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An Introduction to the Mathematics of Financial Derivatives

An Introduction to the Mathematics of Financial Derivatives
  • Author : Salih N. Neftci,Ali Hirsa,Salih N.. Neftci
  • Publisher :Unknown
  • Release Date :2000-06-02
  • Total pages :527
  • ISBN : 9780125153928
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Summary : A step-by-step explanation of the mathematical models used to price derivatives. For this second edition, Salih Neftci has expanded one chapter, added six new ones, and inserted chapter-concluding exercises. He does not assume that the reader has a thorough mathematical background. His explanations of financial calculus seek to be simple and perceptive.

The Mathematics of Financial Derivatives

The Mathematics of Financial Derivatives
  • Author : Paul Wilmott,Susan Howson,Sam Howison,Wilmott-Howison-Dewynne ...,Jeff Dewynne
  • Publisher :Unknown
  • Release Date :1995-09-29
  • Total pages :317
  • ISBN : 0521497892
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Summary : Basic option theory - Numerical methods - Further option theory - Interest rate derivative products.

Financial Calculus

Financial Calculus
  • Author : Martin Baxter,Andrew Rennie,Andrew J. O. Rennie
  • Publisher :Unknown
  • Release Date :1996-09-19
  • Total pages :233
  • ISBN : 0521552893
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Summary : A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

Mathematical Models of Financial Derivatives

Mathematical Models of Financial Derivatives
  • Author : Yue-Kuen Kwok
  • Publisher :Unknown
  • Release Date :2008-07-10
  • Total pages :530
  • ISBN : 3540686886
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Summary : 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.

An Introduction to Financial Mathematics

An Introduction to Financial Mathematics
  • Author : Hugo D. Junghenn
  • Publisher :Unknown
  • Release Date :2019-03-14
  • Total pages :304
  • ISBN : 9780429558962
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Summary : Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of fifteen chapters, the first ten of which develop option valuation techniques in discrete time, the last five describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author’s webpage https://home.gwu.edu/~hdj/.

Financial Derivatives

Financial Derivatives
  • Author : Jamil Baz,George Chacko
  • Publisher :Unknown
  • Release Date :2004-01-12
  • Total pages :338
  • ISBN : 052181510X
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Summary : This book offers a complete, succinct account of the principles of financial derivatives pricing. The first chapter provides readers with an intuitive exposition of basic random calculus. Concepts such as volatility and time, random walks, geometric Brownian motion, and Ito's lemma are discussed heuristically. The second chapter develops generic pricing techniques for assets and derivatives, determining the notion of a stochastic discount factor or pricing kernel, and then uses this concept to price conventional and exotic derivatives. The third chapter applies the pricing concepts to the special case of interest rate markets, namely, bonds and swaps, and discusses factor models and term structure consistent models. The fourth chapter deals with a variety of mathematical topics that underlie derivatives pricing and portfolio allocation decisions such as mean-reverting processes and jump processes and discusses related tools of stochastic calculus such as Kolmogorov equations, martingale techniques, stochastic control, and partial differential equations.

An Introduction to the Mathematics of Financial Derivatives

An Introduction to the Mathematics of Financial Derivatives
  • Author : Ali Hirsa,Salih N. Neftci
  • Publisher :Unknown
  • Release Date :2013-12-18
  • Total pages :454
  • ISBN : 9780123846839
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Summary : An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning Presented intuitively, breaking up complex mathematics concepts into easily understood notions Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching

Derivatives

Derivatives
  • Author : Paul Wilmott
  • Publisher :Unknown
  • Release Date :1998-12-08
  • Total pages :768
  • ISBN : 0471983667
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Summary : Derivatives by Paul Wilmott provides the most comprehensive and accessible analysis of the art of science in financial modeling available. Wilmott explains and challenges many of the tried and tested models while at the same time offering the reader many new and previously unpublished ideas and techniques. Paul Wilmott has produced a compelling and essential new work in this field. The basics of the established theories-such as stochastic calculus, Black-Scholes, binomial trees and interest-rate models-are covered in clear and precise detail, but Derivatives goes much further. Complex models-such as path dependency, non-probabilistic models, static hedging and quasi-Monte Carlo methods-are introduced and explained to a highly sophisticated level. But theory in itself is not enough, an understanding of the role the techniques play in the daily world of finance is also examined through the use of spreadsheets, examples and the inclusion of Visual Basic programs. The book is divided into six parts: Part One: acts as an introduction and explanation of the fundamentals of derivatives theory and practice, dealing with the equity, commodity and currency worlds. Part Two: takes the mathematics of Part One to a more complex level, introducing the concept of path dependency. Part Three: concerns extensions of the Black-Scholes world, both classic and modern. Part Four: deals with models for fixed-income products. Part Five: describes models for risk management and measurement. Part Six: delivers the numerical methods required for implementing the models described in the rest of the book. Derivatives also includes a CD containing a wide variety of implementation material related to the book in the form of spreadsheets and executable programs together with resource material such as demonstration software and relevant contributed articles. At all times the style remains readable and compelling making Derivatives the essential book on every finance shelf.

Financial Derivatives

Financial Derivatives
  • Author : Robert W. Kolb,James A. Overdahl
  • Publisher :Unknown
  • Release Date :2010
  • Total pages :600
  • ISBN : 9780470499108
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Summary : Essential insights on the various aspects of financialderivatives If you want to understand derivatives without getting boggeddown by the mathematics surrounding their pricing and valuation,Financial Derivatives is the book for you. Through in-depthinsights gleaned from years of financial experience, Robert Kolband James Overdahl clearly explain what derivatives are and how youcan prudently use them within the context of your underlyingbusiness activities. Financial Derivatives introduces you to the wide range ofmarkets for financial derivatives. This invaluable guide offers abroad overview of the different types of derivatives-futures,options, swaps, and structured products-while focusing on theprinciples that determine market prices. This comprehensiveresource also provides a thorough introduction to financialderivatives and their importance to risk management in a corporatesetting. Filled with helpful tables and charts, FinancialDerivatives offers a wealth of knowledge on futures, options,swaps, financial engineering, and structured products. Discusses what derivatives are and how you can prudentlyimplement them within the context of your underlying businessactivities Provides thorough coverage of financial derivatives and theirrole in risk management Explores financial derivatives without getting bogged down bythe mathematics surrounding their pricing and valuation This informative guide will help you unlock the incrediblepotential of financial derivatives.

Financial Mathematics, Derivatives and Structured Products

Financial Mathematics, Derivatives and Structured Products
  • Author : Raymond H. Chan,Yves ZY. Guo,Spike T. Lee,Xun Li
  • Publisher :Unknown
  • Release Date :2019-02-27
  • Total pages :395
  • ISBN : 9789811336966
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Summary : This book introduces readers to the financial markets, derivatives, structured products and how the products are modelled and implemented by practitioners. In addition, it equips readers with the necessary knowledge of financial markets needed in order to work as product structurers, traders, sales or risk managers. As the book seeks to unify the derivatives modelling and the financial engineering practice in the market, it will be of interest to financial practitioners and academic researchers alike. Further, it takes a different route from the existing financial mathematics books, and will appeal to students and practitioners with or without a scientific background. The book can also be used as a textbook for the following courses: • Financial Mathematics (undergraduate level) • Stochastic Modelling in Finance (postgraduate level) • Financial Markets and Derivatives (undergraduate level) • Structured Products and Solutions (undergraduate/postgraduate level)

Stochastic Finance

Stochastic Finance
  • Author : Hans Föllmer,Alexander Schied
  • Publisher :Unknown
  • Release Date :2016-07-25
  • Total pages :608
  • ISBN : 9783110463453
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Summary : This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures

Introduction to the Economics and Mathematics of Financial Markets

Introduction to the Economics and Mathematics of Financial Markets
  • Author : Jakša Cvitanić,Fernando Zapatero
  • Publisher :Unknown
  • Release Date :2004
  • Total pages :494
  • ISBN : 0262033208
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Summary : An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models--a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.

Mathematics for Finance

Mathematics for Finance
  • Author : Marek Capinski,Tomasz Zastawniak
  • Publisher :Unknown
  • Release Date :2006-04-18
  • Total pages :314
  • ISBN : 9781852338466
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Summary : This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.

Financial Derivatives in Theory and Practice

Financial Derivatives in Theory and Practice
  • Author : Philip Hunt,Joanne Kennedy
  • Publisher :Unknown
  • Release Date :2004-11-19
  • Total pages :468
  • ISBN : 9780470863602
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Summary : The term Financial Derivative is a very broad term which has come to mean any financial transaction whose value depends on the underlying value of the asset concerned. Sophisticated statistical modelling of derivatives enables practitioners in the banking industry to reduce financial risk and ultimately increase profits made from these transactions. The book originally published in March 2000 to widespread acclaim. This revised edition has been updated with minor corrections and new references, and now includes a chapter of exercises and solutions, enabling use as a course text. Comprehensive introduction to the theory and practice of financial derivatives. Discusses and elaborates on the theory of interest rate derivatives, an area of increasing interest. Divided into two self-contained parts ? the first concentrating on the theory of stochastic calculus, and the second describes in detail the pricing of a number of different derivatives in practice. Written by well respected academics with experience in the banking industry. A valuable text for practitioners in research departments of all banking and finance sectors. Academic researchers and graduate students working in mathematical finance.

The Mathematics of Derivatives Securities with Applications in MATLAB

The Mathematics of Derivatives Securities with Applications in MATLAB
  • Author : Mario Cerrato
  • Publisher :Unknown
  • Release Date :2012-02-24
  • Total pages :248
  • ISBN : 9781119973416
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Summary : Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future. The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling. The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically. Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics.

Elementary Financial Derivatives

Elementary Financial Derivatives
  • Author : Jana Sacks
  • Publisher :Unknown
  • Release Date :2015-11-02
  • Total pages :232
  • ISBN : 9781119076759
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Summary : A step-by-step approach to the mathematical financial theory and quantitative methods needed to implement and apply state-of-the-art valuation techniques Written as an accessible and appealing introduction to financial derivatives, Elementary Financial Derivatives: A Guide to Trading and Valuation with Applications provides the necessary techniques for teaching and learning complex valuation techniques. Filling the current gap in financial engineering literature, the book emphasizes an easy-to-understand approach to the methods and applications of complex concepts without focusing on the underlying statistical and mathematical theories. Organized into three comprehensive sections, the book discusses the essential topics of the derivatives market with sections on options, swaps, and financial engineering concepts applied primarily, but not exclusively, to the futures market. Providing a better understanding of how to assess risk exposure, the book also includes: A wide range of real-world applications and examples detailing the theoretical concepts discussed throughout Numerous homework problems, highlighted equations, and Microsoft® Office Excel® modules for valuation Pedagogical elements such as solved case studies, select answers to problems, and key terms and concepts to aid comprehension of the presented material A companion website that contains an Instructor’s Solutions Manual, sample lecture PowerPoint® slides, and related Excel files and data sets Elementary Financial Derivatives: A Guide to Trading and Valuation with Applications is an excellent introductory textbook for upper-undergraduate courses in financial derivatives, quantitative finance, mathematical finance, and financial engineering. The book is also a valuable resource for practitioners in quantitative finance, industry professionals who lack technical knowledge of pricing options, and readers preparing for the CFA exam. Jana Sacks, PhD, is Associate Professor in the Department of Accounting and Finance at St. John Fisher College in Rochester, New York. A member of The American Finance Association, the National Association of Corporate Directors, and the International Atlantic Economic Society, Dr. Sack’s research interests include risk management, credit derivatives, pricing, hedging, and structured finance.

Martingale Methods in Financial Modelling

Martingale Methods in Financial Modelling
  • Author : Marek Musiela
  • Publisher :Unknown
  • Release Date :2013-06-29
  • Total pages :513
  • ISBN : 9783662221327
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Summary : A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.

Introduction to the Mathematics of Finance

Introduction to the Mathematics of Finance
  • Author : Ruth J. Williams
  • Publisher :Unknown
  • Release Date :2006
  • Total pages :150
  • ISBN : 9780821839034
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Summary : The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.

An Introduction to Mathematical Finance with Applications

An Introduction to Mathematical Finance with Applications
  • Author : Arlie O. Petters,Xiaoying Dong
  • Publisher :Unknown
  • Release Date :2016-06-17
  • Total pages :483
  • ISBN : 9781493937837
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Summary : This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.

Mathematics of Derivative Securities

Mathematics of Derivative Securities
  • Author : Mathematical Finance Programme
  • Publisher :Unknown
  • Release Date :1997-10-13
  • Total pages :582
  • ISBN : 0521584248
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Summary : During 1995 the Isaac Newton Institute for the Mathematical Sciences at Cambridge University hosted a six month research program on financial mathematics. During this period more than 300 scholars and financial practitioners attended to conduct research and to attend more than 150 research seminars. Many of the presented papers were on the subject of financial derivatives. The very best were selected to appear in this volume. They range from abstract financial theory to practical issues pertaining to the pricing and hedging of interest rate derivatives and exotic options in the market place. Hence this book will be of interest to both academic scholars and financial engineers.

Introduction to the Mathematics of Finance

Introduction to the Mathematics of Finance
  • Author : Steven Roman
  • Publisher :Unknown
  • Release Date :2013-12-01
  • Total pages :356
  • ISBN : 9781441990051
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Summary : An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag.