Numerical Methods and Optimization in Finance

Author: Manfred Gilli,Dietmar Maringer,Enrico Schumann

Publisher: Academic Press

ISBN: 0123756626

Category: Business & Economics

Page: 584

View: 7285

This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Numerical Methods and Optimization in Finance

Author: Manfred Gilli,Dietmar Maringer,Enrico Schumann

Publisher: Academic Press

ISBN: 0123756634

Category: Mathematics

Page: 600

View: 8939

This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Numerical Methods in Finance and Economics

A MATLAB-Based Introduction

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 1118625579

Category: Mathematics

Page: 696

View: 7596

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.

Optimization Methods in Finance

Author: Gérard Cornuéjols,Javier Peña,Reha Tütüncü

Publisher: Cambridge University Press

ISBN: 1107056748

Category: Business & Economics

Page: 347

View: 5170

Full treatment, from model formulation to computational implementation, of optimization techniques that solve central problems in finance.

A Workout in Computational Finance

Author: Andreas Binder,Michael Aichinger

Publisher: John Wiley & Sons

ISBN: 111997349X

Category: Business & Economics

Page: 336

View: 7550

A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.

Implementing Models in Quantitative Finance: Methods and Cases

Author: Gianluca Fusai,Andrea Roncoroni

Publisher: Springer Science & Business Media

ISBN: 9783540499596

Category: Business & Economics

Page: 607

View: 2992

This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.

Applied Computational Economics and Finance

Author: Mario J. Miranda,Paul L. Fackler

Publisher: MIT Press

ISBN: 0262291754

Category: Business & Economics

Page: 528

View: 4212

This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book also provides an extensive Web-site library of computer utilities and demonstration programs.The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.

Numerical Optimization

Author: Jorge Nocedal,Stephen Wright

Publisher: Springer Science & Business Media

ISBN: 0387400656

Category: Mathematics

Page: 664

View: 3697

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Numerical Methods in Economics

Author: Kenneth L. Judd

Publisher: MIT Press

ISBN: 9780262100717

Category: Business & Economics

Page: 633

View: 3709

"Judd's book is a masterpiece which will help transform the way economic theory is done. It harnesses the computer revolution in the service of economic theory by collecting together a whole array of numerical methods to simulate and quantify models that used to be purely algebraic and qualitative." -- Avinash K. Dixit, Sherrerd University Professor of Economics, Princeton University To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on "Rn," including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A web site contains supplementary material including programs and answers to exercises.

Financial Modelling

Theory, Implementation and Practice with MATLAB Source

Author: Joerg Kienitz,Daniel Wetterau

Publisher: John Wiley & Sons

ISBN: 1118413296

Category: Business & Economics

Page: 736

View: 3868

Financial Modelling - Theory, Implementation and Practice is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor Market model. Source code used for producing the results and analysing the models is provided on the author’s dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981

Handbook of Computational and Numerical Methods in Finance

Author: Svetlozar T. Rachev

Publisher: Springer Science & Business Media

ISBN: 9780817632199

Category: Business & Economics

Page: 435

View: 1771

Numerical Methods in Finance have recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. They bridge the gap between financial theory and computational practice and provide solutions to problems where analytical methods are often non-applicable. Numerical methods are more and more used in several topics of financial analy sis: computation of complex derivatives; market, credit and operational risk assess ment, asset liability management, optimal portfolio theory, financial econometrics and others. Although numerical methods in finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research focusing on various numerical methods in finance. The contributions cover methodological issues. Genetic Algorithms, Neural Net works, Monte-Carlo methods, Finite Difference Methods, Stochastic Portfolio Opti mization as well as the application of other numerical methods in finance and risk management. As editor, I am grateful to the contributors for their fruitful collaboration. I would particularly like to thankStefan Trueck and Carlo Marinelli for the excellent editorial assistance received over the progress of this project. Thomas Plum did a splendid word-processingjob in preparing the manuscript. lowe much to George Anastassiou (ConsultantEditor, Birkhauser) and Ann Kostant Executive Editor, Mathematics and Physics, Birkhauser for their help and encouragement.

Numerical Methods in Finance with C++

Author: Maciej J. Capiński,Tomasz Zastawniak

Publisher: Cambridge University Press

ISBN: 0521177162

Category: Business & Economics

Page: 175

View: 8181

Provides aspiring quant developers with the numerical techniques and programming skills needed in quantitative finance. No programming background required.

Numerical Methods in Finance

A MATLAB-Based Introduction

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 0471461695

Category: Mathematics

Page: 432

View: 3013

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.

Numerical Methods for Finance

Author: John Miller,David Edelman,John Appleby

Publisher: CRC Press

ISBN: 9781584889267

Category: Mathematics

Page: 312

View: 4774

Featuring international contributors from both industry and academia, Numerical Methods for Finance explores new and relevant numerical methods for the solution of practical problems in finance. It is one of the few books entirely devoted to numerical methods as applied to the financial field. Presenting state-of-the-art methods in this area, the book first discusses the coherent risk measures theory and how it applies to practical risk management. It then proposes a new method for pricing high-dimensional American options, followed by a description of the negative inter-risk diversification effects between credit and market risk. After evaluating counterparty risk for interest rate payoffs, the text considers strategies and issues concerning defined contribution pension plans and participating life insurance contracts. It also develops a computationally efficient swaption pricing technology, extracts the underlying asset price distribution implied by option prices, and proposes a hybrid GARCH model as well as a new affine point process framework. In addition, the book examines performance-dependent options, variance reduction, Value at Risk (VaR), the differential evolution optimizer, and put-call-futures parity arbitrage opportunities. Sponsored by DEPFA Bank, IDA Ireland, and Pioneer Investments, this concise and well-illustrated book equips practitioners with the necessary information to make important financial decisions.

Monte Carlo Methods in Financial Engineering

Author: Paul Glasserman

Publisher: Springer Science & Business Media

ISBN: 0387216170

Category: Mathematics

Page: 596

View: 9100

From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis

Computational Financial Mathematics using MATHEMATICA®

Optimal Trading in Stocks and Options

Author: Srdjan Stojanovic

Publisher: Springer Science & Business Media

ISBN: 1461200431

Category: Business & Economics

Page: 481

View: 8501

Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analytically and numerically in finding practical solutions. This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book. Key features: * No previous knowledge of Mathematica programming is required * The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized * Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging * Black--Scholes and Dupire PDEs are solved symbolically and numerically * Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided * Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors.

Computational Finance

Numerical Methods for Pricing Financial Instruments

Author: George Levy

Publisher: Butterworth-Heinemann

ISBN: 9780750657228

Category: Business & Economics

Page: 443

View: 1092

Accompanying CD-ROM contains ... "working computer code, demonstration applications, and also PDF versions of several research articles that are referred to in the book." -- d.j.

Antieigenvalue Analysis

With Applications to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance and Optimization

Author: Karl Gustafson,Karl E. Gustafson

Publisher: World Scientific

ISBN: 9814366285

Category: Mathematics

Page: 244

View: 9183

Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.