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Look Back Option Pricing Using The Fourier Transform B Spline Method
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Book Synopsis Look-Back Option Pricing Using the Fourier Transform B-Spline Method by : Gareth Gordon Haslip
Download or read book Look-Back Option Pricing Using the Fourier Transform B-Spline Method written by Gareth Gordon Haslip and published by . This book was released on 2013 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a new, efficient closed-form formula approximating the price of discrete look-back options, whose underlying asset price is driven by an exponential semi-martingale process including (jump) diffusions, Levy models, affine processes and other models. The derivation of our pricing formula is based on inverting the Fourier transform using B-spline approximation theory. We give an error bound for our formula and establish its fast rate of convergence to the true price. Our method provides look-back option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods.We provide an alternative proof to the Spitzer formula for the characteristic function of the maximum of a discretely observed stochastic process, which yields a numerically efficient algorithm based on convolutions. This is an important result which could have a wide range of applications where the Spitzer formula is utilized. We illustrate the numerical efficiency of our algorithm by applying it in pricing fixed and floating discrete look-back options under Brownian motion, jump diffusion models, and the variance gamma process.A new efficient and robust methodology is presented for pricing discrete look-back options whose underlying asset price is driven by an exponential semi-martingale process and no analytical pricing formula exists. Using B-spline interpolation we obtain an accurate closed-form representation of the look-back option price under an inverse generalized Fourier transform. This provides look-back option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods.We derive an explicit representation for the characteristic function of the maximum of a discretely observed stochastic process, which provides a significant improvement in terms of numerical efficiency over the Spitzer recurrence formula. This is of fundamental importance and could have a wide range of applications where the Spitzer formula is utilized. Examples considered include pricing fixed and floating discrete look-back options under Brownian motion, jump diffusion models, and the Variance Gamma process.
Book Synopsis A Novel Fourier Transform B-spline Method for Option Pricing by : Gareth Gordon Haslip
Download or read book A Novel Fourier Transform B-spline Method for Option Pricing written by Gareth Gordon Haslip and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new efficient and robust framework for European option pricing under continuous time asset models from the family of exponential semimartingale processes. We introduce B-spline interpolation theory to derivative pricing to provide an accurate closed-form representation of the option price under an inverse Fourier transform.We compare our method with some state-of-the-art option pricing methods, and demonstrate that it is extremely fast and accurate. This suggests a wide range of applications, including the use of more realistic asset models in high frequency trading. Examples considered in the paper include option pricing under asset models, including stochastic volatility and jumps, computation of the Greeks, and the inverse problem of cross-sectional calibration.
Book Synopsis Computational Science and Its Applications - ICCSA 2014 by : Beniamino Murgante
Download or read book Computational Science and Its Applications - ICCSA 2014 written by Beniamino Murgante and published by Springer. This book was released on 2014-07-02 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: The six-volume set LNCS 8579-8584 constitutes the refereed proceedings of the 14th International Conference on Computational Science and Its Applications, ICCSA 2014, held in Guimarães, Portugal, in June/July 2014. The 347 revised papers presented in 30 workshops and a special track were carefully reviewed and selected from 1167. The 289 papers presented in the workshops cover various areas in computational science ranging from computational science technologies to specific areas of computational science such as computational geometry and security.
Book Synopsis On the Pricing of Lookback Options by : Ezra Vitali Nahum
Download or read book On the Pricing of Lookback Options written by Ezra Vitali Nahum and published by . This book was released on 1999 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Fourier Transform Method in Option Pricing by : Yannan Gao
Download or read book The Fourier Transform Method in Option Pricing written by Yannan Gao and published by . This book was released on 2014 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modular Pricing of Options by : Jianwei Zhu
Download or read book Modular Pricing of Options written by Jianwei Zhu and published by Springer. This book was released on 2014-03-12 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a technical point of view, the celebrated Black and Scholes option pricing formula was originally developed using a separation of variables technique. However, already Merton mentioned in his seminal 1973 pa per, that it could have been developed by using Fourier transforms as well. Indeed, as is well known nowadays, Fourier transforms are a rather convenient solution technique for many models involving the fundamental partial differential equation of financial economics. It took the community nearly another twenty years to recognize that Fourier transform is even more useful, if one applies it to problems in financial economics without seeking an explicit analytical inverse trans form. Heston (1993) probably was the first to demonstrate how to solve a stochastic volatility option pricing model quasi analytically using the characteristic function of the problem, which is nothing else than the Fourier transform of the underlying Arrow /Debreu-prices, and doing the inverse transformation numerically. This opened the door for a whole bunch of new closed form solutions in the transformed Fourier space and still is one of the most active research areas in financial economics.
Book Synopsis Efficient Procedure for Valuing American Lookback Put Options by : Xuyan Wang
Download or read book Efficient Procedure for Valuing American Lookback Put Options written by Xuyan Wang and published by . This book was released on 2007 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by \[\max_{k=0, \ldots, t} S_k - S_t, \] where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time.
Book Synopsis A New Algorithm for American Option Pricing by : Zi-Min Lu
Download or read book A New Algorithm for American Option Pricing written by Zi-Min Lu and published by . This book was released on 1995 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis American Options with Lookback Payoff by : Min Dai
Download or read book American Options with Lookback Payoff written by Min Dai and published by . This book was released on 2007 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the early exercise policies and pricing behaviors of one-asset American options with lookback payoff structures. The classes of option models considered include floating strike lookback options, Russian options, fixed strike lookback options and pricing model of protection fund. In each class of the American lookback options, we analyze the characterization of the optimal stopping region, in particular, their asymptotic behaviors at time close to expiration and at infinite time to expiration. The inter-relations between the price functions of these American lookback options are explored. The mathematical technique of analyzing the exercise boundary curves of lookback options at infinitesimally small asset value is also applied to a similar analysis in the American two-asset minimum-put option model.
Book Synopsis A PIDE and a Closed-form Pricing Expression for Look-back Option Under L 'evy Process by : Sudip Chandra
Download or read book A PIDE and a Closed-form Pricing Expression for Look-back Option Under L 'evy Process written by Sudip Chandra and published by . This book was released on 2020 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a PIDE and closed-form Fourier Pricing formula for floating type Look-back option when stock price follows exponential Lévy Process. We first developed a PIDE based on Martingale method and derived a closed-form Fourier formula for pricing contracts. The formula is simple, easy to compute and can work for any class of Lévy Process.
Book Synopsis Tutorials on Multiresolution in Geometric Modelling by : Armin Iske
Download or read book Tutorials on Multiresolution in Geometric Modelling written by Armin Iske and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only textbook available on multiresolution methods in geometric modeling, a central topic in visualization, which is of great importance for industrial applications. Written in tutorial form, the book is introductory in character, and includes supporting exercises. Other supplementary material and software can be downloaded from the website www.ma.tum.de/primus 2001/.
Book Synopsis Wavelets from a Statistical Perspective by : Maarten Jansen
Download or read book Wavelets from a Statistical Perspective written by Maarten Jansen and published by CRC Press. This book was released on 2022-04-18 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.
Book Synopsis Scientific Computing with MATLAB by : Dingyu Xue
Download or read book Scientific Computing with MATLAB written by Dingyu Xue and published by CRC Press. This book was released on 2018-09-03 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Computing with MATLAB®, Second Edition improves students’ ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter. The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.
Book Synopsis Functional Data Analysis with R and MATLAB by : James Ramsay
Download or read book Functional Data Analysis with R and MATLAB written by James Ramsay and published by Springer Science & Business Media. This book was released on 2009-06-29 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems
Book Synopsis Practical Protein Crystallography by : Duncan E. McRee
Download or read book Practical Protein Crystallography written by Duncan E. McRee and published by Elsevier. This book was released on 1999-09-27 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for easy use by both beginning and experienced protein crystallographers, the second edition of Practical Protein Crystallography is an essential handbook for any scientist interested in solving a protein structure. The book includes examples of actual experiments and data, electron density maps, and computer methods. This second edition has new material covering CCP4, SHELX, cryocrystallography, MAD and automated fitting. In-depth coverage of every aspect of crystallography Coverage of the small details that can make or break projects Strongly application-oriented Exceptionally well illustrated Simple and easy-to-follow robust methods Tutorials with actual data available on the Web Useful for a broad spectrum of scientists
Book Synopsis An Introduction to Laplace Transforms and Fourier Series by : P.P.G. Dyke
Download or read book An Introduction to Laplace Transforms and Fourier Series written by P.P.G. Dyke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Book Synopsis Numerical Recipes in C++ by : William H. Press
Download or read book Numerical Recipes in C++ written by William H. Press and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now the acclaimed Second Edition of Numerical Recipes is available in the C++ object-oriented programming language. Including and updating the full mathematical and explanatory contents of Numerical Recipes in C, this new version incorporates completely new C++ versions of the more than 300 Numerical Recipes routines that are widely recognized as the most accessible and practical basis for scientific computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. Highlights include linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations and inverse theory. The authors approach to C++ preserves the efficient execution that C users expect, while simultaneously employing a clear, object-oriented interface to the routines. Tricks and tips for scientific computing in C++ are liberally included. The routines, in ANSI/ISO C++ source code, can thus be used with almost any existing C++ vector/matrix class library, according to user preference. A simple class library for stand-alone use is also included in the book. Both scientific programmers new to C++, and experienced C++ programmers who need access to the Numerical Recipes routines, can benefit from this important new version of an invaluable, classic text.
