Levy Processes In Finance

Author : Wim Schoutens
Publisher : Wiley
Page : 200 pages
File Size : 45,5 Mb
Release : 2003-05-07
Category : Mathematics
ISBN : 0470851562

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Levy Processes in Finance by Wim Schoutens Pdf

Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of L?vy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. L?vy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of L?vy-based models, and features many examples of how they may be used to solve problems in finance. * Provides an introduction to the use of L?vy processes in finance. * Features many examples using real market data, with emphasis on the pricing of financial derivatives. * Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling. * Includes many figures to illustrate the theory and examples discussed. * Avoids unnecessary mathematical formalities. The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers.

Author : Giulia Di Nunno,Bernt Øksendal,Frank Proske
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 54,9 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9783540785729

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Malliavin Calculus for Lévy Processes with Applications to Finance by Giulia Di Nunno,Bernt Øksendal,Frank Proske Pdf

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Author : Wim Schoutens,Jessica Cariboni
Publisher : John Wiley & Sons
Page : 213 pages
File Size : 52,8 Mb
Release : 2010-06-15
Category : Business & Economics
ISBN : 9780470685068

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Levy Processes in Credit Risk by Wim Schoutens,Jessica Cariboni Pdf

This book is an introductory guide to using Lévy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right through to structured credit risk products such as Collateralized Debt Obligations (CDOs), Constant Proportion Portfolio Insurances (CPPIs) and Constant Proportion Debt Obligations (CPDOs) as well as new advanced rating models for Asset Backed Securities (ABSs). Jumps and extreme events are crucial stylized features, essential in the modelling of the very volatile credit markets - the recent turmoil in the credit markets has once again illustrated the need for more refined models. Readers will learn how the classical models (driven by Brownian motions and Black-Scholes settings) can be significantly improved by using the more flexible class of Lévy processes. By doing this, extreme event and jumps can be introduced into the models to give more reliable pricing and a better assessment of the risks. The book brings in high-tech financial engineering models for the detailed modelling of credit risk instruments, setting up the theoretical framework behind the application of Lévy Processes to Credit Risk Modelling before moving on to the practical implementation. Complex credit derivatives structures such as CDOs, ABSs, CPPIs, CPDOs are analysed and illustrated with market data.

Author : Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201977

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Lévy Processes by Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Author : Peter Tankov
Publisher : CRC Press
Page : 552 pages
File Size : 47,5 Mb
Release : 2003-12-30
Category : Business & Economics
ISBN : 9781135437947

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Financial Modelling with Jump Processes by Peter Tankov Pdf

WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Author : David Applebaum
Publisher : Cambridge University Press
Page : 461 pages
File Size : 51,8 Mb
Release : 2009-04-30
Category : Mathematics
ISBN : 9781139477987

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Lévy Processes and Stochastic Calculus by David Applebaum Pdf

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Author : Svetlozar T. Rachev,Young Shin Kim,Michele L. Bianchi,Frank J. Fabozzi
Publisher : John Wiley & Sons
Page : 316 pages
File Size : 53,5 Mb
Release : 2011-02-08
Category : Business & Economics
ISBN : 9780470937266

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Financial Models with Levy Processes and Volatility Clustering by Svetlozar T. Rachev,Young Shin Kim,Michele L. Bianchi,Frank J. Fabozzi Pdf

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.

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 45,8 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9783642376320

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Fluctuations of Lévy Processes with Applications by Andreas E. Kyprianou Pdf

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.

Author : Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
Publisher : Springer
Page : 206 pages
File Size : 43,8 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9783642140075

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Lévy Matters I by Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab Pdf

Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.

Author : Oleg Kudryavtsev,Antonino Zanette
Publisher : Nova Science Publishers
Page : 259 pages
File Size : 43,7 Mb
Release : 2021
Category : Mathematics
ISBN : 1536198498

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Applications of Lévy Processes by Oleg Kudryavtsev,Antonino Zanette Pdf

"Lévy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lévy process in finance is the Black-Scholes model. This book presents important financial applications of Lévy processes. The Editors consider jump-diffusion and pure non-Gaussian Lévy processes, the multi-dimensional Black-Scholes model, and regime-switching Lévy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lévy processes: Monte Carlo simulations, machine learning, the frame projection method, dynamic programming, the Fourier cosine series expansion, finite difference schemes, and the Wiener-Hopf factorization. Various numerical examples are carefully presented in tables and figures to illustrate the methods designed in the book"--

Author : Michał Barski,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 401 pages
File Size : 45,7 Mb
Release : 2020-04-23
Category : Business & Economics
ISBN : 9781107101296

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Mathematics of the Bond Market: A Lévy Processes Approach by Michał Barski,Jerzy Zabczyk Pdf

Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.

Author : Wolfgang Paul,Jörg Baschnagel
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 42,8 Mb
Release : 2013-07-11
Category : Science
ISBN : 9783319003276

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Stochastic Processes by Wolfgang Paul,Jörg Baschnagel Pdf

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

Author : Yoshio Miyahara
Publisher : World Scientific
Page : 200 pages
File Size : 51,5 Mb
Release : 2012
Category : Electronic books
ISBN : 9781848163485

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Option Pricing in Incomplete Markets by Yoshio Miyahara Pdf

This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem

Author : Andreas E. Kyprianou,Juan Carlos Pardo
Publisher : Cambridge University Press
Page : 485 pages
File Size : 54,9 Mb
Release : 2022-04-07
Category : Mathematics
ISBN : 9781108480291

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Stable Lévy Processes via Lamperti-Type Representations by Andreas E. Kyprianou,Juan Carlos Pardo Pdf

A systematic treatment of stable Lévy processes and self-similar Markov processes, for graduate students and researchers in the field.

Author : Sato Ken-Iti
Publisher : Cambridge University Press
Page : 504 pages
File Size : 54,7 Mb
Release : 1999
Category : Distribution (Probability theory)
ISBN : 0521553024

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Lévy Processes and Infinitely Divisible Distributions by Sato Ken-Iti Pdf