Introductory Course On Financial Mathematics

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Introductory Course On Financial Mathematics

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Author : Michael Tretyakov
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-07-23

Introductory Course On Financial Mathematics written by Michael Tretyakov and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-23 with Business & Economics categories.

This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple, but widely used, financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to understand the concepts considered in this book.Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective of quantifying and hedging risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas concerning derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a ‘sandwich’ structure: probability and stochastics are given in situ where mathematics can be readily illustrated by application to finance.The first part of the book introduces one of the main principles in finance — ‘no arbitrage pricing’. It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part deals with pricing and hedging of European- and American-type options in the discrete-time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time discrete-space stochastic processes used in financial modelling are considered. The third part introduces the Wiener process, Ito integrals and stochastic differential equations, but its main focus is the famous Black-Scholes formula for pricing European options. Some guidance for further study within this exciting and rapidly changing field is given in the concluding chapter. There are approximately 100 exercises interspersed throughout the book, and solutions for most problems are provided in the appendices.

Undergraduate Introduction To Financial Mathematics An Third Edition

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Author : J Robert Buchanan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-07-13

Undergraduate Introduction To Financial Mathematics An Third Edition written by J Robert Buchanan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-13 with Business & Economics categories.

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the theory of interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. This third edition expands on the second by including a new chapter on the extensions of the Black-Scholes model of option pricing and a greater number of exercises at the end of each chapter. More background material and exercises added, with solutions provided to the other chapters, allowing the textbook to better stand alone as an introduction to financial mathematics. The reader progresses from a solid grounding in multivariable calculus through a derivation of the Black-Scholes equation, its solution, properties, and applications. The text attempts to be as self-contained as possible without relying on advanced mathematical and statistical topics. The material presented in this book will adequately prepare the reader for graduate-level study in mathematical finance.

Undergraduate Introduction To Financial Mathematics An Fourth Edition

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Author : J Robert Buchanan
language : en
Publisher: World Scientific
Release Date : 2022-10-25

Undergraduate Introduction To Financial Mathematics An Fourth Edition written by J Robert Buchanan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-25 with Business & Economics categories.

Anyone with an interest in learning about the mathematical modeling of prices of financial derivatives such as bonds, futures, and options can start with this book, whereby the only mathematical prerequisite is multivariable calculus. The necessary theory of interest, statistical, stochastic, and differential equations are developed in their respective chapters, with the goal of making this introductory text as self-contained as possible.In this edition, the chapters on hedging portfolios and extensions of the Black-Scholes model have been expanded. The chapter on optimizing portfolios has been completely re-written to focus on the development of the Capital Asset Pricing Model. The binomial model due to Cox-Ross-Rubinstein has been enlarged into a standalone chapter illustrating the wide-ranging utility of the binomial model for numerically estimating option prices. There is a completely new chapter on the pricing of exotic options. The appendix now features linear algebra with sufficient background material to support a more rigorous development of the Arbitrage Theorem.The new edition has more than doubled the number of exercises compared to the previous edition and now contains over 700 exercises. Thus, students completing the book will gain a deeper understanding of the development of modern financial mathematics.

An Introduction To Financial Mathematics

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Author : Hugo D. Junghenn
language : en
Publisher: CRC Press
Release Date : 2019-03-14

An Introduction To Financial Mathematics written by Hugo D. Junghenn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-14 with Business & Economics categories.

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/.

Introduction To Quantitative Finance

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Author : Robert R. Reitano
language : en
Publisher: MIT Press
Release Date : 2010-01-29

Introduction To Quantitative Finance written by Robert R. Reitano and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-29 with Mathematics categories.

An introduction to many mathematical topics applicable to quantitative finance that teaches how to “think in mathematics” rather than simply do mathematics by rote. This text offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems. It emphasizes the thought process and mathematical approach taken to develop each result instead of the memorization of formulas to be applied (or misapplied) automatically. The objective is to provide a deep level of understanding of the relevant mathematical theory and tools that can then be effectively used in practice, to teach students how to “think in mathematics” rather than simply to do mathematics by rote. Each chapter covers an area of mathematics such as mathematical logic, Euclidean and other spaces, set theory and topology, sequences and series, probability theory, and calculus, in each case presenting only material that is most important and relevant for quantitative finance. Each chapter includes finance applications that demonstrate the relevance of the material presented. Problem sets are offered on both the mathematical theory and the finance applications sections of each chapter. The logical organization of the book and the judicious selection of topics make the text customizable for a number of courses. The development is self-contained and carefully explained to support disciplined independent study as well. A solutions manual for students provides solutions to the book's Practice Exercises; an instructor's manual offers solutions to the Assignment Exercises as well as other materials.

Introduction To Financial Mathematics

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Author : Kevin J. Hastings
language : en
Publisher: CRC Press
Release Date : 2024-11-27

Introduction To Financial Mathematics written by Kevin J. Hastings and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-27 with Mathematics categories.

The second edition of this successful and widely recognized textbook again focuses on discrete topics. The author recognizes two distinct paths of study and careers of actuarial science and financial engineering. This text can be very useful as a common core for both. Therefore, there is substantial material in Introduction to Financial Mathematics, Second Edition on the theory of interest (the first half of the book), as well as the probabilistic background necessary for the study of portfolio optimization and derivative valuation (the second half). A course in multivariable calculus is not required. The material in the first two chapters should go a long way toward helping students prepare for the Financial Mathematics (FM) actuarial exam. Also, the discrete material will reveal how beneficial it is for the students to know more about loans in their personal financial lives. The notable changes and updates to this edition are itemized in the Preface, but overall, the presentation has been made more efficient. One example is the chapter on discrete probability, which is rather unique in its emphasis on giving the deterministic problems studied earlier a probabilistic context. The section on Markov chains, which is not essential to the development, has been scaled down. Sample spaces and probability measures, random variables and distributions, expectation, conditional probability, independence, and estimation all follow. Optimal portfolio selection coverage is reorganized and the section on the practicalities of stock transactions has been revised. Market portfolio and Capital Market Theory coverage is expanded. New sections on Swaps and Value-at-Risk have been added. This book, like the first edition, was written so that the print edition could stand alone. At times we simplify complicated algebraic expressions, or solve systems of linear equations, or numerically solve non-linear equations. Also, some attention is given to the use of computer simulation to approximate solutions to problems.

Undergraduate Introduction To Financial Mathematics An Second Edition

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Author : J Robert Buchanan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2008-09-29

Undergraduate Introduction To Financial Mathematics An Second Edition written by J Robert Buchanan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-29 with Mathematics categories.

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses.It introduces the Theory of Interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. The reader progresses from a solid grounding in multi-variable calculus through a derivation of the Black-Scholes equation, its solution, properties, and applications.

A First Course In Options Pricing Theory

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Author : Simone Calogero
language : en
Publisher: SIAM
Release Date : 2023-06-01

A First Course In Options Pricing Theory written by Simone Calogero and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-01 with Mathematics categories.

Among the many branches of applied mathematics, options pricing theory occupies a unique position: it utilizes a wide range of advanced mathematical concepts, making it appealing to mathematicians, and it is regularly applied at financial institutions, making it indispensable to practitioners. The emergence of artificial intelligence in the financial industry has led to further interest in mathematical finance and has increased the demand for literature on this subject that is accessible to a large audience. This book presents a self-contained introduction to options pricing theory and includes a complete discussion of the required concepts in finance and probability theory; an introduction to basic models, emphasizing both critical thinking and practical applications; and over 200 exercises, several Python codes for the analysis and application of the options pricing models, and numerical projects intended to help close the gap between theory and practice. A First Course in Options Pricing Theory is suitable for an advanced undergraduate course on financial mathematics and options pricing theory in engineering, computer science, and applied mathematics programs. The reader is assumed to be familiar with the standard material in calculus and linear algebra. Stochastic calculus is not used in the book.

Computational Finance

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Author : Argimiro Arratia
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-05-08

Computational Finance written by Argimiro Arratia 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 2014-05-08 with Computers categories.

The book covers a wide range of topics, yet essential, in Computational Finance (CF), understood as a mix of Finance, Computational Statistics, and Mathematics of Finance. In that regard it is unique in its kind, for it touches upon the basic principles of all three main components of CF, with hands-on examples for programming models in R. Thus, the first chapter gives an introduction to the Principles of Corporate Finance: the markets of stock and options, valuation and economic theory, framed within Computation and Information Theory (e.g. the famous Efficient Market Hypothesis is stated in terms of computational complexity, a new perspective). Chapters 2 and 3 give the necessary tools of Statistics for analyzing financial time series, it also goes in depth into the concepts of correlation, causality and clustering. Chapters 4 and 5 review the most important discrete and continuous models for financial time series. Each model is provided with an example program in R. Chapter 6 covers the essentials of Technical Analysis (TA) and Fundamental Analysis. This chapter is suitable for people outside academics and into the world of financial investments, as a primer in the methods of charting and analysis of value for stocks, as it is done in the financial industry. Moreover, a mathematical foundation to the seemly ad-hoc methods of TA is given, and this is new in a presentation of TA. Chapter 7 reviews the most important heuristics for optimization: simulated annealing, genetic programming, and ant colonies (swarm intelligence) which is material to feed the computer savvy readers. Chapter 8 gives the basic principles of portfolio management, through the mean-variance model, and optimization under different constraints which is a topic of current research in computation, due to its complexity. One important aspect of this chapter is that it teaches how to use the powerful tools for portfolio analysis from the RMetrics R-package. Chapter 9 is a natural continuation of chapter 8 into the new area of research of online portfolio selection. The basic model of the universal portfolio of Cover and approximate methods to compute are also described.

Monte Carlo Simulation With Applications To Finance

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Author : Hui Wang
language : en
Publisher: CRC Press
Release Date : 2012-05-22

Monte Carlo Simulation With Applications To Finance written by Hui Wang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-22 with Business & Economics categories.

Developed from the author’s course on Monte Carlo simulation at Brown University, Monte Carlo Simulation with Applications to Finance provides a self-contained introduction to Monte Carlo methods in financial engineering. It is suitable for advanced undergraduate and graduate students taking a one-semester course or for practitioners in the financial industry. The author first presents the necessary mathematical tools for simulation, arbitrary free option pricing, and the basic implementation of Monte Carlo schemes. He then describes variance reduction techniques, including control variates, stratification, conditioning, importance sampling, and cross-entropy. The text concludes with stochastic calculus and the simulation of diffusion processes. Only requiring some familiarity with probability and statistics, the book keeps much of the mathematics at an informal level and avoids technical measure-theoretic jargon to provide a practical understanding of the basics. It includes a large number of examples as well as MATLAB® coding exercises that are designed in a progressive manner so that no prior experience with MATLAB is needed.