Finite Difference Methods In Financial Engineering
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Finite Difference Methods In Financial Engineering
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Author : Daniel J. Duffy
language : en
Publisher: John Wiley & Sons
Release Date : 2013-10-28
Finite Difference Methods In Financial Engineering written by Daniel J. Duffy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-28 with Business & Economics categories.
The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Numerical Methods In Finance And Economics
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Author : Paolo Brandimarte
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-06
Numerical Methods In Finance And Economics written by Paolo Brandimarte and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-06 with Mathematics categories.
A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
Financial Engineering
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Author : William Johnson
language : en
Publisher: HiTeX Press
Release Date : 2024-10-10
Financial Engineering written by William Johnson and has been published by HiTeX Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-10 with Business & Economics categories.
"Financial Engineering: Innovating Solutions for Complex Markets" is an illuminating guide that unveils the sophisticated techniques and tools at the heart of modern financial markets. This comprehensive textbook blends theory with practice, offering readers a crystal-clear understanding of the multifaceted role of financial engineering in shaping investment strategies, managing risk, and fostering financial innovation. From foundational mathematical methods to the latest applications of machine learning and algorithmic trading, this book equips readers with the knowledge to navigate the intricate landscape of today's financial ecosystems. Authored by an expert in quantitative finance, this book is meticulously crafted to cater to both beginners and seasoned practitioners. Each chapter is structured to build upon previous concepts, ensuring a logical progression that enhances understanding while exploring the latest trends and emerging technologies in finance. Through clear explanations and real-world examples, readers are not just informed but empowered, gaining the skills necessary to become pioneers in financial engineering. Whether your goal is to enhance your strategic edge, understand the nuances of risk management, or explore the transformative potential of innovations like blockchain and AI, this book is your essential companion in the dynamic world of finance.
Financial Engineering And Computation
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Author : Yuh-Dauh Lyuu
language : en
Publisher: Cambridge University Press
Release Date : 2002
Financial Engineering And Computation written by Yuh-Dauh Lyuu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Business & Economics categories.
A comprehensive text and reference, first published in 2002, on the theory of financial engineering with numerous algorithms for pricing, risk management, and portfolio management.
Callable Mortgage Bonds
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Author : Niels Rom
language : en
Publisher: Springer Nature
Release Date : 2025-06-10
Callable Mortgage Bonds written by Niels Rom and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-10 with Business & Economics categories.
Callable mortgage bonds are utilized by individuals and companies to finance the purchase of real estate, and this asset class therefore plays a crucial role in modern society. Callable mortgage bonds constitute an enormous asset class and often offer long-term stable investments that are very attractive for pension funds. This book focuses on the pricing and calculation of risk numbers of callable fixed-rate mortgage bonds. Owing to the, from a financial perspective, irrational behaviour of borrowers, the pricing of these instruments usually requires the use of numerical solutions. Traditionally, it has been either a Monte Carlo simulation or a Finite Difference method. This book covers both methods and, in addition, the relatively new Fourier technique. This latter technique also creates a link between the interest rate derivatives market and the market for callable mortgage bonds. Finally, a chapter presenting a model for the valuation of a mortgage credit institute’s loan book is included.
Novel Methods In Computational Finance
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Author : Matthias Ehrhardt
language : en
Publisher: Springer
Release Date : 2017-09-19
Novel Methods In Computational Finance written by Matthias Ehrhardt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.
This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.
Financial Instrument Pricing Using C
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Author : Daniel J. Duffy
language : en
Publisher: John Wiley & Sons
Release Date : 2013-10-23
Financial Instrument Pricing Using C written by Daniel J. Duffy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Business & Economics categories.
One of the best languages for the development of financial engineering and instrument pricing applications is C++. This book has several features that allow developers to write robust, flexible and extensible software systems. The book is an ANSI/ISO standard, fully object-oriented and interfaces with many third-party applications. It has support for templates and generic programming, massive reusability using templates (?write once?) and support for legacy C applications. In this book, author Daniel J. Duffy brings C++ to the next level by applying it to the design and implementation of classes, libraries and applications for option and derivative pricing models. He employs modern software engineering techniques to produce industrial-strength applications: Using the Standard Template Library (STL) in finance Creating your own template classes and functions Reusable data structures for vectors, matrices and tensors Classes for numerical analysis (numerical linear algebra ?) Solving the Black Scholes equations, exact and approximate solutions Implementing the Finite Difference Method in C++ Integration with the ?Gang of Four? Design Patterns Interfacing with Excel (output and Add-Ins) Financial engineering and XML Cash flow and yield curves Included with the book is a CD containing the source code in the Datasim Financial Toolkit. You can use this to get up to speed with your C++ applications by reusing existing classes and libraries. 'Unique... Let's all give a warm welcome to modern pricing tools.' -- Paul Wilmott, mathematician, author and fund manager
Financial Engineering With Finite Elements
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Author : Juergen Topper
language : en
Publisher: John Wiley & Sons
Release Date : 2005-06-24
Financial Engineering With Finite Elements written by Juergen Topper and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-24 with Business & Economics categories.
The pricing of derivative instruments has always been a highly complex and time-consuming activity. Advances in technology, however, have enabled much quicker and more accurate pricing through mathematical rather than analytical models. In this book, the author bridges the divide between finance and mathematics by applying this proven mathematical technique to the financial markets. Utilising practical examples, the author systematically describes the processes involved in a manner accessible to those without a deep understanding of mathematics. * Explains little understood techniques that will assist in the accurate more speedy pricing of options * Centres on the practical application of these useful techniques * Offers a detailed and comprehensive account of the methods involved and is the first to explore the application of these particular techniques to the financial markets
Applied Diffusion Processes From Engineering To Finance
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Author : Jacques Janssen
language : en
Publisher: John Wiley & Sons
Release Date : 2013-04-08
Applied Diffusion Processes From Engineering To Finance written by Jacques Janssen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Mathematics categories.
The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance. Contents 1. Diffusion Phenomena and Models. 2. Probabilistic Models of Diffusion Processes. 3. Solving Partial Differential Equations of Second Order. 4. Problems in Finance. 5. Basic PDE in Finance. 6. Exotic and American Options Pricing Theory. 7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance. 8. Numerical Methods. 9. Advanced Topics in Engineering: Nonlinear Models. 10. Lévy Processes. 11. Advanced Topics in Insurance: Copula Models and VaR Techniques. 12. Advanced Topics in Finance: Semi-Markov Models. 13. Monte Carlo Semi-Markov Simulation Methods.
Mathematical Finance
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Author : Christian Fries
language : en
Publisher: John Wiley & Sons
Release Date : 2007-10-19
Mathematical Finance written by Christian Fries and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-19 with Mathematics categories.
A balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models. Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises. While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.