Introductory Course On Financial Mathematics PDF Download

Author: Michael Tretyakov
Publisher: World Scientific Publishing Company
ISBN: 190897740X
Category : Business & Economics
Languages : en
Pages : 277

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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.

Author: Olivier Le Courtois
Publisher:
ISBN: 9781099200199
Category :
Languages : en
Pages : 134

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Book Description
This books presents in a very compact way the fundamental aspects of financial mathematics. It provides the key concepts and tools a student needs to master the Exam FM of the Society of Actuaries (SOA) and the Exam 2 of the Casualty Actuarial Society (CAS). This text benefits from the vision and experience of the author, who is a professor who has taught finance, insurance, and risk management for many years. The author is also a Fellow of the Society of Actuaries. Students interested in econometrics, finance, statistics, mathematics, or other fields, will also find this book a useful tool to help them further their studies. This book can also be warmly recommended as a prerequisite reading to the students who consider taking, or are in the process of taking, the Chartered Financial Analyst (CFA) exams. Indeed, the fixed income and company valuation material studied in the CFA syllabus is fundamentally based on the financial mathematics results shown in this book. This text does not just present the material; it furthers an understanding of the foundations of financial mathematics. This book does not include exercises because it is designed to be used with the (long) series of exercises made freely available by the Society of Actuaries. The tables in the appendix link the exercises of the Society of Actuaries with the equations in the book. These tables can be a very convenient tool for providing hints for the exercises that the student cannot solve - instead of going directly to the solutions. The order in which the contents of this book are presented mostly respects the order of the Society of Actuaries and Casualty Actuarial Society syllabi. Very few adjustments were made to this order and they were done for pedagogical improvement reasons only. This text is the second one in a series dedicated to actuarial associateship exams. In each of these books, conceptual links between the contents of the various exams are provided. This book was also written in such a way that you can use it throughout your career. This book is the book the author would have liked to have when he took the Exam FM of the Society of Actuaries. It contains all the formulas that are useful to solve the official exercises of the SOA. This book is compact, theoretically solid, and not verbose. To benefit fully from this book, a mathematical background of at least one year of calculus after A-level is needed.

Author: Mark S. Joshi
Publisher: Cambridge University Press
ISBN: 0521514088
Category : Business & Economics
Languages : en
Pages : 0

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Book Description
The second edition of a successful text providing the working knowledge needed to become a good quantitative analyst. An ideal introduction to mathematical finance, readers will gain a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice.

Author: R. J. Williams
Publisher: American Mathematical Society
ISBN: 1470460386
Category : Mathematics
Languages : en
Pages : 162

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Book Description
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.

Author: Donald R. Chambers
Publisher: CRC Press
ISBN: 1000370127
Category : Computers
Languages : en
Pages : 581

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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.

Author: Wai-sum Chan
Publisher: World Scientific
ISBN: 9811243298
Category : Business & Economics
Languages : en
Pages : 366

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Book Description
This book provides a thorough understanding of the fundamental concepts of financial mathematics essential for the evaluation of any financial product and instrument. Mastering concepts of present and future values of streams of cash flows under different interest rate environments is core for actuaries and financial economists. This book covers the body of knowledge required by the Society of Actuaries (SOA) for its Financial Mathematics (FM) Exam.The third edition includes major changes such as an addition of an 'R Laboratory' section in each chapter, except for Chapter 9. These sections provide R codes to do various computations, which will facilitate students to apply conceptual knowledge. Additionally, key definitions have been revised and the theme structure has been altered. Students studying undergraduate courses on financial mathematics for actuaries will find this book useful. This book offers numerous examples and exercises, some of which are adapted from previous SOA FM Exams. It is also useful for students preparing for the actuarial professional exams through self-study.

Author: Ernst Eberlein
Publisher: Springer Nature
ISBN: 3030261069
Category : Mathematics
Languages : en
Pages : 774

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Book Description
Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Author: Donald G. Saari
Publisher: Springer Nature
ISBN: 3030254437
Category : Mathematics
Languages : en
Pages : 155

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Book Description
This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.

Author: S. David Promislow
Publisher: John Wiley & Sons
ISBN: 0470978074
Category : Mathematics
Languages : en
Pages : 390

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Book Description
This book provides a comprehensive introduction to actuarial mathematics, covering both deterministic and stochastic models of life contingencies, as well as more advanced topics such as risk theory, credibility theory and multi-state models. This new edition includes additional material on credibility theory, continuous time multi-state models, more complex types of contingent insurances, flexible contracts such as universal life, the risk measures VaR and TVaR. Key Features: Covers much of the syllabus material on the modeling examinations of the Society of Actuaries, Canadian Institute of Actuaries and the Casualty Actuarial Society. (SOA-CIA exams MLC and C, CSA exams 3L and 4.) Extensively revised and updated with new material. Orders the topics specifically to facilitate learning. Provides a streamlined approach to actuarial notation. Employs modern computational methods. Contains a variety of exercises, both computational and theoretical, together with answers, enabling use for self-study. An ideal text for students planning for a professional career as actuaries, providing a solid preparation for the modeling examinations of the major North American actuarial associations. Furthermore, this book is highly suitable reference for those wanting a sound introduction to the subject, and for those working in insurance, annuities and pensions.

Author: Jan Vecer
Publisher: CRC Press
ISBN: 1439812527
Category : Business & Economics
Languages : en
Pages : 339

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Book Description
This classroom-tested text provides a deep understanding of derivative contracts. Unlike much of the existing literature, the book treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quanto, and Asian options. With many examples and exercises, the text relies on intuition and basic principles, rather than technical computations.