Financial Econometrics, Mathematics and Statistics: Theory, Method and Application

Preface
Contents
1 Introduction to Financial Econometrics, Mathematics, and Statistics
	Abstract
	1.1 Introduction
	1.2 Regression and Financial Econometrics
		1.2.1 Single-Equation Regression Methods
		1.2.2 Simultaneous Equation Models
		1.2.3 Panel Data Analysis
		1.2.4 Alternative Methods to Deal with Measurement Error
		1.2.5 Time-Series Analysis
	1.3 Financial Statistics
		1.3.1 Statistical Distributions
		1.3.2 Principle Components and Factor Analysis
		1.3.3 Nonparametric and Semiparametric Analyses
		1.3.4 Cluster Analysis
	1.4 Applications of Financial Econometrics, Mathematics and Statistics
		1.4.1 Asset Pricing
		1.4.2 Corporate Finance
		1.4.3 Financial Institution
		1.4.4 Investment and Portfolio Management
		1.4.5 Option Pricing Model
		1.4.6 Futures and Hedging
		1.4.7 Mutual Fund
		1.4.8 Credit Risk Modeling
		1.4.9 Other Applications
	1.5 Overall Discussion of This Book
		1.5.1 Regression and Financial Econometrics
		1.5.2 Time-Series Analysis and Its Application
		1.5.3 Statistical Distributions and Option Pricing Model
		1.5.4 Statistics, Itô’s Calculus and Option Pricing Model
	1.6 Conclusion
	Appendix: Keywords for Chaps. 2–24
	Bibliography
Regression and Financial Econometrics
2 Multiple Linear Regression
	Abstract
	2.1 Introduction
	2.2 The Model and Its Assumptions
	2.3 Estimating Multiple Regression Parameters
	2.4 The Residual Standard Error and the Coefficient of Determination
	2.5 Tests on Sets and Individual Regression Coefficients
	2.6 Confidence Interval for the Mean Response and Prediction Interval for the Individual Response
	2.7 Business and Economic Applications
	2.8 Using Computer Programs to Do Multiple Regression Analyses
		2.8.1 SAS Program for Multiple Regression Analysis
	2.9 Conclusion
	Appendix 1: Derivation of the Sampling Variance of the Least Squares Slope Estimations
	Appendix 2: Cross-sectional Relationship Among Price Per Share, Dividend Per Share, and Return Earning Per Share
	Bibliography
3 Other Topics in Applied Regression Analysis
	Abstract
	3.1 Introduction
	3.2 Multicollinearity
	3.3 Heteroscedasticity
	3.4 Autocorrelation
	3.5 Model Specification and Specification Bias
	3.6 Nonlinear Models
	3.7 Lagged Dependent Variables
	3.8 Dummy Variables
	3.9 Regression with Interaction Variables
	3.10 Regression Approach to Investigating the Effect of Alternative Business Strategies
	3.11 Logistic Regression and Credit Risk Analysis: Ohlson’s and Shumway’s Methods for Estimating Default Probability
	3.12 Conclusion
	Appendix 1: Dynamic Ratio Analysis
	Appendix 2: Term Structure of Interest Rate
	Appendix 3: Partial Adjustment Dividend Behavior Model
		Behavioral Considerations of Dividend Policy
			Partial Adjustment and Information Content Models
			An Integration Model
	Appendix 4: Logistic Model and Probit Model
	Appendix 5: SAS Code for Hazard Model in Bankruptcy Forecasting
	Bibliography
4 Simultaneous Equation Models
	Abstract
	4.1 Introduction
	4.2 Discussion of Simultaneous Equation System
	4.3 Two-Stage and Three-Stage Least Squares Method
		4.3.1 Identification Problem
		4.3.2 Two-Stage Least Squares
		4.3.3 Three-Stage Least Squares
	4.4 Application of Simultaneous Equation in Finance Research
	4.5 Conclusion
	Bibliography
5 Econometric Approach to Financial Analysis, Planning, and Forecasting
	5.1 Introduction
	5.2 Simultaneous Nature of Financial Analysis, Planning, and Forecasting
		5.2.1 Basic Concepts of Simultaneous Econometric Models
		5.2.2 Interrelationship of Accounting Information
		5.2.3 Interrelationship of Financial Policies
	5.3 The Simultaneity and Dynamics of Corporate-Budgeting Decisions
		5.3.1 Definitions of Endogenous and Exogenous Variables
		5.3.2 Model Specification and Applications
	5.4 Applications of SUR Estimation Method in Financial Analysis and Planning
		5.4.1 The Role of Firm-Related Variables in Capital Asset Pricing
		5.4.2 The Role of Capital Structure in Corporate-Financing Decisions
	5.5 Applications of Structural Econometric Models in Financial Analysis and Planning
		5.5.1 A Brief Review
		5.5.2 AT&T’s Econometric Planning Model
	5.6 Programming Versus Simultaneous Versus Econometric Financial Models
	5.7 Financial Analysis and Business Policy Decisions
	5.8 Conclusion
	Appendix: Johnson & Johnson as a Case Study
		Introduction
		Study of the Company’s Operations
		Analysis of the Company’s Financial Performance
		Variables and Time Horizon
		Model and Empirical Results,
	Bibliography
6 Fixed Effects Versus Random Effects in Finance Research
	Abstract
	6.1 Introduction
	6.2 The Dummy Variable Technique and the Error Component Model
	6.3 Impacts of Firm Effect and Time Effect on Stock Price Variation
	6.4 Functional Form and Pooled Time-Series and Cross-Sectional Data
	6.5 Clustering Effect and Clustered Standard Errors
	6.6 Hausman Test for Determining Either Fixed Effects Model or Random Effects Model
	6.7 Efficient Firm Fixed Effects Estimator and Efficient Correlated Random Effects Estimator
	6.8 Empirical Evidence of Optimal Payout Ratio Under Uncertainty and the Flexibility Hypothesis
	6.9 Conclusion
	Appendix: Optimal Payout Ratio Under Uncertainty and the Flexibility Hypothesis: Theory and Empirical Evidence
		Hypothesis Development
		Sample Description
	Bibliography
7 Alternative Methods to Deal with Measurement Error
	Abstract
	7.1 Introduction
	7.2 Effects of Errors-in-Variables in Different Cases
		7.2.1 Bivariate Normal Case
		7.2.2 Multivariate Case
			7.2.2.1 The Classical Case
			7.2.2.2 The Constrained Classical Case
	7.3 Estimation Methods When Variables Are Subject to Error
		7.3.1 Classical Estimation Method
			7.3.1.1 The Classical Method to a Simple Regression Analysis
			7.3.1.2 The Classical Method to a Multiple Regression Analysis
			7.3.1.3 The Constrained Classical Method
		7.3.2 Grouping Method
		7.3.3 Instrumental Variable Method
		7.3.4 Mathematical Method
			7.3.4.1 Bivariate Case
			7.3.4.2 Multivariate Case
		7.3.5 Maximum Likelihood Method
		7.3.6 LISREL and MIMIC Methods
			7.3.6.1 Structural Model (Lisrel Model)
			7.3.6.2 Mimic Model
		7.3.7 Bayesian Approach
	7.4 Applications of Errors-in-Variables Models in Finance Research
		7.4.1 Cost of Capital
		7.4.2 Capital Asset Pricing Model
		7.4.3 Capital Structure
		7.4.4 Measurement Error in Investment Equation
	7.5 Conclusion
	Bibliography
8 Three Alternative Methods in Testing Capital Asset Pricing Model
	Abstract
	8.1 Introduction
	8.2 Empirical Test on Capital Asset Pricing Model
		8.2.1 Data
		8.2.2 Grouping Method for Testing Capital Asset Pricing Model
		8.2.3 Instrumental Variable Method for Testing Capital Asset Pricing Model
		8.2.4 Applying Instrumental Variable Methods into Grouping Sample
		8.2.5 Maximum Likelihood Method for Testing Capital Asset Pricing Model
		8.2.6 Asset Pricing Model Tests with Individual Stocks
	8.3 Normality Test for Time-Series Estimators and Future Research
	8.4 The Investment Horizon of Beta Estimation
	8.5 Conclusion
	Bibliography
9 Spurious Regression and Data Mining in Conditional Asset Pricing Models
	Abstract
	9.1 Introduction
	9.2 Model Specification
	9.3 Spurious Regression and Data Mining in Predictive Regressions
	9.4 Spurious Regression, Data Mining, and Conditional Asset Pricing
	9.5 The Data
	9.6 The Models
		9.6.1 Predictive Regressions
		9.6.2 Conditional Asset Pricing Models
	9.7 Results for Predictive Regressions
		9.7.1 Pure Spurious Regression
		9.7.2 Spurious Regression and Data Mining
	9.8 Results for Conditional Asset Pricing Models
		9.8.1 Cases with Small Amounts of Persistence
		9.8.2 Cases with Persistence
		9.8.3 Suppressing Time-Varying Alphas
		9.8.4 Suppressing Time-Varying Betas
		9.8.5 A Cross Section of Asset Returns
		9.8.6 Revisiting Previous Evidence
	9.9 Solutions to the Problems of Spurious Regression and Data Mining
		9.9.1 Solutions in Predictive Regressions
		9.9.2 Solutions in Conditional Asset Pricing Models
	9.10 Robustness of the Asset Pricing Results
		9.10.1 Multiple Instruments
		9.10.2 Multiple-Beta Models
		9.10.3 Predicting the Market Return
		9.10.4 Simulations Under the Alternative Hypothesis
	9.11 Conclusion
	Bibliography
Time-Series Analysis and Its Applications
10 Time Series: Analysis, Model, and Forecasting
	10.1 Introduction
	10.2 The Classical Time-Series Component Model
	10.3 Moving Average and Seasonally Adjusted Time Series
	10.4 Linear and Log Linear Time Trend Regressions
	10.5 Exponential Smoothing and Forecasting
	10.6 Autoregressive Forecasting Model
	10.7 ARIMA Models
	10.8 Autoregressive Conditional Heteroscedasticity
		10.8.1 Autoregressive Conditional Heteroscedasticity (ARCH) Models
		10.8.2 Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Model
		10.8.3 The GARCH Universe
	10.9 Composite Forecasting
		10.9.1 Composite Forecasting of Livestock Prices
		10.9.2 Combined Forecasting of the Taiwan Weighted Stock Index
	10.10 Conclusion
	Appendix 1: The Holt–Winters Forecasting Model for Seasonal Series
	Appendix 2: Composite Forecasting Method
	Bibliography
11 Hedge Ratio and Time-Series Analysis
	Abstract
	11.1 Introduction
	11.2 Alternative Theories for Deriving the Optimal Hedge Ratio
		11.2.1 Static Case
			11.2.1.1 Minimum-Variance Hedge Ratio
			11.2.1.2 Optimum Mean-Variance Hedge Ratio
			11.2.1.3 Sharpe Hedge Ratio
			11.2.1.4 Maximum Expected Utility Hedge Ratio
			11.2.1.5 Minimum Mean Extended-Gini Coefficient Hedge Ratio
			11.2.1.6 Optimum Mean-MEG Hedge Ratio
			11.2.1.7 Minimum Generalized Semivariance Hedge Ratio
			11.2.1.8 Optimum Mean-Generalized Semivariance Hedge Ratio
			11.2.1.9 Minimum Value-at-Risk Hedge Ratio
		11.2.2 Dynamic Case
		11.2.3 Case with Production and Alternative Investment Opportunities
	11.3 Alternative Methods for Estimating the Optimal Hedge Ratio
		11.3.1 Estimation of the Minimum-Variance (MV) Hedge Ratio
			11.3.1.1 OLS Method
			11.3.1.2 ARCH and GARCH Methods
			11.3.1.3 Regime-Switching GARCH Model
			11.3.1.4 Random Coefficient Method
			11.3.1.5 Cointegration and Error Correction Method
		11.3.2 Estimation of the Optimum Mean-Variance and Sharpe Hedge Ratios
		11.3.3 Estimation of the Maximum Expected Utility Hedge Ratio
		11.3.4 Estimation of Mean Extended-Gini (MEG) Coefficient-Based Hedge Ratios
		11.3.5 Estimation of Generalized Semivariance (GSV) Based Hedge Ratios
	11.4 Hedging Horizon, Maturity of Futures Contract, Data Frequency, and Hedging Effectiveness
	11.5 Empirical Results of Hedge Ratio Estimation
		11.5.1 OLS Method
		11.5.2 ARCH GARCH
		11.5.3 EGARCH
		11.5.4 GJR-GARCH
		11.5.5 TGARCH
	11.6 Conclusion
	Appendix 1: Theoretical Models
	Appendix 2: Empirical Models
	Appendix 3: Monthly Data of S&P 500 Index and Its Futures
	Bibliography
Statistical Distributions, Option Pricing Model and Risk Management
12 The Binomial, Multinomial Distributions, and Option Pricing Model
	Abstract
	12.1 Introduction
	12.2 Binomial Distribution
	12.3 The Simple Binomial Option Pricing Model
	12.4 The Generalized Binomial Option Pricing Model
	12.5 Multinomial Option Pricing Model
		12.5.1 Derivation of the Option Pricing Model
		12.5.2 The Black and Scholes Model as a Limiting Case
	12.6 A Lattice Framework for Option Pricing
		12.6.1 Modification of the Two-State Approach for a Single-State Variable
		12.6.2 A Lattice Model for Valuation of Options on Two Underlying Assets
	12.7 Conclusion
	Bibliography
13 Two Alternative Binomial Option Pricing Model Approaches to Derive Black–Scholes Option Pricing Model
	Abstract
	13.1 Introduction
	13.2 The Two-State Option Pricing Model of Rendleman and Bartter
		13.2.1 The Discrete-Time Model
		13.2.2 The Continuous Time Model
	13.3 The Binomial Option Pricing Model of CRR
		13.3.1 The Binomial Option Pricing Formula of CRR
		13.3.2 Limiting Case
	13.4 Comparison of the Two Approaches
	13.5 Conclusion
	Appendix: The Binomial Theorem
	Bibliography
14 Normal, Lognormal Distribution, and Option Pricing Model
	Abstract
	14.1 Introduction
	14.2 The Normal Distribution
	14.3 The Lognormal Distribution
	14.4 The Lognormal Distribution and Its Relationship to the Normal Distribution
	14.5 Multivariate Normal and Lognormal Distributions
	14.6 The Normal Distribution as an Application to the Binomial and Poisson Distributions
	14.7 Applications of the Lognormal Distribution in Option Pricing
	14.8 The Bivariate Normal Density Function
	14.9 American Call Options
		14.9.1 Price American Call Options by the Bivariate Normal Distribution
		14.9.2 Pricing an American Call Option: An Example
	14.10 Price Bounds for Options
		14.10.1 Options Written on Nondividend- Paying Stocks
		14.10.2 Options Written on Dividend-Paying Stocks
	14.11 Conclusion
	Appendix 1: Microsoft Excel Program for Calculating Cumulative Bivariate Normal Density Function
	Appendix 2: Microsoft Excel Program for Calculating the American Call Options
	Bibliography
15 Copula, Correlated Defaults, and Credit VaR
	Abstract
	15.1 Introduction
	15.2 Methodology
		15.2.1 CreditMetrics
			15.2.1.1 Value at Risk Due to Credit
			15.2.1.2 Exposures
			15.2.1.3 Correlations
		15.2.2 Copula Function
			15.2.2.1 Copula Function
			15.2.2.2 Sklar’s Theorem
			15.2.2.3 Copula of F
		15.2.3 Factor Copula Model
	15.3 Experimental Results
		15.3.1 Data
			15.3.1.1 Requirements of Data Input
		15.3.2 Simulation
		15.3.3 Discussion
			15.3.3.1 Tool and Interface Preview
				Basic Information of Experimental Data: (Pie Chart)
				Information According to Experimental Data: (Statistic Numbers)
				Set Criteria and Derive Fundamental Experimental Result
				Report of Overall VaR Contributor
			15.3.3.2 Experimental Result and Discussion
	15.4 Conclusion
	Bibliography
16 Multivariate Analysis: Discriminant Analysis and Factor Analysis
	Abstract
	16.1 Introduction
	16.2 Important Concepts of Linear Algebra
	16.3 Two-Group Discriminant Analysis
	16.4 k-Group Discriminant Analysis
	16.5 Factor Analysis and Principal Component Analysis
	16.6 Conclusion
	Appendix 1: Relationship Between Discriminant Analysis and Dummy Regression Analysis
	Appendix 2: Principal Component Analysis
	Bibliography
Statistics, Itô’s Calculus and Option Pricing Model
17 Stochastic Volatility Option Pricing Models
	Abstract
	17.1 Introduction
	17.2 Nonclosed-Form Type of Option Pricing Model
	17.3 Review of Characteristic Function
	17.4 Closed-Form Type of Option Pricing Model
	17.5 Conclusion
	Appendix: The Market Price of the Risk
	Bibliography
18 Alternative Methods to Estimate Implied Variance: Review and Comparison
	Abstract
	18.1 Introduction
	18.2 Numerical Search Method and Closed-Form Derivation Method to Estimate Implied Variance
	18.3 MATLAB Approach to Estimate Implied Variance
	18.4 Approximation Approach to Estimate Implied Variance
	18.5 Some Empirical Results
		18.5.1 Cases from USA—Individual Stock Options
		18.5.2 Cases from China—ETF 50 Options
	18.6 Conclusion
	Bibliography
19 Numerical Valuation of Asian Options with Higher Moments in the Underlying Distribution
	Abstract
	19.1 Introduction
	19.2 Definitions and the Basic Binomial Model
	19.3 Edgeworth Binomial Model for Asian Option Valuation
	19.4 Upper Bound and Lower Bound for European-Asian Options
	19.5 Upper Bound and Lower Bound for American-Asian Options
	19.6 Numerical Examples
		19.6.1 Pricing European-Asian Options Under Lognormal Distribution
		19.6.2 Pricing American-Asian Options Under Lognormal Distribution
		19.6.3 Pricing European-Asian Options Under Distributions with Higher Moments
		19.6.4 Pricing American-Asian Options Under Distributions with Higher Moments
	19.7 Conclusion
	Bibliography
20 Itô’s Calculus: Derivation of the Black–Scholes Option Pricing Model
	Abstract
	20.1 Introduction
	20.2 The Itô Process and Financial Modeling
	20.3 Itô Lemma
	20.4 Stochastic Differential Equation Approach to Stock-Price Behavior
	20.5 The Pricing of an Option
	20.6 A Reexamination of Option Pricing
	20.7 Remarks on Option Pricing
	20.8 Conclusion
	Appendix: An Alternative Method to Derive the Black–Scholes Option Pricing Model
		Assumptions and the Present Value of the Expected Terminal Option Price
		Present Value of the Partial Expectation of the Terminal Stock Price
		Present Value of the Exercise Price Under Uncertainty
	Bibliography
21 Alternative Methods to Derive Option Pricing Models
	Abstract
	21.1 Introduction
	21.2 A Brief Review of Alternative Approaches for Deriving Option Pricing Model
		21.2.1 Binomial Model
		21.2.2 Black–Scholes Model
	21.3 Relationship Between Binomial OPM and Black–Scholes OPM
	21.4 Compare Cox et al. and Rendleman and Bartter Methods to Derive OPM
		21.4.1 Cox et al. Method
		21.4.2 Rendleman and Bartter Method
	21.5 Lognormal Distribution Approach to Derive Black–Scholes Model
	21.6 Using Stochastic Calculus to Derive Black–Scholes Model
	21.7 Conclusion
	Appendix: The Relationship Between Binomial Distribution and Normal Distribution
	Bibliography
22 Constant Elasticity of Variance Option Pricing Model: Integration and Detailed Derivation
	Abstract
	22.1 Introduction
	22.2 The CEV Diffusion and Its Transition Probability Density Function
	22.3 Review of Noncentral Chi-Square Distribution
	22.4 The Noncentral Chi-Square Approach to Option Pricing Model
		22.4.1 Detailed Derivations of C1 and C2
		22.4.2 Some Computational Considerations
	22.5 Conclusion
	Appendix: Proof of Feller’s Lemma
	Bibliography
23 Option Pricing and Hedging Performance Under Stochastic Volatility and Stochastic Interest Rates
	Abstract
	23.1 Introduction
	23.2 The Option Pricing Model
		23.2.1 Pricing Formula for European Options
		23.2.2 Hedging and Hedge Ratios
			23.2.2.1 Delta-Neutral Hedges
			23.2.2.2 Single-Instrument Minimum-Variance Hedges
		23.2.3 Implementation
	23.3 Data Description
	23.4 Empirical Tests
		23.4.1 Static Performance
		23.4.2 Dynamic Hedging Performance
			23.4.2.1 Effectiveness of Delta-Neutral Hedges
			23.4.2.2 Effectiveness of Single-Instrument Minimum-Variance Hedges
		23.4.3 Regression Analysis of Option Pricing and Hedging Errors
		23.4.4 Robustness of Empirical Results
	23.5 Conclusion
	Acknowledgments
	Appendix 1: Derivation of Stochastic Interest Model and Stochastic Volatility Model
	Bibliography
24 Nonparametric Method for European Option Bounds
	Abstract
	24.1 Introduction
	24.2 The Bounds
	24.3 Comparisons
	24.4 Extensions
	24.5 Empirical Study
	24.6 Conclusion
	Acknowledgements
	Appendix 1: Related Option Studies Adopting Nonparametric Method
	Appendix 2: Asset Pricing Model with a Stochastic Kernel
	Bibliography
Author Index
Subject Index