Svetlozar T. Rachev, Young Shim Kim, Michele L. Bianchi, Frank J. Fabozzi

Financial Models with Levy Processes and Volatility Clustering (eBook, PDF)

• Format: PDF

Produktbeschreibung

An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy 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 Lévy 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 events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 416
• Erscheinungstermin: 4. Februar 2011
• Englisch
• ISBN-13: 9780470937167
• Artikelnr.: 37300844

Autorenporträt

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.

Inhaltsangabe

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 alpha-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.