Financial Models with Levy Processes and Volatility Clustering - Hardcover

by Svetlozar T. Rachev (Author), Young Shin Kim (Author), Michele L. Bianchi (Author)

An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management

In 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 events

Financial Models with L vy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Front Jacket

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, improving the flexibility and statistical reliability of existing models, in addition to developing better models, is essential for both financial practitioners and academics seeking to explain and prevent extreme events.

Nobody understands this better than the expert author team of Svetlozar Rachev, Young Shin Kim, Michele Leonardo Bianchi, and Frank Fabozzi, and in Financial Models with Lévy Processes and Volatility Clustering, they present a framework for modeling the behavior of stock returns in a univariate and multivariate setting--providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distributions in financial modeling and the best methodologies for employing them.

This reliable resource includes detailed discussions of 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. This practical guide:

• 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 for explaining joint extreme events

• And much more

Filled with in-depth insights and expert advice, Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to both current probability distribution methods and brand new methodologies for financial modeling.

Back Jacket

FINANCIAL MODELS WITH LéVY PROCESSES AND VOLATILITY CLUSTERING

The failure of financial models has been identified by some market observers as a major contributor to the global financial crisis. More specifically, it's been argued that the underlying assumption made in most of these models--that distributions of prices and returns are normally distributed--have been responsible for their undoing.

Financial crises and black swan events may not be precisely predictable by models, but improving the reliability and flexibility of those models is essential for both financial practitioners and academics intent on limiting the impact of major market crashes.

In Financial Models with Lévy Processes and Volatility Clustering, authors Svetlozar Rachev, Young Shin Kim, Michele Leonardo Bianchi, and Frank Fabozzi focus on the application of non-normal distributions for modeling the behavior of stock price returns. Opening with a brief introduction to the basics of probability distributions, this practical resource quickly moves on to:

• Address a wide array of methods for the simulation of infinitely divisible distributions and Lévy processes with a view toward option pricing.

• Discuss two approaches to deal with non-normal multivariate distributions, providing insight into portfolio allocation assuming a multi-tail t distribution and a non-Gaussian multivariate model.

• Examine discrete time option pricing models with volatility clustering--namely non-Gaussian GARCH models.

• Provide guidance on pricing American options with Monte Carlo methods.

If you want to gain a better understanding of how financial models can be used to capture the dynamics of economic and financial variables, Financial Models with Lévy Processes and Volatility Clustering is the best place to start.

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.