Distributional Regularities of Financial Returns

Seminar Paper , 2008 , 28 Pages , Grade: 1,7

Economics - Finance

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.

Inhaltsverzeichnis (Table of Contents)

• Introduction
• Mandelbrot and the Lévy-stable Distributions
  • The Lévy-stable distributions
    • Stability and Power-law Tail Behavior
    • Parameters
  • The Generalization of the Central Limit Theorem
  • Empirical Evidence of Mandelbrot's Hypothesis
    • The Data
    • Frequency Distributions
    • Normal Probability Graphs
• Research in the post-Mandelbrot Era
  • Recent Contributions: Power-law Behavior Outside the Lévy-Regime
  • Explanation for the Power-law Tail Behavior
• Summary

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This paper aims to present theoretical models that account for the distributional regularities in financial returns and illustrate the empirical analysis. It provides a comprehensive overview of the evolution of research on distributional properties of financial returns over a century. Key themes explored include:

• The historical development of theories explaining financial return distributions
• The rejection of the normal distribution hypothesis and the introduction of Lévy-stable distributions
• Empirical evidence supporting Mandelbrot's findings and the existence of power-law tail behavior
• The influence of Mandelbrot's work on subsequent research in the field
• Recent contributions and explanations for power-law tail behavior beyond the Lévy regime

Zusammenfassung der Kapitel (Chapter Summaries)

Introduction

This chapter introduces the topic of distributional regularities of financial returns, emphasizing their importance in financial systems. It highlights the historical development of research on this topic, starting from the turn of the 19th century, and outlines the paper's objective to showcase both theoretical models and empirical analysis of these regularities.

Mandelbrot and the Lévy-stable Distributions

This chapter delves into the work of Louis Bachelier and his initial theory of security price behavior, based on the normal distribution hypothesis. It then explores Benoît Mandelbrot's groundbreaking work that challenged this hypothesis, presenting empirical evidence for the existence of outliers that contradicted the normal distribution. Mandelbrot introduced the Lévy-stable distributions as an alternative, explaining the leptokurtotic behavior observed in financial data.

Research in the post-Mandelbrot Era

This chapter explores recent research that followed Mandelbrot's findings. It examines contributions that expanded upon the power-law behavior observed in financial data, moving beyond the Lévy regime, and provides explanations for the existence of these power-law tails.

Schlüsselwörter (Keywords)

This paper focuses on the distributional properties of financial returns, specifically examining the historical development of theories, the rejection of the normal distribution hypothesis, the introduction of Lévy-stable distributions, empirical evidence supporting Mandelbrot's findings, and recent contributions and explanations for power-law behavior in financial data. Key terms include: financial returns, distributional regularities, normal distribution, Lévy-stable distributions, power-law tail behavior, empirical analysis, and Mandelbrot's hypothesis.

• College: Christian-Albrechts-University of Kiel
• Grade: 1,7
• Author: Jakob Blatz (Author)
• Publication Year: 2008
• Pages: 28
• Catalog Number: V128878
• ISBN (eBook): 9783640832194
• ISBN (Book): 9783640833016
• Language: English
• Tags: Finanzmarktrenditen, statistische verteilung, statistical properties, financial returns, risk management, financial markets, normal distribution