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Option Pricing Using Fourier Transform With A Focus On The Cosine Expansion
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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.
Book Synopsis The Numerical Solution of the American Option Pricing Problem by : Carl Chiarella
Download or read book The Numerical Solution of the American Option Pricing Problem written by Carl Chiarella and published by World Scientific. This book was released on 2014-10-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers'' experiences with these approaches over the years. Contents: Introduction; The Merton and Heston Model for a Call; American Call Options under Jump-Diffusion Processes; American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics OCo The Transform Approach; Representation and Numerical Approximation of American Option Prices under Heston; Fourier Cosine Expansion Approach; A Numerical Approach to Pricing American Call Options under SVJD; Conclusion; Bibliography; Index; About the Authors. Readership: Post-graduates/ Researchers in finance and applied mathematics with interest in numerical methods for American option pricing; mathematicians/physicists doing applied research in option pricing. Key Features: Complete discussion of different numerical methods for American options; Able to handle stochastic volatility and/or jump diffusion dynamics; Able to produce hedge ratios efficiently and accurately"
Book Synopsis Numerical Solution Of The American Option Pricing Problem, The: Finite Difference And Transform Approaches by : Carl Chiarella
Download or read book Numerical Solution Of The American Option Pricing Problem, The: Finite Difference And Transform Approaches written by Carl Chiarella and published by World Scientific. This book was released on 2014-10-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers' experiences with these approaches over the years.
Book Synopsis Numerical Methods in Finance by : René Carmona
Download or read book Numerical Methods in Finance written by René Carmona and published by Springer Science & Business Media. This book was released on 2012-03-23 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
Book Synopsis Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes by : Cornelis W Oosterlee
Download or read book Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes written by Cornelis W Oosterlee and published by World Scientific. This book was released on 2019-10-29 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.
Book Synopsis Progress in Industrial Mathematics at ECMI 2008 by : Alistair D. Fitt
Download or read book Progress in Industrial Mathematics at ECMI 2008 written by Alistair D. Fitt and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 15th European Conference on Mathematics for Industry was held in the agreeable surroundings of University College London, just 5 minutes walk from the British Museum in the heart of London, over the ?ve warm, sunny days from 30 June to 4 July 2008. Participants from all over the world met with the commonaimofreinforcingthe roleofmathematics asanoverarching resource for industry and business. The conference attracted over 300 participants from 30 countries, most of them participating with either a contributed talk, a minisymposium pres- tation or a plenary lecture. ‘Mathematics in Industry’ was interpreted in its widest sense as can be seen from the range of applications and techniques described in this volume. We mention just two examples. The Alan Tayler Lecture was given by Mario Primicerio on a problem arising from moving oil through pipelines when temperature variations a?ect the shearing properties of wax and thus modify the ?ow. The Wacker Prize winner, Master’s student Lauri Harhanen from the Helsinki University of Technology, showed how a novel piece of mathematics allowed new software to capture real-time images of teeth from the data supplied by present day dental machinery (see ECMI Newsletter 44). The meeting was attended by leading ?gures from government, bu- ness and science who all shared the same aim – to promote the application of innovative mathematics to industry, and identify industrial sectors that o?er the most exciting opportunities for mathematicians to provide new insight and new ideas.
Book Synopsis The Fourier Transform and Its Applications by : Ronald Newbold Bracewell
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
Book Synopsis Fast Fourier Transforms by : James S. Walker
Download or read book Fast Fourier Transforms written by James S. Walker and published by CRC Press. This book was released on 2017-11-22 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :
Book Synopsis Fourier Transform Methods in Finance by : Umberto Cherubini
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
Book Synopsis Fourier Analysis by : Elias M. Stein
Download or read book Fourier Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2011-02-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Book Synopsis The Intuitive Guide to Fourier Analysis & Spectral Estimation with MATLAB by : Charan Langton
Download or read book The Intuitive Guide to Fourier Analysis & Spectral Estimation with MATLAB written by Charan Langton and published by . This book was released on 2017 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Heston Model and its Extensions in Matlab and C# by : Fabrice D. Rouah
Download or read book The Heston Model and its Extensions in Matlab and C# written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Book Synopsis The Sparse Fourier Transform by : Haitham Hassanieh
Download or read book The Sparse Fourier Transform written by Haitham Hassanieh and published by Morgan & Claypool. This book was released on 2018-02-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications. The fastest algorithm for computing the Fourier transform is the Fast Fourier Transform (FFT), which runs in near-linear time making it an indispensable tool for many applications. However, today, the runtime of the FFT algorithm is no longer fast enough especially for big data problems where each dataset can be few terabytes. Hence, faster algorithms that run in sublinear time, i.e., do not even sample all the data points, have become necessary. This book addresses the above problem by developing the Sparse Fourier Transform algorithms and building practical systems that use these algorithms to solve key problems in six different applications: wireless networks; mobile systems; computer graphics; medical imaging; biochemistry; and digital circuits. This is a revised version of the thesis that won the 2016 ACM Doctoral Dissertation Award.
Book Synopsis Computational Methods in Finance by : Ali Hirsa
Download or read book Computational Methods in Finance written by Ali Hirsa and published by CRC Press. This book was released on 2016-04-19 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping readers accurately price a vast array of derivatives, this self-contained text explains how to solve complex functional equations through numerical methods. It addresses key computational methods in finance, including transform techniques, the finite difference method, and Monte Carlo simulation. Developed from his courses at Columbia University and the Courant Institute of New York University, the author also covers model calibration and optimization and describes techniques, such as Kalman and particle filters, for parameter estimation.
Book Synopsis Fast Fourier Transform - Algorithms and Applications by : K.R. Rao
Download or read book Fast Fourier Transform - Algorithms and Applications written by K.R. Rao and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
