Option Pricing Using Levy Processes

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Levy Processes in Finance

Author : Wim Schoutens
Publisher : Wiley
ISBN 13 : 9780470851562
Total Pages : 200 pages
Book Rating : 4.8/5 (515 download)

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Book Synopsis Levy Processes in Finance by : Wim Schoutens

Download or read book Levy Processes in Finance written by Wim Schoutens and published by Wiley. This book was released on 2003-05-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Option Pricing in Incomplete Markets

Author : Yoshio Miyahara
Publisher : World Scientific
ISBN 13 : 1848163487
Total Pages : 200 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Option Pricing in Incomplete Markets by : Yoshio Miyahara

Download or read book Option Pricing in Incomplete Markets written by Yoshio Miyahara and published by World Scientific. This book was released on 2012 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

PDE and Martingale Methods in Option Pricing

Author : Andrea Pascucci
Publisher : Springer Science & Business Media
ISBN 13 : 8847017815
Total Pages : 727 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis PDE and Martingale Methods in Option Pricing by : Andrea Pascucci

Download or read book PDE and Martingale Methods in Option Pricing written by Andrea Pascucci and published by Springer Science & Business Media. This book was released on 2011-04-15 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.

Mathematics of the Bond Market

Author : Michał Barski
Publisher : Cambridge University Press
ISBN 13 : 1108882846
Total Pages : 401 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Mathematics of the Bond Market by : Michał Barski

Download or read book Mathematics of the Bond Market written by Michał Barski and published by Cambridge University Press. This book was released on 2020-04-23 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

Financial Models with Levy Processes and Volatility Clustering

Author : Svetlozar T. Rachev
Publisher : John Wiley & Sons
ISBN 13 : 0470937262
Total Pages : 316 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Financial Models with Levy Processes and Volatility Clustering by : Svetlozar T. Rachev

Download or read book Financial Models with Levy Processes and Volatility Clustering written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes and Stochastic Calculus

Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 1139477986
Total Pages : 461 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum

Download or read book Lévy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Malliavin Calculus for Lévy Processes with Applications to Finance

Author : Giulia Di Nunno
Publisher : Springer Science & Business Media
ISBN 13 : 3540785728
Total Pages : 421 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Malliavin Calculus for Lévy Processes with Applications to Finance by : Giulia Di Nunno

Download or read book Malliavin Calculus for Lévy Processes with Applications to Finance written by Giulia Di Nunno and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 1461201977
Total Pages : 414 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lévy Processes by : Ole E Barndorff-Nielsen

Download or read book Lévy Processes written by Ole E Barndorff-Nielsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Financial Modelling with Jump Processes

Author : Peter Tankov
Publisher : CRC Press
ISBN 13 : 1135437947
Total Pages : 552 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Financial Modelling with Jump Processes by : Peter Tankov

Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
ISBN 13 : 3642376320
Total Pages : 461 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou

Download or read book Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applications of Lévy Processes

Author : Oleg Kudryavtsev
Publisher : Nova Science Publishers
ISBN 13 : 9781536198492
Total Pages : 259 pages
Book Rating : 4.1/5 (984 download)

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Book Synopsis Applications of Lévy Processes by : Oleg Kudryavtsev

Download or read book Applications of Lévy Processes written by Oleg Kudryavtsev and published by Nova Science Publishers. This book was released on 2021 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--

Paris-Princeton Lectures on Mathematical Finance 2010

Author : Areski Cousin
Publisher : Springer Science & Business Media
ISBN 13 : 3642146597
Total Pages : 374 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Paris-Princeton Lectures on Mathematical Finance 2010 by : Areski Cousin

Download or read book Paris-Princeton Lectures on Mathematical Finance 2010 written by Areski Cousin and published by Springer Science & Business Media. This book was released on 2011-06-29 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.

Introductory Lectures on Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
ISBN 13 : 3540313435
Total Pages : 382 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Introductory Lectures on Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou

Download or read book Introductory Lectures on Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2006-12-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. 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 transparency and explicitness.

Exotic Option Pricing and Advanced Lévy Models

Author : Andreas Kyprianou
Publisher : John Wiley & Sons
ISBN 13 : 0470017201
Total Pages : 344 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Exotic Option Pricing and Advanced Lévy Models by : Andreas Kyprianou

Download or read book Exotic Option Pricing and Advanced Lévy Models written by Andreas Kyprianou and published by John Wiley & Sons. This book was released on 2006-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward

Long Memory in Economics

Author : Gilles Teyssière
Publisher : Springer Science & Business Media
ISBN 13 : 3540346252
Total Pages : 394 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Long Memory in Economics by : Gilles Teyssière

Download or read book Long Memory in Economics written by Gilles Teyssière and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assembles three different strands of long memory analysis: statistical literature on the properties of, and tests for, LRD processes; mathematical literature on the stochastic processes involved; and models from economic theory providing plausible micro foundations for the occurrence of long memory in economics.

From Lévy-Type Processes to Parabolic SPDEs

Author : Davar Khoshnevisan
Publisher : Birkhäuser
ISBN 13 : 3319341200
Total Pages : 214 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis From Lévy-Type Processes to Parabolic SPDEs by : Davar Khoshnevisan

Download or read book From Lévy-Type Processes to Parabolic SPDEs written by Davar Khoshnevisan and published by Birkhäuser. This book was released on 2016-12-22 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lecture notes from two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. René Schilling’s notes are an expanded version of his course on Lévy and Lévy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Lévy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lévy-Itô decomposition. On the other, it identifies the infinitesimal generator of the Lévy process as a pseudo-differential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lévy processes. The presentation is self-contained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan’s course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparison-type results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative space-time white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lévy process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples.

Limit Theorems for Stochastic Processes

Author : Jean Jacod
Publisher : Springer Science & Business Media
ISBN 13 : 3662025140
Total Pages : 620 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Limit Theorems for Stochastic Processes by : Jean Jacod

Download or read book Limit Theorems for Stochastic Processes written by Jean Jacod and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.