An Introduction to Financial Option Valuation

Mathematics, Stochastics and Computation

Author: Desmond J. Higham

Publisher: Cambridge University Press

ISBN: 9780521547574

Category: Business & Economics

Page: 273

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This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.
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An Introduction to Computational Finance

Author: ™mr U?ur

Publisher: Imperial College Press

ISBN: 1848161921

Category: Mathematics

Page: 298

View: 3214

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Although there are several publications on similar subjects, this book mainly focuses on pricing of options and bridges the gap between Mathematical Finance and Numerical Methodologies. The author collects the key contributions of several monographs and selected literature, values and displays their importance, and composes them here to create a work which has its own characteristics in content and style.This invaluable book provides working Matlab codes not only to implement the algorithms presented in the text, but also to help readers code their own pricing algorithms in their preferred programming languages. Availability of the codes under an Internet site is also offered by the author.Not only does this book serve as a textbook in related undergraduate or graduate courses, but it can also be used by those who wish to implement or learn pricing algorithms by themselves. The basic methods of option pricing are presented in a self-contained and unified manner, and will hopefully help readers improve their mathematical and computational backgrounds for more advanced topics.Errata(s)Errata
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Mathematical Models, Methods and Applications

Author: Abul Hasan Siddiqi,Pammy Manchanda,Rashmi Bhardwaj

Publisher: Springer

ISBN: 9812879730

Category: Mathematics

Page: 298

View: 8371

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The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.
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Option Theory with Stochastic Analysis

An Introduction to Mathematical Finance

Author: Fred Espen Benth

Publisher: Springer Science & Business Media

ISBN: 9783540405023

Category: Business & Economics

Page: 162

View: 3799

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This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
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An Introduction to Exotic Option Pricing

Author: Peter Buchen

Publisher: CRC Press

ISBN: 1420091026

Category: Mathematics

Page: 296

View: 8059

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In an easy-to-understand, nontechnical yet mathematically elegant manner, An Introduction to Exotic Option Pricing shows how to price exotic options, including complex ones, without performing complicated integrations or formally solving partial differential equations (PDEs). The author incorporates much of his own unpublished work, including ideas and techniques new to the general quantitative finance community. The first part of the text presents the necessary financial, mathematical, and statistical background, covering both standard and specialized topics. Using no-arbitrage concepts, the Black–Scholes model, and the fundamental theorem of asset pricing, the author develops such specialized methods as the principle of static replication, the Gaussian shift theorem, and the method of images. A key feature is the application of the Gaussian shift theorem and its multivariate extension to price exotic options without needing a single integration. The second part focuses on applications to exotic option pricing, including dual-expiry, multi-asset rainbow, barrier, lookback, and Asian options. Pushing Black–Scholes option pricing to its limits, the author introduces a powerful formula for pricing a class of multi-asset, multiperiod derivatives. He gives full details of the calculations involved in pricing all of the exotic options. Taking an applied mathematics approach, this book illustrates how to use straightforward techniques to price a wide range of exotic options within the Black–Scholes framework. These methods can even be used as control variates in a Monte Carlo simulation of a stochastic volatility model.
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Mathematics Today

Bulletin of the Institute of Mathematics and Its Applications

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8573

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Stochastic Finance

An Introduction with Market Examples

Author: Nicolas Privault

Publisher: CRC Press

ISBN: 1466594039

Category: Business & Economics

Page: 441

View: 7159

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Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of
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An Elementary Introduction to Mathematical Finance

Options and Other Topics

Author: Sheldon M. Ross

Publisher: Cambridge University Press

ISBN: 9780521814294

Category: Business & Economics

Page: 253

View: 3672

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Contains a new chapter on optimization methods in finance, a new section on Value at Risk and Conditional Value at Risk, plus much more.
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Applied stochastic processes and control for Jump-diffusions

modeling, analysis, and computation

Author: Floyd B. Hanson

Publisher: Society for Industrial Mathematics

ISBN: 9780898716337

Category: Mathematics

Page: 443

View: 809

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This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump-diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. The book emphasizes modeling and problem solving and presents sample applications in financial engineering and biomedical modeling. Computational and analytic exercises and examples are included throughout. While classical applied mathematics is used in most of the chapters to set up systematic derivations and essential proofs, the final chapter bridges the gap between the applied and the abstract worlds to give readers an understanding of the more abstract literature on jump-diffusions. An additional 160 pages of online appendices are available on a Web page that supplements the book.Audience This book is written for graduate students in science and engineering who seek to construct models for scientific applications subject to uncertain environments. Mathematical modelers and researchers in applied mathematics, computational science, and engineering will also find it useful, as will practitioners of financial engineering who need fast and efficient solutions to stochastic problems.Contents List of Figures; List of Tables; Preface; Chapter 1. Stochastic Jump and Diffusion Processes: Introduction; Chapter 2. Stochastic Integration for Diffusions; Chapter 3. Stochastic Integration for Jumps; Chapter 4. Stochastic Calculus for Jump-Diffusions: Elementary SDEs; Chapter 5. Stochastic Calculus for General Markov SDEs: Space-Time Poisson, State-Dependent Noise, and Multidimensions; Chapter 6. Stochastic Optimal Control: Stochastic Dynamic Programming; Chapter 7. Kolmogorov Forward and Backward Equations and Their Applications; Chapter 8. Computational Stochastic Control Methods; Chapter 9. Stochastic Simulations; Chapter 10. Applications in Financial Engineering; Chapter 11. Applications in Mathematical Biology and Medicine; Chapter 12. Applied Guide to Abstract Theory of Stochastic Processes; Bibliography; Index; A. Online Appendix: Deterministic Optimal Control; B. Online Appendix: Preliminaries in Probability and Analysis; C. Online Appendix: MATLAB Programs
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