Financial Models With Levy Processes and Volatility Clustering

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  • Format: Hardcover
  • Copyright: 2011-02-08
  • Publisher: Wiley
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An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment managementIn Financial Models with L_vy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it.The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential L_vy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme eventsFinancial Models with L_vy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Author Biography

SVETLOZAR T. RACHEV is Chair-Professor in Statistics, Econometrics, and Mathematical Finance at the Karlsruhe Institute of Technology (KIT) in the School of Economics and Business Engineering; Professor Emeritus at the University of California, Santa Barbara; and Chief Scientist at FinAnalytica Inc.

YOUNG SHIN KIM is a scientific assistant in the Department of Statistics, Econometrics, and Mathematical Finance at the Karlsruhe Institute of Technology (KIT).

MICHELE Leonardo BIANCHI is an analyst in the Division of Risk and Financial Innovation Analysis at the Specialized Intermediaries Supervision Department of the Bank of Italy.

FRANK J. FABOZZI is Professor in the Practice of Finance and Becton Fellow at the Yale School of Management and Editor of the Journal of PortfolioManagement. He is an Affiliated Professor at the University of Karlsruhe's Institute of Statistics, Econometrics, and Mathematical Finance and serves on the Advisory Council for the Department of Operations Research and Financial Engineering at Princeton University.

Table of Contents

The need for better financial modeling of asset prices
The family of stable distribution and its properties
Option pricing with volatility clustering
Model dependencies
Monte Carlo
Organization of the book
Probability distributions
Basic concepts
Discrete probability distributions
Continuous probability distributions
Statistic moments and quantiles
Characteristic function
Joint probability distributions
Stable and tempered stable distributions
┐-Stable distribution
Tempered stable distributions
Infinitely divisible distributions
Exponential Moments
Stochastic Processes in Continuous Time
Some preliminaries
Poisson Process
Pure jump process
Brownian motion
Time-Changed Brownian motion
LÚvy process
Conditional Expectation and Change of Measure
Events, ┐-fields, and filtration
Conditional expectation
Change of measures
Exponential LÚvy Models
Exponential LÚvy Models
Fitting ┐-stable and tempered stable distributions
Illustration: Parameter estimation for tempered stable distributions
Appendix: Numerical approximation of probability density and cumulative distribution functions
Option Pricing in Exponential LÚvy Models
Option contract
Boundary conditions for the price of an option
No-arbitrage pricing and equivalent martingale measure
Option pricing under the Black-Scholes model
European option pricing under exponential tempered stable
The subordinated stock price model
Random number generators
Simulation techniques for LÚvy processes
Tempered stable processes
Tempered infinitely divisible processes
Time-changed Brownian motion
Monte Carlo methods
Multi-tail t distribution
Principal component analysis
Estimating parameters
Empirical results
Non-Gaussian portfolio allocation
Multi-factor linear model
Modeling dependencies
Average value-at-risk
Optimal portfolios
The algorithm
An empirical test
Normal GARCH models
GARCH dynamics with normal innovation
Market estimation
Risk-neutral estimation
Smoothly truncated stable GARCH models
A Generalized NGARCH Option Pricing Model
Empirical Analysis
Infinitely divisible GARCH models
Stock price dynamic
Risk-neutral dynamic
Non-normal infinitely divisible GARCH
Simulate infinitely divisible GARCH
Option Pricing with Monte Carlo
Data set
Performance of Option Pricing Models
American Option Pricing with Monte Carlo Methods
American option pricing in discrete time
The Least Squares Monte Carlo method
LSM method in GARCH option pricing model
Empirical illustration
Table of Contents provided by Publisher. All Rights Reserved.

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