an undergraduate introduction to financial mathematics

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An Undergraduate Introduction To Financial Mathematics

Author : J. Robert Buchanan
ISBN : 9789812835352
Genre : Mathematics
File Size : 69. 27 MB
Format : PDF
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"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, random variables and probability, stochastic processes, arbitrage, option pricing, hedging, and portfolio optimization. The student progresses from knowing only elementary calculus to understanding the derivation and solution of the Black-Scholes partial differential equation and its solutions. This is one of the few books on the subject of financial mathematics which is accessible to undergraduates having only a thorough grounding in elementary calculus. It explains the subject matter without 'hand waving' arguments and includes numerous examples. Every chapter concludes with a set of exercises which test the chapter's concepts and fill in details of derivations." -- Publisher's description.

An Undergraduate Introduction To Financial Mathematics Third Edition

Author : J Robert Buchanan
ISBN : 9789814407465
Genre : Mathematics
File Size : 44. 37 MB
Format : PDF, ePub
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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.

Introduction To Financial Mathematics

Author : Kevin J. Hastings
ISBN : 9781498723916
Genre : Mathematics
File Size : 27. 51 MB
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Introduction to Financial Mathematics is ideal for an introductory undergraduate course. Unlike most textbooks aimed at more advanced courses, the text motivates students through a discussion of personal finances and portfolio management. The author then goes on to cover valuation of financial derivatives in discrete time, using all of closed form, recursive, and simulation methods. The text covers nearly all of the syllabus topics of the Financial Mathematics Actuarial examination, providing students with the foundation they require for future studies and throughout their careers. It begins by covering standard material on the mathematics of interest, including compound interest, present value, annuities, loans, several versions of the rate of return on an investment, and interest in continuous time. The text explains how to value bonds at their issue dates, at coupon times, between coupon times, and in cases where the bonds are terminated early. Next, it supplies a rapid-fire overview of the main ideas and techniques of discrete probability, including sample spaces and probability measures, random variables and distributions, expectation, conditional probability, and independence. The author introduces the basic terminology of stocks and stock trading. He also explains how to derive the rate of return on a portfolio and how to use the idea of risk aversion to model the investor tradeoff between risk and return. The text also discusses the estimation of parameters of asset models from real data. The text closes with a detailed discussion of how to value financial derivatives using anti-arbitrage assumptions. The one-step and multi-step cases are covered, and exotic options such as barrier options are also introduced, to which simulation methods are applied. Many of the examples in the book involve numerical solution of complicated non-linear equations; others ask students to produce algorithms which beg to be implemented as programs. For maximum flexibility, the author has produced the text without adhering to any particular computational platform. A digital version of this text is also available in the form of Mathematica notebooks that contain additional content.

Mathematics For Finance

Author : Marek Capiński
ISBN : 1852333308
Genre : Mathematics
File Size : 36. 78 MB
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Designed to form the basis of an undergraduate course in mathematical finance, this book builds on mathematical models of bond and stock prices and covers three major areas of mathematical finance that all have an enormous impact on the way modern financial markets operate, namely: Black-Scholesâ arbitrage pricing of options and other derivative securities; Markowitz portfolio optimization theory and the Capital Asset Pricing Model; and interest rates and their term structure. Assuming only a basic knowledge of probability and calculus, it covers the material in a mathematically rigorous and complete way at a level accessible to second or third year undergraduate students. The text is interspersed with a multitude of worked examples and exercises, so it is ideal for self-study and suitable not only for students of mathematics, but also students of business management, finance and economics, and anyone with an interest in finance who needs to understand the underlying theory.

Mathematics For Finance

Author : Marek Capinski
ISBN : 9781852338466
Genre : Business & Economics
File Size : 51. 62 MB
Format : PDF
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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.

Option Valuation

Author : Hugo D. Junghenn
ISBN : 9781439889114
Genre : Business & Economics
File Size : 21. 3 MB
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Option Valuation: A First Course in Financial Mathematics provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models. Developing the requisite mathematical background as needed, the text presents an introduction to probability theory and stochastic calculus suitable for undergraduate students in mathematics, economics, and finance. The first nine chapters of the book describe option valuation techniques in discrete time, focusing on the binomial model. The author shows how the binomial model offers a practical method for pricing options using relatively elementary mathematical tools. The binomial model also enables a clear, concrete exposition of fundamental principles of finance, such as arbitrage and hedging, without the distraction of complex mathematical constructs. The remaining chapters illustrate the theory in continuous time, with an emphasis on the more mathematically sophisticated Black-Scholes-Merton model. Largely self-contained, this classroom-tested text offers a sound introduction to applied probability through a mathematical finance perspective. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. The exercises range from routine applications to spreadsheet projects to the pricing of a variety of complex financial instruments. Hints and solutions to odd-numbered problems are given in an appendix and a full solutions manual is available for qualifying instructors.

Financial Mathematics

Author : Giuseppe Campolieti
ISBN : 9781315360485
Genre : Business & Economics
File Size : 23. 27 MB
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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.

Elementary Calculus Of Financial Mathematics

Author : A. J. Roberts
ISBN : 0898718228
Genre : Calculus
File Size : 23. 68 MB
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Financial mathematics and its calculus introduced in an accessible manner for undergraduate students. Topics covered include financial indices as stochastic processes, Ito's stochastic calculus, the Fokker-Planck Equation and extra MATLAB/SCILAB code.

Solutions Manual For Introduction To The Economics And Mathematics Of Financial Markets

Author : Jakša Cvitanić
ISBN : 026253259X
Genre : Business & Economics
File Size : 88. 20 MB
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This textbook in financial economics provides a rigorous overview of the subject that -- because of an innovative presentation -- is suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three levels 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.

Mathematical Modeling

Author : Stefan Heinz
ISBN : 3642203116
Genre : Computers
File Size : 21. 48 MB
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The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions. Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed. Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods. Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed – which is an important problem of current research.

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