Switching Levy Models in Continuous Time

Switching Levy Models in Continuous Time
Author: Kyriakos Chourdakis
Publisher:
Total Pages: 39
Release: 2008
Genre:
ISBN:

This paper introduces a general regime switching Levy process, and constructs the characteristic function in closed form. Correlations between the underlying Markov chain and the asset returns are also allowed, by imposing asset price jumps whenever a regime change takes place. Based on the characteristic function the conditional densities and vanilla option prices can be rapidly computed using FFT. It is shown that the regime switching model has the potential to capture a wide variety of implied volatility skews. The paper also discusses the pricing of exotic contracts, like barrier, Bermudan and American options, by implementation of a quadrature method. A detailed numerical experiment illustrates the application of the regime switching framework.

Financial Models with Levy Processes and Volatility Clustering

Financial Models with Levy Processes and Volatility Clustering
Author: Svetlozar T. Rachev
Publisher: John Wiley & Sons
Total Pages: 316
Release: 2011-02-08
Genre: Business & Economics
ISBN: 0470937262

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.

Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads

Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads
Author: Charles Shaw
Publisher:
Total Pages: 21
Release: 2019
Genre:
ISBN:

A regime-switching Levy framework, where all parameter values depend on the value of a continuous time Markov chain as per Chevallier and Goutte (2017), is employed to study US Corporate Option-Adjusted Spreads (OASs). For modelling purposes we assume a Normal Inverse Gaussian distribution, allowing heavier tails and skewness. After the Expectation-Maximization algorithm is applied to this general class of regime switching models, we compare the obtained results with time series models without jumps, including one with regime switching and one without. We find that a regime-switching Levy model clearly defines two regimes for A-, AA-, and AAA-rated OASs. We find further evidence of regime-switching effects, with data showing relatively pronounced jump intensity around the time of major crisis periods, thereby confirming the presence and importance of volatility regimes. Results indicate that ignoring the complex and dynamic dependence structure in favour of certain model assumptions may lead to a significant underestimation of risk.

Change of Time Methods in Quantitative Finance

Change of Time Methods in Quantitative Finance
Author: Anatoliy Swishchuk
Publisher: Springer
Total Pages: 140
Release: 2016-05-31
Genre: Mathematics
ISBN: 331932408X

This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its properties. An emphasis is given on many applications of CTM in financial and energy markets, and the presented numerical examples are based on real data. The change of time method is applied to derive the well-known Black-Scholes formula for European call options, and to derive an explicit option pricing formula for a European call option for a mean-reverting model for commodity prices. Explicit formulas are also derived for variance and volatility swaps for financial markets with a stochastic volatility following a classical and delayed Heston model. The CTM is applied to price financial and energy derivatives for one-factor and multi-factor alpha-stable Levy-based models. Readers should have a basic knowledge of probability and statistics, and some familiarity with stochastic processes, such as Brownian motion, Levy process and martingale.

Fluctuations of Lévy Processes with Applications

Fluctuations of Lévy Processes with Applications
Author: Andreas E. Kyprianou
Publisher: Springer Science & Business Media
Total Pages: 461
Release: 2014-01-09
Genre: Mathematics
ISBN: 3642376320

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.

Levy-Based Interest Rate Derivatives

Levy-Based Interest Rate Derivatives
Author: Anatoliy V. Swishchuk
Publisher:
Total Pages: 0
Release: 2009
Genre:
ISBN:

In this paper, we show how to calculate the price of zero-coupon bonds for many Gaussian and Levy one-factor and multi-factor models of r(t) using change of time method. These models include, in particular, Ornshtein-Uhlenbeck (1930), Vasicek (1977), Cox-Ingersoll-Ross (1985), continuous-time GARCH, Ho-Lee (1986), Hull-White (1990) and Heath-Jarrrow-Morton (1992) models and their various combinations. We also derive partial integro-differential equations (PIDEs) for the values of swaps, caps, floors and options on them, swaptions, captions and floortions, respectively. We apply the change of time method to price the interest rate derivatives for the interest rates r(t) described by various stochastic differential equations driven by alpha-stable Levy processes.

Harry Markowitz

Harry Markowitz
Author: Harry Markowitz
Publisher: World Scientific
Total Pages: 719
Release: 2009-03-03
Genre: Business & Economics
ISBN: 981283365X

Harry M Markowitz received the Nobel Prize in Economics in 1990 for his pioneering work in portfolio theory. He also received the von Neumann Prize from the Institute of Management Science and the Operations Research Institute of America in 1989 for his work in portfolio theory, sparse matrices and the SIMSCRIPT computer language. While Dr Markowitz is well-known for his work on portfolio theory, his work on sparse matrices remains an essential part of linear optimization calculations. In addition, he designed and developed SIMSCRIPT OCo a computer programming language. SIMSCRIPT has been widely used for simulations of systems such as air transportation and communication networks."

Understanding and Facilitating Organizational Change in the 21st Century: Recent Research and Conceptualizations

Understanding and Facilitating Organizational Change in the 21st Century: Recent Research and Conceptualizations
Author: Adrianna Kezar
Publisher: John Wiley & Sons
Total Pages: 192
Release: 2011-10-06
Genre: Education
ISBN: 1118229525

There is a widespread discontent with the quality of education and levels of college student achievement, particularly for undergraduates preparing for the professions. This report examines the educational challenges in preparing professionals, reviews the specific types of curriculum innovations that faculty and administrators have created or significantly revised to strengthen college graduates' abilities, and focuses on the societal changes and expectations produced by the acceleration in technology.

Handbook of High-Frequency Trading and Modeling in Finance

Handbook of High-Frequency Trading and Modeling in Finance
Author: Ionut Florescu
Publisher: John Wiley & Sons
Total Pages: 452
Release: 2016-04-25
Genre: Business & Economics
ISBN: 1118443985

Reflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: • Contributions by well-known experts within the academic, industrial, and regulatory fields • A well-structured outline on the various data analysis methodologies used to identify new trading opportunities • Newly emerging quantitative tools that address growing concerns relating to high-frequency data such as stochastic volatility and volatility tracking; stochastic jump processes for limit-order books and broader market indicators; and options markets • Practical applications using real-world data to help readers better understand the presented material The Handbook of High-Frequency Trading and Modeling in Finance is an excellent reference for professionals in the fields of business, applied statistics, econometrics, and financial engineering. The handbook is also a good supplement for graduate and MBA-level courses on quantitative finance, volatility, and financial econometrics. Ionut Florescu, PhD, is Research Associate Professor in Financial Engineering and Director of the Hanlon Financial Systems Laboratory at Stevens Institute of Technology. His research interests include stochastic volatility, stochastic partial differential equations, Monte Carlo Methods, and numerical methods for stochastic processes. Dr. Florescu is the author of Probability and Stochastic Processes, the coauthor of Handbook of Probability, and the coeditor of Handbook of Modeling High-Frequency Data in Finance, all published by Wiley. Maria C. Mariani, PhD, is Shigeko K. Chan Distinguished Professor in Mathematical Sciences and Chair of the Department of Mathematical Sciences at The University of Texas at El Paso. Her research interests include mathematical finance, applied mathematics, geophysics, nonlinear and stochastic partial differential equations and numerical methods. Dr. Mariani is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley. H. Eugene Stanley, PhD, is William Fairfield Warren Distinguished Professor at Boston University. Stanley is one of the key founders of the new interdisciplinary field of econophysics, and has an ISI Hirsch index H=128 based on more than 1200 papers. In 2004 he was elected to the National Academy of Sciences. Frederi G. Viens, PhD, is Professor of Statistics and Mathematics and Director of the Computational Finance Program at Purdue University. He holds more than two dozen local, regional, and national awards and he travels extensively on a world-wide basis to deliver lectures on his research interests, which range from quantitative finance to climate science and agricultural economics. A Fellow of the Institute of Mathematics Statistics, Dr. Viens is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.

Markov Processes for Stochastic Modeling

Markov Processes for Stochastic Modeling
Author: Oliver Ibe
Publisher: Newnes
Total Pages: 515
Release: 2013-05-22
Genre: Mathematics
ISBN: 0124078397

Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. - Presents both the theory and applications of the different aspects of Markov processes - Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented - Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.