Topics In Numerical Methods For Finance
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Topics In Numerical Methods For Finance
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Author : Mark Cummins
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-15
Topics In Numerical Methods For Finance written by Mark Cummins and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-15 with Mathematics categories.
Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing and risk measurement. Using a moving least squares reconstruction, a numerical approach is then developed that allows for the construction of arbitrage-free surfaces. Free boundary problems are considered next, with particular focus on stochastic impulse control problems that arise when the cost of control includes a fixed cost, common in financial applications. The text proceeds with the development of a fear index based on equity option surfaces, allowing for the measurement of overall fear levels in the market. The problem of American option pricing is considered next, applying simulation methods combined with regression techniques and discussing convergence properties. Changing focus to integral transform methods, a variety of option pricing problems are considered. The COS method is practically applied for the pricing of options under uncertain volatility, a method developed by the authors that relies on the dynamic programming principle and Fourier cosine series expansions. Efficient approximation methods are next developed for the application of the fast Fourier transform for option pricing under multifactor affine models with stochastic volatility and jumps. Following this, fast and accurate pricing techniques are showcased for the pricing of credit derivative contracts with discrete monitoring based on the Wiener-Hopf factorisation. With an energy theme, a recombining pentanomial lattice is developed for the pricing of gas swing contracts under regime switching dynamics. The book concludes with a linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets.
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.
Numerical Methods In Finance
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Author : Paolo Brandimarte
language : en
Publisher: John Wiley & Sons
Release Date : 2003-09-29
Numerical Methods In Finance 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 2003-09-29 with Mathematics categories.
Balanced coverage of the methodology and theory of numerical methods in finance Numerical Methods in Finance bridges the gap between financial theory and computational practice while helping students and practitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numerical analysis and provides background material that suits the needs of students from both financial engineering and economics perspectives. Classical numerical analysis methods; optimization, including less familiar topics such as stochastic and integer programming; simulation, including low discrepancy sequences; and partial differential equations are covered in detail. Extensive illustrative examples of the application of all of these methodologies are also provided. The text is primarily focused on MATLAB-based application, but also includes descriptions of other readily available toolboxes that are relevant to finance. Helpful appendices on the basics of MATLAB and probability theory round out this balanced coverage. Accessible for students-yet still a useful reference for practitioners-Numerical Methods in Finance offers an expert introduction to powerful tools in finance.
Topics In Numerical Methods For Finance
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Author : Mark Cummins
language : en
Publisher: Springer
Release Date : 2012-07-16
Topics In Numerical Methods For Finance written by Mark Cummins and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-16 with Mathematics categories.
Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing and risk measurement. Using a moving least squares reconstruction, a numerical approach is then developed that allows for the construction of arbitrage-free surfaces. Free boundary problems are considered next, with particular focus on stochastic impulse control problems that arise when the cost of control includes a fixed cost, common in financial applications. The text proceeds with the development of a fear index based on equity option surfaces, allowing for the measurement of overall fear levels in the market. The problem of American option pricing is considered next, applying simulation methods combined with regression techniques and discussing convergence properties. Changing focus to integral transform methods, a variety of option pricing problems are considered. The COS method is practically applied for the pricing of options under uncertain volatility, a method developed by the authors that relies on the dynamic programming principle and Fourier cosine series expansions. Efficient approximation methods are next developed for the application of the fast Fourier transform for option pricing under multifactor affine models with stochastic volatility and jumps. Following this, fast and accurate pricing techniques are showcased for the pricing of credit derivative contracts with discrete monitoring based on the Wiener-Hopf factorisation. With an energy theme, a recombining pentanomial lattice is developed for the pricing of gas swing contracts under regime switching dynamics. The book concludes with a linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets.
Numerical Methods And Optimization In Finance
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Author : Manfred Gilli
language : en
Publisher: Academic Press
Release Date : 2019-08-16
Numerical Methods And Optimization In Finance written by Manfred Gilli and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Business & Economics categories.
Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems—ranging from asset allocation to risk management and from option pricing to model calibration—can be efficiently handled using modern computational techniques. Numerical Methods and Optimization in Finance presents such computational techniques, with an emphasis on simulation and optimization, particularly so-called heuristics. This book treats quantitative analysis as an essentially computational discipline in which applications are put into software form and tested empirically. This revised edition includes two new chapters, a self-contained tutorial on implementing and using heuristics, and an explanation of software used for testing portfolio-selection models. Postgraduate students, researchers in programs on quantitative and computational finance, and practitioners in banks and other financial companies can benefit from this second edition of Numerical Methods and Optimization in Finance. - Introduces numerical methods to readers with economics backgrounds - Emphasizes core simulation and optimization problems - Includes MATLAB and R code for all applications, with sample code in the text and freely available for download
Advanced Mathematical Methods For Finance
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Author : Julia Di Nunno
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-29
Advanced Mathematical Methods For Finance written by Julia Di Nunno and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-29 with Mathematics categories.
This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.
Numerical Methods Unraveled Mastering Computational Techniques
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-20
Numerical Methods Unraveled Mastering Computational Techniques written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-20 with Mathematics categories.
In the realm of scientific inquiry and engineering endeavors, numerical methods stand as indispensable tools, empowering researchers, engineers, and scientists to delve into complex problems that defy analytical solutions. "Numerical Methods Unraveled: Mastering Computational Techniques" is a comprehensive guide to the fundamentals and applications of numerical methods, unlocking the power of computation for problem-solving and discovery. Through clear explanations, engaging examples, and hands-on exercises, this book takes readers on a journey from the basic concepts of numerical methods to advanced techniques employed in various scientific disciplines. It covers a wide spectrum of topics, including linear systems, nonlinear equations, interpolation and approximation, differential equations, optimization, and numerical linear algebra. With a strong emphasis on practical implementation, the book provides detailed instructions for using popular software packages such as MATLAB, Python, and C++ to implement numerical methods. This hands-on approach enables readers to apply the learned techniques to their own research and projects, fostering a deeper understanding and appreciation for the power of computational methods. Recognizing the dynamic nature of the field, the book dedicates a chapter to the frontiers of numerical methods, exploring emerging techniques such as machine learning, quantum computing, and high-performance computing. These cutting-edge developments provide a glimpse into the future of numerical methods and their potential to revolutionize diverse fields of science and engineering. "Numerical Methods Unraveled: Mastering Computational Techniques" is an essential resource for students, researchers, engineers, and anyone seeking to master the art of numerical methods and unlock the power of computation in their respective fields. Its comprehensive coverage, engaging narrative, and practical orientation make it an invaluable guide to the ever-expanding world of numerical methods. If you like this book, write a review!
Current Topics In Quantitative Finance
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Author : Elio Canestrelli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Current Topics In Quantitative Finance written by Elio Canestrelli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
The present volume collects a selection of revised papers which were presented at the 21st Euro Working Group on Financial Modelling Meeting, held in Venice (Italy), on October 29-31, 1997. The Working Group was founded in September 1986 in Lisbon with the objective of providing an international forum for the exchange of information and experience; encouraging research and interaction be tween financial economic theory and practice of financial decision mak ing, as well as circulating information among universities and financial institutions throughout Europe. The attendance to the Meeting was large and highly qualified. More than 80 participants, coming from 20 different Countries debated on 5 invited lectures and 40 communications in regular sessions. The sessions were located at the Island of San Servolo, on the Venetian lagoon, just in front of the Doges Palace. San Servolo Island is a natural oasis, in the midst of a unique urban setting, offering great relaxation in a peaceful park and a panoramic view of Venice. The friendly atmosphere added great benefit to the formal and informal discussions among the participants, -which is typical of E.W.G.F.M. Meetings. It is interesting to consider the story of the Meeting. The previous locations were held at Cyprus, Crete and Dubrovnik - former mile stones of the Venitian Republic influence on the Mediterranean Sea. Therefore, that this Meeting should be harboured in the heart of the Republic itself (namely, the Saint Mark basin), was only a matter of consequence.
Numerical Methods In Finance
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Author : Michèle Breton
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Numerical Methods In Finance written by Michèle Breton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Business & Economics categories.
GERAD celebrates this year its 25th anniversary. The Center was created in 1980 by a small group of professors and researchers of HEC Montreal, McGill University and of the Ecole Polytechnique de Montreal. GERAD's activities achieved sufficient scope to justify its conversion in June 1988 into a Joint Research Centre of HEC Montreal, the Ecole Polytechnique de Montreal and McGill University. In 1996, the U- versite du Quebec a Montreal joined these three institutions. GERAD has fifty members (professors), more than twenty research associates and post doctoral students and more than two hundreds master and Ph.D. students. GERAD is a multi-university center and a vital forum for the devel- ment of operations research. Its mission is defined around the following four complementarily objectives: • The original and expert contribution to all research fields in GERAD's area of expertise; • The dissemination of research results in the best scientific outlets as well as in the society in general; • The training of graduate students and post doctoral researchers; • The contribution to the economic community by solving important problems and providing transferable tools.
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.