A Course In Financial Calculus

Author: Alison Etheridge
Publisher: Cambridge University Press
ISBN: 9780521890779
Size: 30.39 MB
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Finance provides a dramatic example of the successful application of mathematics to the practical problem of pricing financial derivatives. This self-contained text is designed for first courses in financial calculus. Key concepts are introduced in the discrete time framework: proofs in the continuous-time world follow naturally. The second half of the book is devoted to financially sophisticated models and instruments. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts are applied to realistic financial questions.

A Course In Financial Calculus

Author: Alison Etheridge
Publisher: Cambridge University Press
ISBN: 1139434551
Size: 29.31 MB
Format: PDF, Docs
View: 7762
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Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.

Financial Calculus

Author: Martin Baxter
Publisher: Cambridge University Press
ISBN: 1139643274
Size: 33.27 MB
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The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders.

Stochastic Calculus And Financial Applications

Author: J. Michael Steele
Publisher: Springer Science & Business Media
ISBN: 1468493051
Size: 48.22 MB
Format: PDF
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Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH

Elementary Stochastic Calculus With Finance In View

Author: Thomas Mikosch
Publisher: World Scientific
ISBN: 9789810235437
Size: 68.36 MB
Format: PDF, Kindle
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Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

A Course In Derivative Securities

Author: Kerry Back
Publisher: Springer Science & Business Media
ISBN: 3540279008
Size: 54.58 MB
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"Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory....The book...succeeds in presenting intuitively advanced derivative modelling... it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS

Brownian Motion Calculus

Author: Ubbo F. Wiersema
Publisher: John Wiley & Sons
ISBN: 0470021713
Size: 70.61 MB
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Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website.

Option Valuation

Author: Hugo D. Junghenn
Publisher: CRC Press
ISBN: 1439889112
Size: 17.70 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.

Applied Probabilistic Calculus For Financial Engineering

Author: Bertram K. C. Chan
Publisher: John Wiley & Sons
ISBN: 111938804X
Size: 33.81 MB
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Illustrates how R may be used successfully to solve problems in quantitative finance Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering—walking the reader through building an effective financial model from the Geometric Brownian Motion (GBM) Model via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed—along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN. Covers optimization methodologies in probabilistic calculus for financial engineering Answers the question: What does a "Random Walk" Financial Theory look like? Covers the GBM Model and the Random Walk Model Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R s an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.

Financial Decisions And Markets

Author: John Y. Campbell
Publisher: Princeton University Press
ISBN: 1400888220
Size: 37.49 MB
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From the field's leading authority, the most authoritative and comprehensive advanced-level textbook on asset pricing In Financial Decisions and Markets, John Campbell, one of the field’s most respected authorities, provides a broad graduate-level overview of asset pricing. He introduces students to leading theories of portfolio choice, their implications for asset prices, and empirical patterns of risk and return in financial markets. Campbell emphasizes the interplay of theory and evidence, as theorists respond to empirical puzzles by developing models with new testable implications. The book shows how models make predictions not only about asset prices but also about investors’ financial positions, and how they often draw on insights from behavioral economics. After a careful introduction to single-period models, Campbell develops multiperiod models with time-varying discount rates, reviews the leading approaches to consumption-based asset pricing, and integrates the study of equities and fixed-income securities. He discusses models with heterogeneous agents who use financial markets to share their risks, but also may speculate against one another on the basis of different beliefs or private information. Campbell takes a broad view of the field, linking asset pricing to related areas, including financial econometrics, household finance, and macroeconomics. The textbook works in discrete time throughout, and does not require stochastic calculus. Problems are provided at the end of each chapter to challenge students to develop their understanding of the main issues in financial economics. The most comprehensive and balanced textbook on asset pricing available, Financial Decisions and Markets is an essential resource for all graduate students and practitioners in finance and related fields. Integrated treatment of asset pricing theory and empirical evidence Emphasis on investors’ decisions Broad view linking the field to financial econometrics, household finance, and macroeconomics Topics treated in discrete time, with no requirement for stochastic calculus Solutions manual for problems available to professors