process .297
11.2.5 Real-time trading systems.299
11.3 Transaction costs and dynamic trading.300
11.3.1 Estimation and analysis of transaction costs.300
11.3.2 Heterogeneous trading objectives and strategies.300
11.3.3 Multiperiod trading and dynamic strategies.301
Exercises .302
12 Statistical Methods in Risk Management.305
12.1 Financial risks and measures of market risk.306
12.1.1 Types of financial risks.306
12.1.2 Internal models for capital requirements.307
12.1.3 Vail and other measures of market risk .307
12.2 Statistical models for Vail and ES.309
12.2.1 The Gaussian convention and the ^-modification.309
12.2.2 Applications of PCA and an example.310
12.2.3 Time series models.311
12.2.4 Backtesting VaR models .311
12.3 Measuring risk for nonlinear portfolios.312
12.3.1 Local valuation via Taylor expansions.312
12.3.2 Full valuation via Monte Carlo.314
12.3.3 Multivariate copula functions.314
12.3.4 Variance reduction techniques.316
12.4 Stress testing and extreme value theory .318
12.4.1 Stress testing.318
12.4.2 Extraordinary losses and extreme value theory.318
12.4.3 Scenario analysis and Monte Carlo simulations.321
Exercises .321
xx Contents
Appendix A. Martingale Theory and Central Limit Theorems . 325
Appendix B. Limit Theorems for Stationary Processes.331
Appendix C. Limit Theorems Underlying Unit-Root Tests
and Cointegration.333
References.337
Index.349 |
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| index_date | 2024-07-02T19:46:14Z |
| indexdate | 2024-07-09T21:11:08Z |
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| isbn | 9780387778266 |
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| spelling | Lai, Tze Leung 1945- Verfasser (DE-588)135683971 aut Statistical models and methods for financial markets Tze Leung Lai ; Haipeng Xing New York, NY Springer 2008 XX, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Finances - Modèles mathématiques Finances - Méthodes statistiques Finanças (métodos estatísticos;modelos matemáticos) larpcal Martingais larpcal Matemática aplicada larpcal Processos estocásticos larpcal Mathematisches Modell Finance Mathematical models Finance Statistical methods Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s DE-604 Kreditmarkt (DE-588)4073788-3 s Xing, Haipeng Verfasser (DE-588)13193113X aut Erscheint auch als Online-Ausgabe 978-0-387-77827-3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016307695&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lai, Tze Leung 1945- Xing, Haipeng Statistical models and methods for financial markets Finances - Modèles mathématiques Finances - Méthodes statistiques Finanças (métodos estatísticos;modelos matemáticos) larpcal Martingais larpcal Matemática aplicada larpcal Processos estocásticos larpcal Mathematisches Modell Finance Mathematical models Finance Statistical methods Kreditmarkt (DE-588)4073788-3 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4073788-3 (DE-588)4017195-4 (DE-588)4123623-3 |
| title | Statistical models and methods for financial markets |
| title_auth | Statistical models and methods for financial markets |
| title_exact_search | Statistical models and methods for financial markets |
| title_exact_search_txtP | Statistical models and methods for financial markets |
| title_full | Statistical models and methods for financial markets Tze Leung Lai ; Haipeng Xing |
| title_fullStr | Statistical models and methods for financial markets Tze Leung Lai ; Haipeng Xing |
| title_full_unstemmed | Statistical models and methods for financial markets Tze Leung Lai ; Haipeng Xing |
| title_short | Statistical models and methods for financial markets |
| title_sort | statistical models and methods for financial markets |
| topic | Finances - Modèles mathématiques Finances - Méthodes statistiques Finanças (métodos estatísticos;modelos matemáticos) larpcal Martingais larpcal Matemática aplicada larpcal Processos estocásticos larpcal Mathematisches Modell Finance Mathematical models Finance Statistical methods Kreditmarkt (DE-588)4073788-3 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finances - Modèles mathématiques Finances - Méthodes statistiques Finanças (métodos estatísticos;modelos matemáticos) Martingais Matemática aplicada Processos estocásticos Mathematisches Modell Finance Mathematical models Finance Statistical methods Kreditmarkt Finanzmathematik Lehrbuch |
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