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Author: Siu-ah Ng Publisher: World Scientific ISBN: 9814492337 Category : Business & Economics Languages : en Pages : 313
Book Description
At the beginning of the new millennium, two unstoppable processes are taking place in the world: (1) globalization of the economy; (2) information revolution. As a consequence, there is greater participation of the world population in capital market investment, such as bonds and stocks and their derivatives. Hence there is a need for risk management and analytic theory explaining the market. This leads to quantitative tools based on mathematical methods, i.e. the theory of mathematical finance.Ever since the pioneer work of Black, Scholes and Merton in the 70's, there has been rapid growth in the study of mathematical finance, involving ever more sophisticated mathematics. However, from the practitioner's point of view, it is desirable to have simpler and more useful mathematical tools.This book introduces research students and practitioners to the intuitive but rigorous hypermodel techniques in finance. It is based on Robinson's infinitesimal analysis, which is easily grasped by anyone with as little background as first-year calculus. It covers topics such as pricing derivative securities (including the Black-Scholes formula), hedging, term structure models of interest rates, consumption and equilibrium. The reader is introduced to mathematical tools needed for the aforementioned topics. Mathematical proofs and details are given in an appendix. Some programs in MATHEMATICA are also included.
Author: Siu-ah Ng Publisher: World Scientific ISBN: 9814492337 Category : Business & Economics Languages : en Pages : 313
Book Description
At the beginning of the new millennium, two unstoppable processes are taking place in the world: (1) globalization of the economy; (2) information revolution. As a consequence, there is greater participation of the world population in capital market investment, such as bonds and stocks and their derivatives. Hence there is a need for risk management and analytic theory explaining the market. This leads to quantitative tools based on mathematical methods, i.e. the theory of mathematical finance.Ever since the pioneer work of Black, Scholes and Merton in the 70's, there has been rapid growth in the study of mathematical finance, involving ever more sophisticated mathematics. However, from the practitioner's point of view, it is desirable to have simpler and more useful mathematical tools.This book introduces research students and practitioners to the intuitive but rigorous hypermodel techniques in finance. It is based on Robinson's infinitesimal analysis, which is easily grasped by anyone with as little background as first-year calculus. It covers topics such as pricing derivative securities (including the Black-Scholes formula), hedging, term structure models of interest rates, consumption and equilibrium. The reader is introduced to mathematical tools needed for the aforementioned topics. Mathematical proofs and details are given in an appendix. Some programs in MATHEMATICA are also included.
Author: Siu-Ah Ng Publisher: World Scientific ISBN: 9812564527 Category : Business & Economics Languages : en Pages : 313
Book Description
At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives
Author: Thomas Barrau Publisher: Springer Nature ISBN: 3030973190 Category : Mathematics Languages : en Pages : 182
Book Description
This book introduces the novel artificial intelligence technique of polymodels and applies it to the prediction of stock returns. The idea of polymodels is to describe a system by its sensitivities to an environment, and to monitor it, imitating what a natural brain does spontaneously. In practice this involves running a collection of non-linear univariate models. This very powerful standalone technique has several advantages over traditional multivariate regressions. With its easy to interpret results, this method provides an ideal preliminary step towards the traditional neural network approach. The first two chapters compare the technique with other regression alternatives and introduces an estimation method which regularizes a polynomial regression using cross-validation. The rest of the book applies these ideas to financial markets. Certain equity return components are predicted using polymodels in very different ways, and a genetic algorithm is described which combines these different predictions into a single portfolio, aiming to optimize the portfolio returns net of transaction costs. Addressed to investors at all levels of experience this book will also be of interest to both seasoned and non-seasoned statisticians.
Author: Cornelis W Oosterlee Publisher: World Scientific ISBN: 1786347962 Category : Business & Economics Languages : en Pages : 1310
Book Description
This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact [email protected].
Author: Pierre Bernhard Publisher: Birkhäuser ISBN: 9781489985804 Category : Mathematics Languages : en Pages : 0
Book Description
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: · probability-free Black-Scholes theory; · fair-price interval of an option; · representation formulas and fast algorithms for option pricing; · rainbow options; · tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.
Author: John van der Hoek Publisher: Springer Science & Business Media ISBN: 9780387258980 Category : Business & Economics Languages : en Pages : 328
Book Description
This book deals with many topics in modern financial mathematics in a way that does not use advanced mathematical tools and shows how these models can be numerically implemented in a practical way. The book is aimed at undergraduate students, MBA students, and executives who wish to understand and apply financial models in the spreadsheet computing environment. The basic building block is the one-step binomial model where a known price today can take one of two possible values at the next time. In this simple situation, risk neutral pricing can be defined and the model can be applied to price forward contracts, exchange rate contracts, and interest rate derivatives. The simple one-period framework can then be extended to multi-period models. The authors show how binomial tree models can be constructed for several applications to bring about valuations consistent with market prices. The book closes with a novel discussion of real options. John van der Hoek is Senior Lecturer in Applied Mathematics at the University of Adelaide. He has developed courses in finance for a number of years at various levels and is a regular plenary speaker at major conferences on Quantitative Finance. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary. He is the author of over 300 research papers and several books, including Mathematics of Financial Markets, Second Edition (with P. Ekkehard Kopp), Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and Measure Theory and Filtering: Theory and Applications (with Lakhdar Aggoun). He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications, and the Canadian Applied Mathematics Quarterly.
Author: Yue-Kuen Kwok Publisher: Springer ISBN: 9783540862550 Category : Mathematics Languages : en Pages : 530
Book Description
This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.
Author: Douglas Kennedy Publisher: Chapman & Hall/CRC ISBN: 9781138381452 Category : Languages : en Pages : 264
Book Description
Filling the void between surveys of the field with relatively light mathematical content and books with a rigorous, formal approach to stochastic integration and probabilistic ideas,Stochastic Financial Modelsprovides a sound introduction to mathematical finance. The author takes a classical applied mathematical approach, focusing on calculations rather than seeking the greatest generality. Developed from the esteemed author's advanced undergraduate and graduate courses at the University of Cambridge, the text begins with the classical topics of utility and the mean-variance approach to portfolio choice. The remainder of the book deals with derivative pricing. The author fully explains the binomial model since it is central to understanding the pricing of derivatives by self-financing hedging portfolios. He then discusses the general discrete-time model, Brownian motion and the Black-Scholes model. The book concludes with a look at various interest-rate models. Concepts from measure-theoretic probability and solutions to the end-of-chapter exercises are provided in the appendices. By exploring the important and exciting application area of mathematical finance, this text encourages students to learn more about probability, martingales and stochastic integration. It shows how mathematical concepts, such as the Black-Scholes and Gaussian random-field models, are used in financial situations.