Although there are many books on mathematical finance, few deal with the statistical aspects of modern data analysis as applied to financial problems. This book fills this gap by addressing some of the most challenging issues facing any financial engineer. It shows how sophisticated mathematics and modern statistical techniques can be used in concrete financial problems.

Concerns of risk management are addressed by the control of extreme values, the fitting of distributions with heavy tails, the computation of values at risk (VaR), and other measures of risk. Data description techniques such as principal component analysis (PCA), smoothing, and regression are applied to the construction of yield and forward curve. Nonparametric estimation and nonlinear filtering are used for option pricing and earnings prediction.

The book is intended for undergraduate students majoring in financial engineering, or graduate students in a Master in finance or MBA program. Because it was designed as a teaching vehicle, it is sprinkled with practical examples using market data, and each chapter ends with exercises. Practical examples are solved in the computing environment of S-PLUS. They illustrate problems occurring in the commodity and energy markets, the fixed income markets as well as the equity markets, and even some new emerging markets like the weather markets.

The book can help quantitative analysts by guiding them through the details of statistical model estimation and implementation. It will also be of interest to researchers wishing to manipulate financial data, implement abstract concepts, and test mathematical theories, especially by addressing practical issues that are often neglected in the presentation of the theory.

Rene Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over seventy articles and six books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and he is on the editorial board of several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching of statistics, for research in signal analysis, and more recently, he contributed the library EVANESCE for the analysis of heavy tail distributions and copulas. The latter was included in the latest version of S-Plus. He has worked for many years on energy and weather derivatives, and he is recognized as a leading researcher and consultant in this area.

Klappentext

This is the first book at the graduate textbook level to discuss analyzing financial data with S-PLUS. Its originality lies in the introduction of tools for the estimation and simulation of heavy tail distributions and copulas, the computation of measures of risk, and the principal component analysis of yield curves. The book is aimed at undergraduate students in financial engineering; master students in finance and MBA's, and to practitioners with financial data analysis concerns.

Inhalt

Contents Part I Data Exploration, Estimation And Simulation 1 Univariate Exploratory Data Analysis 1.1 Data, Random Variables and Their Distributions 1.1.1 The PCS Data 1.1.2 The S&P 500 Index and Financial Returns 1.1.3 Random Variables and Their Distributions 1.1.4 Examples of Probability Distribution Families 1.2 First Exploratory Data Analysis Tools 1.2.1 Random Samples 1.2.2 Histograms 1.3 More Nonparametric Density Estimation 1.3.1 Kernel Density Estimation 1.3.2 Comparison with the Histogram 1.3.3 S&P Daily Returns 1.3.4 Importance of the Choice of the Bandwidth 1.4 Quantiles and Q-Q Plots 1.4.1 Understanding the Meaning of Q-Q Plots 1.4.2 Value at Risk and Expected Shortfall 1.5 Estimation from Empirical Data 1.5.1 The Empirical Distribution Function 1.5.2 Order Statistics 1.5.3 Empirical Q-Q Plots 1.6 Random Generators and Monte Carlo Samples 1.7 Extremes and Heavy Tail Distributions 1.7.1 S&P Daily Returns, Once More 1.7.2 The Example of the PCS Index 1.7.3 The Example of the Weekly S&P Returns Problems Notes & Complements 2 Multivariate Data Exploration 2.1 Multivariate Data and First Measure of Dependence 2.1.1 Density Estimation 2.1.2 The Correlation Coefficient 2.2 The Multivariate Normal Distribution 2.2.1 Simulation of Random Samples 2.2.2 The Bivariate Case 2.2.3 A Simulation Example 2.2.4 Let's Have Some Coffee 2.2.5 Is the Joint Distribution Normal? 2.3 Marginals and More Measures of Dependence 2.3.1 Estimation of the Coffee Log-Return Distributions 2.3.2 More Measures of Dependence 2.4 Copulas and Random Simulations 2.4.1 Copulas 2.4.2 First Examples of Copula Families 2.4.3 Copulas and General Bivariate Distributions 2.4.4 Fitting Copulas 2.4.5 Monte Carlo Simulations with Copulas 2.4.6 A Risk Management Example 2.5Principal Component Analysis 2.5.1 Identification of the Principal Components of a Data Set 2.5.2 PCA with S-Plus 2.5.3 Effective Dimension of the Space of Yield Curves 2.5.4 Swap Rate Curves Appendix 1: Calculus with Random Vectors and Matrices Appendix 2: Families of Copulas Problems Notes & Complements Part II Regression 3 Parametric Regression 3.1 Simple Linear Regression 3.1.1 Getting the Data 3.1.2 First Plots 3.1.3 Regression Set-up 3.1.4 Simple Linear Regression 3.1.5 Cost Minimizations 3.1.6 Regression as a Minimization Problem 3.2 Regression for Prediction & Sensitivities 3.2.1 Prediction 3.2.2 Introductory Discussion of Sensitivity and Robustness 3.2.3 Comparing L2 and L1 Regressions 3.2.4 Taking Another Look at the Coffee Data 3.3 Smoothing versus Distribution Theory 3.3.1 Regression and Conditional Expectation 3.3.2 Maximum Likelihood Approach 3.4 Multiple Regression 3.4.1 Notation 3.4.2 The S-Plus Function lm 3.4.3 R2 as a Regression Diagnostic 3.5 Matrix Formulation and Linear Models 3.5.1 Linear Models 3.5.2 Least Squares (Linear) Regression Revisited 3.5.3 First Extensions 3.5.4 Testing the CAPM 3.6 Polynomial Regression 3.6.1 Polynomial Regression as a Linear Model 3.6.2 Example of S-Plus Commands 3.6.3 Important Remark 3.6.4 Prediction with Polynomial Regression 3.6.5 Choice of the Degree p 3.7 Nonlinear Regression 3.8 Term Structure of Interest Rates: A Crash Course 3.9 Parametric Yield Curve Estimation 3.9.1 Estimation Procedures 3.9.2 Practical Implementation 3.9.3 S-Plus Experiments 3.9.4 Concluding Remarks Appendix: Cautionary Notes on Some S-Plus Idiosyncracies Problems Notes & Complements 4 Local & Nonparametric Regression 4.1 Review of the Regression Setup 4.2 Natural Splines as Local Smoothers 4.3 Non