Nonparametric Finance.

Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Statistical Finance -- 1.2 Risk Management -- 1.3 Portfolio Management -- 1.4 Pricing of Securities -- Part I Statistical Finance -- Chapter 2 Financial Instruments -- 2.1 Stocks -- 2.1.1 Stock Indexes -- 2.1.1.1 Definition of a Stock Index -- 2.1.1.2 Uses of Stock Indexes -- 2.1.1.3 Examples of Stock Indexes -- 2.1.2 Stock Prices and Returns -- 2.1.2.1 Initial Price Data -- 2.1.2.2 Sampling of Prices -- 2.1.2.3 Stock Returns -- 2.2 Fixed Income Instruments -- 2.2.1 Bonds -- 2.2.2 Interest Rates -- 2.2.2.1 Definitions of Interest Rates -- 2.2.2.2 The Risk Free Rate -- 2.2.3 Bond Prices and Returns -- 2.3 Derivatives -- 2.3.1 Forwards and Futures -- 2.3.1.1 Forwards -- 2.3.1.2 Futures -- 2.3.2 Options -- 2.3.2.1 Calls and Puts -- 2.3.2.2 Applications of Options -- 2.3.2.3 Exotic Options -- 2.4 Data Sets -- 2.4.1 Daily S&amp -- P 500 Data -- 2.4.2 Daily S&amp -- P 500 and Nasdaq‐100 Data -- 2.4.3 Monthly S&amp -- P 500, Bond, and Bill Data -- 2.4.4 Daily US Treasury 10 Year Bond Data -- 2.4.5 Daily S&amp -- P 500 Components Data -- Chapter 3 Univariate Data Analysis -- 3.1 Univariate Statistics -- 3.1.1 The Center of a Distribution -- 3.1.1.1 The Mean and the Conditional Mean -- 3.1.1.2 The Median and the Conditional Median -- 3.1.1.3 The Mode and the Conditional Mode -- 3.1.2 The Variance and Moments -- 3.1.2.1 The Variance and the Conditional Variance -- 3.1.2.2 The Upper and Lower Partial Moments -- 3.1.2.3 The Upper and Lower Conditional Moments -- 3.1.3 The Quantiles and the Expected Shortfalls -- 3.1.3.1 The Quantiles and the Conditional Quantiles -- 3.1.3.2 The Expected Shortfalls -- 3.2 Univariate Graphical Tools -- 3.2.1 Empirical Distribution Function Based Tools -- 3.2.1.1 The Empirical Distribution Function -- 3.2.1.2 The Tail Plots.

3.2.1.3 Regression Plots of Tails -- 3.2.1.4 The Empirical Quantile Function -- 3.2.2 Density Estimation Based Tools -- 3.2.2.1 The Histogram -- 3.2.2.2 The Kernel Density Estimator -- 3.3 Univariate Parametric Models -- 3.3.1 The Normal and Log‐normal Models -- 3.3.1.1 The Normal and Log‐normal Distributions -- 3.3.1.2 Modeling Stock Prices -- 3.3.2 The Student Distributions -- 3.3.2.1 Properties of Student Distributions -- 3.3.2.2 Estimation of the Parameters of a Student Distribution -- 3.4 Tail Modeling -- 3.4.1 Modeling and Estimating Excess Distributions -- 3.4.1.1 Modeling Excess Distributions -- 3.4.1.2 Estimation -- 3.4.2 Parametric Families for Excess Distributions -- 3.4.2.1 The Exponential Distributions -- 3.4.2.2 The Pareto Distributions -- 3.4.2.3 The Gamma Distributions -- 3.4.2.4 The Generalized Pareto Distributions -- 3.4.2.5 The Weibull Distributions -- 3.4.2.6 A Three Parameter Family -- 3.4.3 Fitting the Models to Return Data -- 3.4.3.1 S&amp -- P 500 Daily Returns: Maximum Likelihood -- 3.4.3.2 Tail Index Estimation for S&amp -- P 500 Components -- 3.5 Asymptotic Distributions -- 3.5.1 The Central Limit Theorems -- 3.5.1.1 Sums of Independent Random Variables -- 3.5.1.2 Sums of Independent and Identically Distributed Random Variables -- 3.5.1.3 Sums of Dependent Random Variables -- 3.5.2 The Limit Theorems for Maxima -- 3.5.2.1 Weak Convergence of Maxima -- 3.5.2.2 Extreme Value Distributions -- 3.5.2.3 Convergence to an Extreme Value Distribution -- 3.5.2.4 Generalized Pareto Distributions -- 3.5.2.5 Convergence to a Generalized Pareto Distribution -- 3.6 Univariate Stylized Facts -- Chapter 4 Multivariate Data Analysis -- 4.1 Measures of Dependence -- 4.1.1 Correlation Coefficients -- 4.1.1.1 Linear Correlation -- 4.1.1.2 Spearman's Rank Correlation -- 4.1.1.3 Kendall's Rank Correlation.

4.1.1.4 Relations between the Correlation Coefficients -- 4.1.2 Coefficients of Tail Dependence -- 4.1.2.1 Tail Coefficients in Terms of the Copula -- 4.1.2.2 Estimation of Tail Coefficients -- 4.1.2.3 Tail Coefficients for Parametric Families -- 4.2 Multivariate Graphical Tools -- 4.2.1 Scatter Plots -- 4.2.2 Correlation Matrix: Multidimensional Scaling -- 4.2.2.1 Correlation Matrix -- 4.2.2.2 Multidimensional Scaling -- 4.3 Multivariate Parametric Models -- 4.3.1 Multivariate Gaussian Distributions -- 4.3.2 Multivariate Student Distributions -- 4.3.3 Normal Variance Mixture Distributions -- 4.3.4 Elliptical Distributions -- 4.4 Copulas -- 4.4.1 Standard Copulas -- 4.4.1.1 Finding the Copula of a Multivariate Distribution -- 4.4.1.2 Constructing a Multivariate Distribution from a Copula -- 4.4.2 Nonstandard Copulas -- 4.4.3 Sampling from a Copula -- 4.4.3.1 Simulation from a Copula -- 4.4.3.2 Transforming the Sample -- 4.4.3.3 Transforming the Sample by Estimating the Margins -- 4.4.3.4 Empirical Copula -- 4.4.3.5 Maximum Likelihood Estimation -- 4.4.4 Examples of Copulas -- 4.4.4.1 The Gaussian Copulas -- 4.4.4.2 The Student Copulas -- 4.4.4.3 Other Copulas -- 4.4.4.4 Empirical Results -- Chapter 5 Time Series Analysis -- 5.1 Stationarity and Autocorrelation -- 5.1.1 Strict Stationarity -- 5.1.1.1 Random Walk -- 5.1.2 Covariance Stationarity and Autocorrelation -- 5.1.2.1 Autocovariance and Autocorrelation for Scalar Time Series -- 5.1.2.2 Autocovariance for Vector Time Series -- 5.2 Model Free Estimation -- 5.2.1 Descriptive Statistics for Time Series -- 5.2.2 Markov Models -- 5.2.3 Time Varying Parameter -- 5.2.3.1 Local Likelihood -- 5.2.3.2 Local Least Squares -- 5.2.3.3 Time Varying Estimators for the Excess Distribution -- 5.3 Univariate Time Series Models -- 5.3.1 Prediction and Conditional Expectation -- 5.3.2 ARMA Processes.

5.3.2.1 Innovation Processes -- 5.3.2.2 Moving Average Processes -- 5.3.2.3 Autoregressive Processes -- 5.3.2.4 ARMA Processes -- 5.3.3 Conditional Heteroskedasticity Models -- 5.3.3.1 ARCH Processes -- 5.3.3.2 GARCH Processes -- 5.3.3.3 ARCH(∞) Model -- 5.3.3.4 Asymmetric GARCH Processes -- 5.3.3.5 The Moment Generating function -- 5.3.3.6 Parameter Estimation -- 5.3.3.7 Fitting the GARCH(1,1) Model -- 5.3.4 Continuous Time Processes -- 5.3.4.1 The Brownian Motion -- 5.3.4.2 Diffusion Processes and Itô's Lemma -- 5.3.4.3 The Geometric Brownian Motion -- 5.3.4.4 Girsanov's Theorem -- 5.4 Multivariate Time Series Models -- 5.4.1 MGARCH Models -- 5.4.2 Covariance in MGARCH Models -- 5.5 Time Series Stylized Facts -- Chapter 6 Prediction -- 6.1 Methods of Prediction -- 6.1.1 Moving Average Predictors -- 6.1.1.1 One‐Sided Moving Average -- 6.1.1.2 Exponential Moving Average -- 6.1.2 State Space Predictors -- 6.1.2.1 Linear Regression -- 6.1.2.2 Kernel Regression -- 6.2 Forecast Evaluation -- 6.2.1 The Sum of Squared Prediction Errors -- 6.2.1.1 Out‐of‐Sample Sum of Squares -- 6.2.1.2 In‐Sample Sum of Squares -- 6.2.1.3 Visual Diagnostics -- 6.2.2 Testing the Prediction Accuracy -- 6.2.2.1 Diebold-Mariano Test -- 6.2.2.2 Tests Using Sample Correlation and Covariance -- 6.3 Predictive Variables -- 6.3.1 Risk Indicators -- 6.3.1.1 Default Spread -- 6.3.1.2 Credit Spreads -- 6.3.1.3 Volatility Indexes -- 6.3.2 Interest Rate Variables -- 6.3.2.1 Term Spread -- 6.3.2.2 Real Yield -- 6.3.3 Stock Market Indicators -- 6.3.3.1 Dividend Price Ratio and Dividend Yield -- 6.3.3.2 Valuation in Stock Markets -- 6.3.3.3 Relative Valuation -- 6.3.4 Sentiment Indicators -- 6.3.4.1 Purchasing Managers Index -- 6.3.4.2 Investor and Consumer Sentiment -- 6.3.5 Technical Indicators -- 6.4 Asset Return Prediction -- 6.4.1 Prediction of S&amp -- P 500 Returns -- 6.4.1.1 S&amp.

P 500 Returns -- 6.4.1.2 Linear Regression for Predicting S&amp -- P 500 Returns -- 6.4.2 Prediction of 10‐Year Bond Returns -- 6.4.2.1 10‐Year Bond Returns -- 6.4.2.2 Linear Regression for Predicting 10‐Year Bond Returns -- Part II Risk Management -- Chapter 7 Volatility Prediction -- 7.1 Applications of Volatility Prediction -- 7.1.1 Variance and Volatility Trading -- 7.1.2 Covariance Trading -- 7.1.3 Quantile Estimation -- 7.1.4 Portfolio Selection -- 7.1.5 Option Pricing -- 7.2 Performance Measures for Volatility Predictors -- 7.3 Conditional Heteroskedasticity Models -- 7.3.1 GARCH Predictor -- 7.3.1.1 Predicting the Squared Returns -- 7.3.1.2 Predicting the Realized Volatility -- 7.3.1.3 S&amp -- P 500 Volatility Prediction with GARCH(1,1) -- 7.3.2 ARCH Predictor -- 7.3.2.1 Predicting the Squared Returns -- 7.3.2.2 S&amp -- P 500 Volatility Prediction with ARCH(p) -- 7.4 Moving Average Methods -- 7.4.1 Sequential Sample Variance -- 7.4.2 Exponentially Weighted Moving Average -- 7.4.2.1 Asymmetric Exponentially Weighted Moving Average -- 7.5 State Space Predictors -- 7.5.1 Linear Regression Predictor -- 7.5.1.1 Prediction with Volatility and Mean -- 7.5.1.2 Prediction with Past Squared Returns -- 7.5.2 Kernel Regression Predictor -- Chapter 8 Quantiles and Value‐at‐Risk -- 8.1 Definitions of Quantiles -- 8.2 Applications of Quantiles -- 8.2.1 Reserve Capital -- 8.2.1.1 Value‐at‐Risk of a Portfolio -- 8.2.1.2 Decomposition of the Loss of a Portfolio -- 8.2.1.3 Losses over Several Periods -- 8.2.2 Margin Requirements -- 8.2.3 Quantiles as a Risk Measure -- 8.3 Performance Measures for Quantile Estimators -- 8.3.1 Measuring the Probability of Exceedances -- 8.3.1.1 Cross‐Validation -- 8.3.1.2 Probability Differences -- 8.3.1.3 Confidence of the Performance Measure -- 8.3.1.4 Probability Differences Over All Time Intervals.

8.3.2 A Loss Function for Quantile Estimation.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.