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Financial Mathematics

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Financial Mathematics

Financial Mathematics Book
Author : Giuseppe Campolieti,Roman N. Makarov
Publisher : CRC Press
Release : 2018-10-24
ISBN : 1315360489
Language : En, Es, Fr & De

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Book Description :

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

Financial Mathematics Derivatives and Structured Products

Financial Mathematics  Derivatives and Structured Products Book
Author : Raymond H. Chan,Yves ZY. Guo,Spike T. Lee,Xun Li
Publisher : Springer
Release : 2019-02-27
ISBN : 9811336962
Language : En, Es, Fr & De

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Book Description :

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)

Introduction to Financial Mathematics

Introduction to Financial Mathematics Book
Author : Donald R. Chambers,Qin Lu
Publisher : CRC Press
Release : 2021-06-17
ISBN : 1000370127
Language : En, Es, Fr & De

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Book Description :

This book’s primary objective is to educate aspiring finance professionals about mathematics and computation in the context of financial derivatives. The authors offer a balance of traditional coverage and technology to fill the void between highly mathematical books and broad finance books. The focus of this book is twofold: To partner mathematics with corresponding intuition rather than diving so deeply into the mathematics that the material is inaccessible to many readers. To build reader intuition, understanding and confidence through three types of computer applications that help the reader understand the mathematics of the models. Unlike many books on financial derivatives requiring stochastic calculus, this book presents the fundamental theories based on only undergraduate probability knowledge. A key feature of this book is its focus on applying models in three programming languages –R, Mathematica and EXCEL. Each of the three approaches offers unique advantages. The computer applications are carefully introduced and require little prior programming background. The financial derivative models that are included in this book are virtually identical to those covered in the top financial professional certificate programs in finance. The overlap of financial models between these programs and this book is broad and deep.

Mathematics for Finance

Mathematics for Finance Book
Author : Marek Capinski,Tomasz Zastawniak
Publisher : Springer
Release : 2006-04-18
ISBN : 1852338466
Language : En, Es, Fr & De

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Book Description :

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 Mathematics

Financial Mathematics Book
Author : Bruno Biais,Centro internazionale matematico estivo. Session,Thomas Björk,Centro internazionale matematico estivo,Jaksa Cvitanic,Centro Internazionale Matematico Estivo Staff,Nicole El Karoui,Elyes Jouini,J.C. Rochet
Publisher : Springer Science & Business Media
Release : 1997-03-20
ISBN : 9783540626428
Language : En, Es, Fr & De

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Book Description :

Financial Mathematics is an exciting, emerging field of application. The five sets of course notes in this book provide a bird's eye view of the current "state of the art" and directions of research. For graduate students it will therefore serve as an introduction to the field while reseachers will find it a compact source of reference. The reader is expected to have a good knowledge of the basic mathematical tools corresponding to an introductory graduate level, and sufficient familiarity with probabilistic methods, in particular stochastic analysis. B. Biais, J.C. Rochet: Risk-sharing, adverse selection and market structure.- T. Björk: Interest-rate theory.- J. Cvitanic: Optimal trading under constraints.- N. El Karoui, M.C. Quenez: Nonlinear pricing theory and backward stochastic differential equations.- E. Jouini: Market imperfections, equilibrium and arbitrage.

Stochastic Financial Models

Stochastic Financial Models Book
Author : Douglas Kennedy
Publisher : CRC Press
Release : 2016-04-19
ISBN : 1439882711
Language : En, Es, Fr & De

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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 Models provides 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.

Financial Mathematics

Financial Mathematics Book
Author : Giuseppe Campolieti,Roman N. Makarov
Publisher : CRC Press
Release : 2022-12-21
ISBN : 0429889097
Language : En, Es, Fr & De

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Book Description :

The book has been tested and refined through years of classroom teaching experience. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. This textbook provides complete coverage of discrete-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. Key features: In-depth coverage of discrete-time theory and methodology Numerous, fully worked out examples and exercises in every chapter Mathematically rigorous and consistent yet bridging various basic and more advanced concepts Judicious balance of financial theory, mathematical, and computational methods Guide to Material This revision contains: Almost 200 pages worth of new material in all chapters A new chapter on elementary probability theory An expanded the set of solved problems and additional exercises Answers to all exercises This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics. The text complements Financial Mathematics: A Comprehensive Treatment in Continuous Time, by the same authors, also published by CRC Press.

Understanding the Mathematics of Personal Finance

Understanding the Mathematics of Personal Finance Book
Author : Lawrence N. Dworsky
Publisher : John Wiley & Sons
Release : 2009-09-22
ISBN : 9780470538388
Language : En, Es, Fr & De

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Book Description :

A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance Understanding the Mathematics of Personal Finance explains how mathematics, a simple calculator, and basic computer spreadsheets can be used to break down and understand even the most complex loan structures. In an easy-to-follow style, the book clearly explains the workings of basic financial calculations, captures the concepts behind loans and interest in a step-by-step manner, and details how these steps can be implemented for practical purposes. Rather than simply providing investment and borrowing strategies, the author successfully equips readers with the skills needed to make accurate and effective decisions in all aspects of personal finance ventures, including mortgages, annuities, life insurance, and credit card debt. The book begins with a primer on mathematics, covering the basics of arithmetic operations and notations, and proceeds to explore the concepts of interest, simple interest, and compound interest. Subsequent chapters illustrate the application of these concepts to common types of personal finance exchanges, including: Loan amortization and savings Mortgages, reverse mortgages, and viatical settlements Prepayment penalties Credit cards The book provides readers with the tools needed to calculate real costs and profits using various financial instruments. Mathematically inclined readers will enjoy the inclusion of mathematical derivations, but these sections are visually distinct from the text and can be skipped without the loss of content or complete understanding of the material. In addition, references to online calculators and instructions for building the calculations involved in a spreadsheet are provided. Furthermore, a related Web site features additional problem sets, the spreadsheet calculators that are referenced and used throughout the book, and links to various other financial calculators. Understanding the Mathematics of Personal Finance is an excellent book for finance courses at the undergraduate level. It is also an essential reference for individuals who are interested in learning how to make effective financial decisions in their everyday lives.

C for Financial Mathematics

C   for Financial Mathematics Book
Author : John Armstrong
Publisher : CRC Press
Release : 2017-01-06
ISBN : 1498750060
Language : En, Es, Fr & De

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Book Description :

If you know a little bit about financial mathematics but don’t yet know a lot about programming, then C++ for Financial Mathematics is for you. C++ is an essential skill for many jobs in quantitative finance, but learning it can be a daunting prospect. This book gathers together everything you need to know to price derivatives in C++ without unnecessary complexities or technicalities. It leads the reader step-by-step from programming novice to writing a sophisticated and flexible financial mathematics library. At every step, each new idea is motivated and illustrated with concrete financial examples. As employers understand, there is more to programming than knowing a computer language. As well as covering the core language features of C++, this book teaches the skills needed to write truly high quality software. These include topics such as unit tests, debugging, design patterns and data structures. The book teaches everything you need to know to solve realistic financial problems in C++. It can be used for self-study or as a textbook for an advanced undergraduate or master’s level course.

Financial Mathematics Volatility and Covariance Modelling

Financial Mathematics  Volatility and Covariance Modelling Book
Author : Julien Chevallier,Stéphane Goutte,David Guerreiro,Sophie Saglio,Bilel Sanhaji
Publisher : Routledge
Release : 2019-06-28
ISBN : 1351669095
Language : En, Es, Fr & De

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Book Description :

This book provides an up-to-date series of advanced chapters on applied financial econometric techniques pertaining the various fields of commodities finance, mathematics & stochastics, international macroeconomics and financial econometrics. Financial Mathematics, Volatility and Covariance Modelling: Volume 2 provides a key repository on the current state of knowledge, the latest debates and recent literature on financial mathematics, volatility and covariance modelling. The first section is devoted to mathematical finance, stochastic modelling and control optimization. Chapters explore the recent financial crisis, the increase of uncertainty and volatility, and propose an alternative approach to deal with these issues. The second section covers financial volatility and covariance modelling and explores proposals for dealing with recent developments in financial econometrics This book will be useful to students and researchers in applied econometrics; academics and students seeking convenient access to an unfamiliar area. It will also be of great interest established researchers seeking a single repository on the current state of knowledge, current debates and relevant literature.

Introductory Course on Financial Mathematics

Introductory Course on Financial Mathematics Book
Author : M V Tretyakov
Publisher : World Scientific Publishing Company
Release : 2013-07-23
ISBN : 190897740X
Language : En, Es, Fr & De

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Book Description :

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.

Risk Neutral Pricing and Financial Mathematics

Risk Neutral Pricing and Financial Mathematics Book
Author : Peter M. Knopf,John L. Teall
Publisher : Elsevier
Release : 2015-07-29
ISBN : 0128017279
Language : En, Es, Fr & De

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Book Description :

Risk Neutral Pricing and Financial Mathematics: A Primer provides a foundation to financial mathematics for those whose undergraduate quantitative preparation does not extend beyond calculus, statistics, and linear math. It covers a broad range of foundation topics related to financial modeling, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, and term structure models, along with related valuation and hedging techniques. The joint effort of two authors with a combined 70 years of academic and practitioner experience, Risk Neutral Pricing and Financial Mathematics takes a reader from learning the basics of beginning probability, with a refresher on differential calculus, all the way to Doob-Meyer, Ito, Girsanov, and SDEs. It can also serve as a useful resource for actuaries preparing for Exams FM and MFE (Society of Actuaries) and Exams 2 and 3F (Casualty Actuarial Society). Includes more subjects than other books, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, term structure models, valuation, and hedging techniques Emphasizes introductory financial engineering, financial modeling, and financial mathematics Suited for corporate training programs and professional association certification programs

Lectures on Financial Mathematics

Lectures on Financial Mathematics Book
Author : Greg Anderson,Alec Kercheval
Publisher : Springer Nature
Release : 2022-06-01
ISBN : 3031023994
Language : En, Es, Fr & De

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Book Description :

This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage", the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book. The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful. Table of Contents: Overture: Single-Period Models / The General Discrete Model / The Fundamental Theorems of Asset Pricing / Forwards and Futures / Incomplete Markets

An Introduction to Financial Mathematics

An Introduction to Financial Mathematics Book
Author : Hugo D. Junghenn
Publisher : CRC Press
Release : 2019-03-14
ISBN : 0429558961
Language : En, Es, Fr & De

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Book Description :

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/.

Martingales and Financial Mathematics in Discrete Time

Martingales and Financial Mathematics in Discrete Time Book
Author : Benoîte de Saporta,Mounir Zili
Publisher : John Wiley & Sons
Release : 2021-12-20
ISBN : 1119885027
Language : En, Es, Fr & De

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Book Description :

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time. The book offers a combination of mathematical teaching and numerous exercises for wide appeal. It is a useful reference for students at the master’s or doctoral level who are specializing in applied mathematics or finance as well as teachers, researchers in the field of economics or actuarial science, or professionals working in the various financial sectors. Martingales and Financial Mathematics in Discrete Time is also for anyone who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics, or in the application of the martingale theory in finance

An Undergraduate Introduction to Financial Mathematics Third Edition

An Undergraduate Introduction to Financial Mathematics   Third Edition Book
Author : J Robert Buchanan
Publisher : World Scientific Publishing Company
Release : 2012-07-13
ISBN : 9814407461
Language : En, Es, Fr & De

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Book Description :

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.

The Financial Mathematics of Market Liquidity

The Financial Mathematics of Market Liquidity Book
Author : Olivier Gueant
Publisher : CRC Press
Release : 2016-03-30
ISBN : 1498725481
Language : En, Es, Fr & De

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Book Description :

This book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problems-inspired from the Almgren-Chriss app

Computational Financial Mathematics using MATHEMATICA

Computational Financial Mathematics using MATHEMATICA   Book
Author : Srdjan Stojanovic
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461200431
Language : En, Es, Fr & De

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Book Description :

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.

Mastering Financial Mathematics in Microsoft Excel

Mastering Financial Mathematics in Microsoft Excel Book
Author : Alastair Day
Publisher : Pearson UK
Release : 2013-02-25
ISBN : 0273746723
Language : En, Es, Fr & De

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Book Description :

A practical guide for business calculations Mastering Financial Mathematics in Microsoft © Excel provides a comprehensive set of tools, methods and formulas which apply Excel to solving mathematical problems. The book: Explains basic calculations for mathematical finance Shows how to use formulas using straightforward Excel templates Provides a CD of basic templates This fully revised and updated guide is an essential companion for anyone involved in finance, from company accountants, through to analysts, treasury managers and business students. Explaining basic calculations and using examples and exercises, the book covers: Cash flows Bonds calculations and bonds risks Amortization and depreciation Forward interest rates and futures Foreign exchange Valuation Leasing Mastering Financial Mathematics in Microsoft Excel is a practical guide to using Excel for financial mathematics. This new edition includes: Excel 2007 Addition of a glossary of key terms Functions list in English and Euro languages Continuity check on all formats, layouts and charts More worked examples Addition of exercises at the end of each chapter to help build models About the authors Alastair Day has worked in the finance industry for more than 25 years in treasury and marketing functions and was formerly a director of a vendor leasing company specializing in the IT and technology industries. After sale to a public company he established Systematic Finance as a consultancy specializing in: ■ Financial modelling – review, design, build and audit ■ Training in financial modelling, corporate finance, leasing and credit analysis on an in-house and public basis throughout Europe, Middle East, Africa, Asia and America ■ Finance and operating lease structuring as a consultant and lessor Alastair is author of three modelling books published by FT Prentice Hall: Mastering Financial Modelling, Mastering Risk Modelling and Mastering Financial Mathematics in Excel, all of which are in their second editions, as well as other books and publications on financial analysis and leasing. Alastair has a degree in Economics and German from London University and an MBA from the Open University Business School. * * * * * * *

Convex Duality and Financial Mathematics

Convex Duality and Financial Mathematics Book
Author : Peter Carr,Qiji Jim Zhu
Publisher : Springer
Release : 2018-07-18
ISBN : 3319924923
Language : En, Es, Fr & De

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Book Description :

This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims