Financial Models with Levy Processes and Volatility Clustering
Published on 4. February 2011
394 pages
978-0-470-93716-7 (ISBN)
Description
An in-depth guide to understanding probability distributions andfinancial modeling for the purposes of investment management
In Financial Models with Lévy Processes and VolatilityClustering, the expert author team provides a framework tomodel the behavior of stock returns in both a univariate and amultivariate setting, providing you with practical applications tooption pricing and portfolio management. They also explain thereasons for working with non-normal distribution in financialmodeling and the best methodologies for employing it.
The book's framework includes the basics of probabilitydistributions and explains the alpha-stable distribution and thetempered stable distribution. The authors also explore discretetime option pricing models, beginning with the classical normalmodel with volatility clustering to more recent models thatconsider both volatility clustering and heavy tails.
* Reviews the basics of probability distributions
* Analyzes a continuous time option pricing model (the so-calledexponential Lévy model)
* Defines a discrete time model with volatility clustering andhow to price options using Monte Carlo methods
* Studies two multivariate settings that are suitable to explainjoint extreme events
Financial Models with Lévy Processes and VolatilityClustering is a thorough guide to classical probabilitydistribution methods and brand new methodologies for financialmodeling.
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Svetlozar T. Rachev | Young Shim Kim | Michele L. Bianchi
Financial Models with Levy Processes and Volatility Clustering
Book
03/2011
Wiley
€101.50
Shipment within 10-20 days
Persons
SVETLOZAR T. RACHEV is Chair-Professor in Statistics,Econometrics, and Mathematical Finance at the Karlsruhe Instituteof Technology (KIT) in the School of Economics and BusinessEngineering; Professor Emeritus at the University of California,Santa Barbara; and Chief Scientist at FinAnalytica Inc.
YOUNG SHIN KIM is a scientific assistant in theDepartment of Statistics, Econometrics, and Mathematical Finance atthe Karlsruhe Institute of Technology (KIT).
MICHELE Leonardo BIANCHI is an analyst in the Division ofRisk and Financial Innovation Analysis at the SpecializedIntermediaries Supervision Department of the Bank of Italy.
FRANK J. FABOZZI is Professor in the Practice of Financeand Becton Fellow at the Yale School of Management and Editor ofthe Journal of PortfolioManagement. He is an Affiliated Professorat the University of Karlsruhe's Institute of Statistics,Econometrics, and Mathematical Finance and serves on the AdvisoryCouncil for the Department of Operations Research and FinancialEngineering at Princeton University.
Content
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.
1.3 Option pricing with volatility clustering.
1.4 Model dependencies.
1.5 Monte Carlo.
1.6 Organization of the book.
Chapter 2 Probability distributions.
2.1 Basic concepts.
2.2 Discrete probability distributions.
2.3 Continuous probability distributions.
2.4 Statistic moments and quantiles.
2.5 Characteristic function.
2.6 Joint probability distributions.
2.7 Summary.
Chapter 3 Stable and tempered stable distributions.
3.1 a-Stable distribution.
3.2 Tempered stable distributions.
3.3 Infinitely divisible distributions.
3.4 Summary.
3.5 Appendix.
Chapter 4 Stochastic Processes in Continuous Time.
4.1 Some preliminaries.
4.2 Poisson Process.
4.3 Pure jump process.
4.4 Brownian motion.
4.5 Time-Changed Brownian motion.
4.6 Lévy process.
4.7 Summary.
Chapter 5 Conditional Expectation and Change of Measure.
5.1 Events, s-fields, and filtration.
5.2 Conditional expectation.
5.3 Change of measures.
5.4 Summary.
Chapter 6 Exponential Lévy Models.
6.1 Exponential Lévy Models.
6.2 Fitting a-stable and tempered stable distributions.
6.3 Illustration: Parameter estimation for tempered stable distributions.
6.4 Summary.
6.5 Appendix : Numerical approximation of probability density and cumulative distribution functions.
Chapter 7 Option Pricing in Exponential Lévy Models.
7.1 Option contract.
7.2 Boundary conditions for the price of an option.
7.3 No-arbitrage pricing and equivalent martingale measure.
7.4 Option pricing under the Black-Scholes model.
7.5 European option pricing under exponential tempered stable Models.
7.6 The subordinated stock price model.
7.7 Summary.
Chapter 8 Simulation.
8.1 Random number generators.
8.2 Simulation techniques for Lévy processes.
8.3 Tempered stable processes.
8.4 Tempered infinitely divisible processes.
8.5 Time-changed Brownian motion.
8.6 Monte Carlo methods.
Chapter 9 Multi-Tail t-distribution.
9.1 Introduction.
9.2 Principal component analysis.
9.3 Estimating parameters.
9.4 Empirical results.
9.5 Conclusion.
Chapter 10 Non-Gaussian portfolio allocation.
10.1 Introduction.
10.2 Multifactor linear model.
10.3 Modeling dependencies.
10.4 Average value-at-risk.
10.5 Optimal portfolios.
10.6 The algorithm.
10.7 An empirical test.
10.8 Summary.
Chapter 11 Normal GARCH models.
11.1 Introduction.
11.2 GARCH dynamics with normal innovation.
11.3 Market estimation.
11.4 Risk-neutral estimation.
11.5 Summary.
Chapter 12 Smoothly truncated stable GARCH models.
12.1 Introduction.
12.2 A Generalized NGARCH Option Pricing Model.
12.3 Empirical Analysis.
12.4 Conclusion.
Chapter 13 Infinitely divisible GARCH models.
13.1 Stock price dynamic.
13.2 Risk-neutral dynamic.
13.3 Non-normal infinitely divisible GARCH.
13.4 Simulate infinitely divisible GARCH.
Chapter 14 Option Pricing with Monte Carlo Methods.
14.1 Introduction.
14.2 Data set.
14.3 Performance of Option Pricing Models.
14.4 Summary.
Chapter 15 American Option Pricing with Monte Carlo Methods.
15.1 American option pricing in discrete time.
15.2 The Least Squares Monte Carlo method.
15.3 LSM method in GARCH option pricing model.
15.4 Empirical illustration.
15.5 Summary.
Index.
