Distributional Regularities of Financial Returns E-Book

Jakob Blatz

• Herausgeber: GRIN Verlag
• Sprache: Englisch

Veröffentlichungsjahr: 2011

Beschreibung

Seminar paper from the year 2008 in the subject Economics - Finance, grade: 1,7, Christian-Albrechts-University of Kiel, language: English, abstract: There is a long tradition of scholars seeking to understand the distributional regularities of financial returns. Research traces back to the turn of the 19th century. Since then, it underwent a lot of drastic changes, which are to be shown in this paper. The aim of this paper is to show theoretical models that account for the distributional regularities in financial returns as well as to illustrate the empirical analysis. It is necessary to understand the evolution of research on this topic because it came about in a consecutive manner. Thus, this paper will document over one hundred years of research on distributional properties of financial returns. The second chapter will start with the results of Louis Bachelier and his normal distribution hypothesis. Then it will describe Benoît Mandelbrot's groundbreaking results, which rejected Bachelier's normal hypothesis and introduced the Lévy-stable distributions. Mandelbrot's work had such an impact that it will be described in greater detail. The third chapter will present the results of research that followed after Mandelbrot's findings. It will also display and explain the results of recent research.

Leseprobe

Table of Content

List of Figures

List of Tables

1 Introduction

2 Mandelbrot and the L´ evy-stable Distributions

2.1 The L´ evy-stable distributions

2.1.1 Stability and Power-law Tail Behavior

2.1.2 Parameters

2.2 The Generalization of the Central Limit Theorem

2.3 Empirical Evidence of Mandelbrot’s Hypothesis

2.3.1 The Data

2.3.2 Frequency Distributions

2.3.3 Normal Probability Graphs

3 Research in the post-Mandelbrot Era

3.1 Recent Contributions: Power-law Behavior Outside the L´ evy-Regime

3.2 Explanation for the Power-law Tail Behavior

4 Summary

5 Appendix

Page 2

List of Figures

1 Leptokurtotic Behavior of the Empirical Distribution of Wool Price Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Normal Probability Graphs . . . . . . . . . . . . . . . . . . . . . 11 3 Normal Probability Graphs cont. . . . . . . . . . . . . . . . . . . 12 4 Comparison of Normal Distribution, L´ evy Distribution and Data of S&P 500 Price Changes . . . . . . . . . . . . . . . . . . . . . . 15 5 Regimes in the Empirical Distribution of S&P 500 Returns . . . . 16 6 Empirical Cumulative Distributions of the Daily Returns of three Stock Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 7 Empirical Cumulative Distributions of Different-Sized Companies 18 8 Daily Returns of the DAX . . . . . . . . . . . . . . . . . . . . . . 21 9 Daily Returns of the Deutsche Bank Stock . . . . . . . . . . . . . 22

Page 3

List of Tables

1 Frequency Distributions of the Dow Jones Industrial Average Stocks 8 2 Comparison of Frequency Distributions and the Normal Distribution 9