Stochastic Calculus for Finance I

Author: Steven Shreve
Publisher: Springer Science & Business Media
ISBN: 0387225277
Format: PDF, ePub, Mobi
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Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume. Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance. Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful. Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

Stochastic Calculus for Finance II

Author: Steven E. Shreve
Publisher: Springer Science & Business Media
ISBN: 9780387401010
Format: PDF, ePub, Mobi
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This is the second volume in a two-volume sequence on Stochastic calculus models in finance. This second volume, which does not require the first volume as a prerequisite, covers infinite state models and continuous time stochastic calculus. The book is suitable for beginning masters-level students in mathematical finance and financial engineering.

Stochastic Calculus for Finance II

Author: Steven Shreve
Publisher: Springer
ISBN: 9781441923110
Format: PDF, Kindle
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"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Financial Calculus

Author: Martin Baxter
Publisher: Cambridge University Press
ISBN: 1139643274
Format: PDF, Docs
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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.

Elementary Stochastic Calculus with Finance in View

Author: Thomas Mikosch
Publisher: World Scientific
ISBN: 9789810235437
Format: PDF, ePub
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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
Format: PDF, ePub
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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

Stochastic Calculus and Financial Applications

Author: J. Michael Steele
Publisher: Springer Science & Business Media
ISBN: 1468493051
Format: PDF, ePub, Docs
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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

Martingale Methods in Financial Modelling

Author: Marek Musiela
Publisher: Springer Science & Business Media
ISBN: 3662221322
Format: PDF, Kindle
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A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.

Essentials of Stochastic Finance

Author: Albert N Shiryaev
Publisher: World Scientific
ISBN: 9814495662
Format: PDF, Docs
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This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks. Contents:Facts. Models:Main Concepts, Structures, and Instruments. Aims and Problems of Financial Theory and Financial EngineeringStochastic Models. Discrete TimeStochastic Models. Continuous TimeStatistical Analysis of Financial DataTheory:Theory of Arbitrage in Stochastic Financial Models. Discrete TimeTheory of Pricing in Stochastic Financial Models. Discrete TimeTheory of Arbitrage in Stochastic Financial Models. Continuous TimeTheory of Pricing in Stochastic Financial Models. Continuous Time Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos. Keywords:Stochastic Finance;Financial Theory;Financial Engineering;Financial MathematicsReviews: “This is a remarkable text, containing a huge amount of interesting material on modern stochastic finance. Especially the young (novice) researcher in the field will find it a very useful basis of results essential for further research. The set of references is impressive and the level of writing is clear and pedagogically sound … a much more in-depth treatment of a very wide and encompassing range of stochastic models is given. In summary: a text to be recommended warmly.” International Statistical Institute “It is a very comprehensive survey of the results from the theories of stochastic processes, time series and related statistical procedures relevant to finance applications. It also develops classical pricing models and results. It is written in a very lively style, in which the author effortlessly jumps from abstract mathematical frameworks to interesting historical remarks.” Mathematical Reviews “The author's choice of material is outstanding and well worth the time and effort it will require to get through … For anyone interested or working in the field and who have a good mathematical background, this book will be a valuable resource and a rich and stimulating source of intellectual pleasure.” Journal of Applied Mathematics and Stochastic Analysis “… as an encyclopedia of results and methods for financial analysis it is very impressive and certainly very useful as well.” Mathematics Abstracts

Methods of Mathematical Finance

Author: Ioannis Karatzas
Publisher: Springer
ISBN: 1493968459
Format: PDF, ePub, Mobi
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This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.