Financial Models with Levy Processes and Volatility Clustering.

Financial Models with Levy Processes and Volatility Clustering.

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The financial crisis that began in the summer of 2007 has led to criticisms that the financial models used by risk managers, portfolio managers, and even regulators simply do not reflect the realities of today's markets. While one tool cannot be blamed for the entire global financial crisis, im...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Authors: Kim, Young Shin (Author), Bianchi, Michele Leonardo (Author), Fabozzi, Frank J. (Author)
Format: eBook
Language:English
Published: Wiley 2011.
Series:Frank J. Fabozzi series.
Subjects:
Capital assets pricing model.
Lévy processes.
Finance > Mathematical models.
Probabilities.
Electronic book.
Table of Contents:
  • Cover
  • Contents
  • Preface
  • About the Authors
  • Chapter 1 Introduction
  • 1.1 The Need for Better Financial Modeling of Asset Prices
  • 1.2 The Family of Stable Distribution and Its Properties
  • 1.2.1 Parameterization of the Stable Distribution
  • 1.2.2 Desirable Properties of the Stable Distributions
  • 1.2.3 Considerations in the Use of the Stable Distribution
  • 1.3 Option Pricing With Volatility Clustering
  • 1.3.1 Non-Gaussian Garch Models
  • 1.4 Model Dependencies
  • 1.5 Monte Carlo
  • 1.6 Organization of the Book
  • References
  • Chapter 2 Probability Distributions
  • 2.1 Basic Concepts
  • 2.2 Discrete Probability Distributions
  • 2.2.1 Bernoulli Distribution
  • 2.2.2 Binomial Distribution
  • 2.2.3 Poisson Distribution
  • 2.3 Continuous Probability Distributions
  • 2.3.1 Probability Distribution Function, Probability Density Function, and Cumulative Distribution Function
  • 2.3.2 Normal Distribution
  • 2.3.3 Exponential Distribution
  • 2.3.4 Gamma Distribution
  • 2.3.5 Variance Gamma Distribution
  • 2.3.6 Inverse Gaussian Distribution
  • 2.4 Statistic Moments and Quantiles
  • 2.4.1 Location
  • 2.4.2 Dispersion
  • 2.4.3 Asymmetry
  • 2.4.4 Concentration in Tails
  • 2.4.5 Statistical Moments
  • 2.4.6 Quantiles
  • 2.4.7 Sample Moments
  • 2.5 Characteristic Function
  • 2.6 Joint Probability Distributions
  • 2.6.1 Conditional Probability
  • 2.6.2 Joint Probability Distribution Defined
  • 2.6.3 Marginal Distribution
  • 2.6.4 Dependence of Random Variables
  • 2.6.5 Covariance and Correlation
  • 2.6.6 Multivariate Normal Distribution
  • 2.6.7 Elliptical Distributions
  • 2.6.8 Copula Functions
  • 2.7 Summary
  • References
  • Chapter 3 Stable and Tempered Stable Distributions
  • 3.1 945;-Stable Distribution
  • 3.1.1 Definition of An 945;-Stable Random Variable
  • 3.1.2 Useful Properties of An 945;-Stable Random Variable
  • 3.1.3 Smoothly Truncated Stable Distribution
  • 3.2 Tempered Stable Distributions
  • 3.2.1 Classical Tempered Stable Distribution
  • 3.2.2 Generalized Classical Tempered Stable Distribution
  • 3.2.3 Modified Tempered Stable Distribution
  • 3.2.4 Normal Tempered Stable Distribution
  • 3.2.5 Kim-Rachev Tempered Stable Distribution
  • 3.2.6 Rapidly Decreasing Tempered Stable Distribution
  • 3.3 Infinitely Divisible Distributions
  • 3.3.1 Exponential Moments
  • 3.4 Summary
  • 3.5 Appendix
  • 3.5.1 The Hypergeometric Function
  • 3.5.2 The Confluent Hypergeometric Function
  • References
  • Chapter 4 Stochastic Processes in Continuous Time
  • 4.1 Some Preliminaries
  • 4.2 Poisson Process
  • 4.2.1 Compounded Poisson Process
  • 4.3 Pure Jump Process
  • 4.3.1 Gamma Process
  • 4.3.2 Inverse Gaussian Process
  • 4.3.3 Variance Gamma Process
  • 4.3.4 945;-Stable Process
  • 4.3.5 Tempered Stable Process
  • 4.4 Brownian Motion
  • 4.4.1 Arithmetic Brownian Motion
  • 4.4.2 Geometric Brownian Motion
  • 4.5 Time-Changed Brownian Motion
  • 4.5.1 Variance Gamma Process
  • 4.5.2 Normal Inverse Gaussian Process
  • 4.5.3 N.

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