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Author : Rossella Agliardi
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (127 download)
Download or read book Option Pricing Under Levy Processes: a Unifying Formula written by Rossella Agliardi and published by . This book was released on 2009 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yoshio Miyahara
Publisher : World Scientific
ISBN 13 : 1848163479
Total Pages : 200 pages
Book Rating : 4.8/5 (481 download)
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 Lvy 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 problems.
Author : Andreas Kyprianou
Publisher : John Wiley & Sons
ISBN 13 : 0470017201
Total Pages : 344 pages
Book Rating : 4.4/5 (7 download)
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
Author : Lishang Jiang
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106557
Total Pages : 343 pages
Book Rating : 4.8/5 (131 download)
Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Author : Lishang Jiang
Publisher : World Scientific
ISBN 13 : 9812563695
Total Pages : 344 pages
Book Rating : 4.8/5 (125 download)
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Author : Peter Carr
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (129 download)
Download or read book Time-Changed Levy Process and Option Pricing written by Peter Carr and published by . This book was released on 2001 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: We apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under appropriate measure change. We extend the traditional measure theory into the complex domain and define the measure change by a class of complex valued exponential martingales. We provide extensive examples to illustrate its applications and its link to existing models in the literature.
Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 0521738652
Total Pages : 491 pages
Book Rating : 4.5/5 (217 download)
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 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully revised and appended edition of this unique volume, which develops together these two important subjects.
Author : Umberto Cherubini
Publisher : John Wiley & Sons
ISBN 13 : 0470684925
Total Pages : 326 pages
Book Rating : 4.4/5 (76 download)
Download or read book Fourier Transform Methods in Finance written by Umberto Cherubini and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to: compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques perform a change of measure on the characteristic function in order to make the price process a martingale recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps. Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9
Author : Andrea Pascucci
Publisher : Springer Science & Business Media
ISBN 13 : 8847017815
Total Pages : 727 pages
Book Rating : 4.8/5 (47 download)
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.
Author :
Publisher : ScholarlyEditions
ISBN 13 : 149010593X
Total Pages : 1225 pages
Book Rating : 4.4/5 (91 download)
Download or read book Issues in Applied Mathematics: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Applied Mathematics / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Physics. The editors have built Issues in Applied Mathematics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Physics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author : Benoît Delahaut
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (877 download)
Download or read book Option Pricing Models Built from Lévy Processes written by Benoît Delahaut and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis seeks to studying two different methods of option pricing - one introduced in Carr and Madan (1999), and the other one in F.Fang and Oosterlee (2008) - suitable for stock prices following stochastic processes whose characteristic function is known. The advantage of these methods is that they do not require an explicit formula for the density function. For each method, we determine good computation parameters before comparing them in terms of efficiency and accuracy. As an intermediary step, and because the Carr-Madan method is not compatible with a customised strike grid, we study two interpolation methods : the linear and the natural cubic spline interpolations. We also discuss the calibration problem, explain why it is not as straightforward as it may seem, and compare the results obtained for both models.
Author : Thanh Long Nguyen
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (129 download)
Download or read book Analytical Approach to Value Options with State Variables of a Levy System written by Thanh Long Nguyen and published by . This book was released on 2003 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present an analytical method in pricing European contingent assets, whose state variables follow a multi-dimensional Levy process. We give an explicit formula for the hypothetical European quot;two-pricequot; call option price by means of the conditional characteristic transform. The work not only unifies and extends the option pricing literature, which focuses on the use of the characteristic function, but also provides the way to formalize and and unify the valuation of the option price, the valuation of the discount bond price, the valuation of the scaled-forward price, and the valuation of the pricing measure in incomplete markets.
Author : Eric Benhamou
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (129 download)
Download or read book Option Pricing with Levy Process written by Eric Benhamou and published by . This book was released on 2001 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices.This enables us to generate an implicit volatility surface implied by market data. This model is of particular interest since it extends the seminal Black Scholes [1973] model consistently with volatility smile.
Author : Andrey Itkin
Publisher : Birkhäuser
ISBN 13 : 1493967924
Total Pages : 318 pages
Book Rating : 4.4/5 (939 download)
Download or read book Pricing Derivatives Under Lévy Models written by Andrey Itkin and published by Birkhäuser. This book was released on 2017-02-27 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.
Author : Thomas Duquesne
Publisher : Springer
ISBN 13 : 3642140076
Total Pages : 216 pages
Book Rating : 4.6/5 (421 download)
Download or read book Lévy Matters I written by Thomas Duquesne and published by Springer. This book was released on 2010-09-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Eleftheria Chatzipanagou
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Computational Option Pricing Under Jump Diffusion and Lévy Processes written by Eleftheria Chatzipanagou and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jasper Valstar
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (7 download)
Download or read book Option Pricing in a Lévy Process Setting written by Jasper Valstar and published by . This book was released on 2008 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
