Empirical Techniques in Finance (eBook)

Ramaprasad Bhar, Shigeyuki Hamori (Autoren)

eBook Download: PDF

2005 | 2005
XII, 243 Seiten
Springer Berlin (Verlag)
978-3-540-27642-5 (ISBN)

Infos

Includes traditional elements of financial econometrics but is not yet another volume in econometrics.

Discusses statistical and probability techniques commonly used in quantitative finance.

The reader will be able to explore more complex structures without getting inundated with the underlying mathematics.

 

Inhalt

Acknowledgements 7
Table of Contents 9
1 Introduction 13
2 Basic Probability Theory and Markov Chains 17
2.1 Random Variables 17
2.2 Function of Random Variable 19
2.3 Normal Random Variable 20
2.4 Lognormal Random Variable 21
2.5 Markov Chains 22
2.6 Passage Time 26
2.7 Examples and Exercises 28
References 29
3 Estimation Techniques 31
3.1 Models, Parameters and Likelihood - An Overview 31
3.2 Maximum Likelihood Estimation and Covariance Matrix of Parameters 32
3.3 MLE Example - Classical Linear Regression 34
3.4 Dependent Observations 35
3.5 Prediction Error Decomposition 36
3.6 Serially Correlated Errors - Overview 37
3.7 Constrained Optimization and the Covariance Matrix 39
3.8 Examples and Exercises 40
References 41
4 Non-Parametric Method of Estimation 43
4.1 Background 43
4.2 Non-Parametric Approach 44
4.3 Kernel Regression 45
4.4 Illustration 1 (EViews) 47
4.5 Optimal Bandwidth Seiection 48
4.6 Illustration 2 (EViews) 48
4.7 Examples and Exercises 50
References 51
5 Unit Root, Cointegration and Related Issues 53
5.1 Stationary Process 53
5.2 Unit Root 56
5.3 Dickey-Fuller Test 58
5.4 Cointegration 61
5.5 Residual-based Cointegration Test 62
5.6 Unit Root in a Regression Model 63
5.7 Application to Stocic Markets 64
References 66
6 VAR Modeling 67
6.1 Stationary Process 67
6.2 Granger Causality 69
6.3 Cointegration and Error Correction 71
6.4 Johansen Test 73
6.5 LA-VAR 74
6.6 Application to Stocic Prices 76
References 77
7 Time Varying Volatility Models 79
7.1 Background 79
7.2 ARCH and GARCH Models 80
7.3 TGARCH and EGARCH Models 83
7.4 Causality-in-Variance Approach 86
7.5 Information Flow between Price Change and Trading Volume 89
References 93
8 State-Space Models (I) 95
8.1 Background 95
8.2 Classical Regression 95
8.3 Important Time Series Processes 98
8.4 Recursive Least Squares 101
8.5 State-Space Representation 103
8.6 Examples and Exercises 106
References 115
9 State-Space Models (II) 117
9.1 Likelihood Function Maximization 117
9.2 EM Algorithm 120
9.3 Time Varying Parameters and Changing Conditional Variance (EViews) 123
9.4 GARCH and Stochastic Variance Model for Exchange Rate (EViews) 125
9.5 Examples and Exercises 128
References 138
10 Discrete Time Real Asset Valuation Model 139
10.1 Asset Price Basics 139
10.2 Mining Project Background 141
10.3 Example 1 142
10.4Example2 143
10.5 Example 3 145
10.6 Example4 147
Appendix 150
References 152
11 Discrete Time Model of Interest Rate 153
11.1 Preliminaries of Short Rate Lattice 153
11.2 Forward Recursion for Lattice and Elementary Price 157
11.3 Matching the Current Term Structure 160
11.4 Immunization: Application of Short Rate Lattice 161
11.5 Valuing Callable Bond 164
11.6 Exercises 165
References 166
12 Global Bubbles in Stock Markets and Linkages 167
12.1 Introduction 167
12.2 Speculative Bubbles 168
12.3 Review of Key Empirical Papers 170
12.3.1 Flood and Garber (1980) 170
12,3.2 West (1987) 172
12.3.3 Ikeda and Shibata (1992) 173
12.3.4 Wu (1997) 175
12.3.5 Wu (1995) 176
12.4 New Contribution 176
12.5 Global Stock Market Integration 177
12.6 Dynamic Linear Models for Bubble Solutions 179
12.7 Dynamic Linear Models for No-Bubble Solutions 184
12.8 Subset VAR for Linkages between Markets 186
12.9 Results and Discussions 187
12.10 Summary 198
References 199
13 Forward FX Market and the Risk Premium 205
13.1 Introduction 205
13.2 Alternative Approach to Model Risk Premia 207
13.3 The Proposed Model 208
13.4 State-Space Framework 213
13.5 Brief Description of Wolff/Cheung Model 216
13.6 Application of the Model and Data Description 217
13.7 Summary and Conclusions 221
Appendix 222
References 223
14 Equity Risk Premia from Derivative Prices 227
14.1 Introduction 227
14.2 The Theory behind the Modeling Framework 229
14.3 The Continuous Time State-Space Framework 232
14.4 Setting Up The Filtering Framework 235
14.5 The Data Set 240
14.6 Estimation Results 240
14.7 Summary and Conclusions 247
References 248
Index 251
About the Authors 254

Textauszug

4 Non-Parametric Method of Estimation (p.31)

4.1 Background

In some financial applications we may face a functional relationship between two variables Y and X without the benefit of a structural model to restrict the parametric form of the relation. In these situations, we can apply nonparametric estimation techniques to capture a wide variety of non- Hnearities without recourse to any one particular specification of the nonUnear relation. In contrast to a highly structured or parametric approach to estimating non-linearities, nonparametric estimation requires few assumptions about the nature of the non-linearities.

This is not to say that the approach is free of drawbacks. To begin with, the highly data-intensive nature of the process can make it somewhat costly. Further, nonparametric estimation is poorly suited to small samples and has been found to over fit the data. A regression curve describes the general relationship between an explanatory variable X and a response variable Y. Having observed X, the average value of Y is given by the regression function. The form of the regression function may teil us where higher Y-values are to be expected for certain values of X or where a special sort of dependence is indicated. A pre-selected parametric model might be too restricted to fit unexpected features of the data. The term "non-parametric" refers to the flexible functional form of the regression curve.

The non-parametric approach to a regression curve serves four main functions. First, it provides a versatile method for exploring a general relationship between two variables. Second, it gives predictions of observations yet to be made without reference to a fixed parametric model. Third, it provides a tool for finding spurious observations by studying the influence of isolated points. Fourth, it constitutes a flexible method for substituting missing values or interpolating between adjacent X values. The flexibility of the method is extremely helpful in a preliminary and exploratory Statistical analysis of a data set. When no a priori model Information about the regression curve is available, non-parametric analysis can help in providing simple parametric formulations of the regression relationship.

Produkt-Details

• Erscheint lt. Verlag: 28.12.2005
• Reihe/Serie: Springer Finance
• Reihe/Serie: Springer Finance
• Zusatzinfo: XII, 243 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• Schlagworte: Econometrics • Empirical Techniques • Expectation Maximisation • Finance • Financial Econometrics • Financial Markets • Investment • Markov Chain • markov chains • Modeling • Quantitative Finance
• ISBN-10: 3-540-27642-4 / 3540276424
• ISBN-13: 978-3-540-27642-5 / 9783540276425