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Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance
Stochastic finance and financial engineering have been rapidlyexpanding fields of science over the past four decades, mainly dueto the success of sophisticated quantitative methodologies inhelping professionals manage financial risks. In recent years, wehave witnessed a tremendous acceleration in research efforts aimedat better comprehending, modeling and hedging this kind ofrisk. These two volumes aim to provide a foundation course on appliedstochastic finance. They are designed for three groups of readers:firstly, students of various backgrounds seeking a core knowledgeon the subject of stochastic finance; secondly financial analystsand practitioners in the investment, banking and insuranceindustries; and finally other professionals who are interested inlearning advanced mathematical and stochastic methods, which arebasic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financialinstruments and the fundamental principles of financial modelingand arbitrage valuation of derivatives. Next, we use thediscrete-time binomial model to introduce all relevant concepts.The mathematical simplicity of the binomial model also provides uswith the opportunity to introduce and discuss in depth conceptssuch as conditional expectations and martingales in discrete time.However, we do not expand beyond the needs of the stochasticfinance framework. Numerous examples, each highlighted and isolatedfrom the text for easy reference and identification, areincluded. The book concludes with the use of the binomial model tointroduce interest rate models and the use of the Markov chainmodel to introduce credit risk. This volume is designed in such away that, among other uses, makes it useful as an undergraduatecourse.
Arnd Lodowicks analysiert, wie ein Unternehmen unter Berücksichtigung von Insolvenzrisiken auf Grundlage der Discounted-Cashflow-Theorie bewertet werden kann. Er entwickelt ein Modell zur Bewertung von Insolvenzkosten, das sowohl Zahlungsunfähigkeit als auch Überschuldung als Insolvenzauslöser berücksichtigt. Dabei greift er auf exotische Optionen zurück.
"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
This book deals with many topics in modern financial mathematics in a way that does not use advanced mathematical tools and shows how these models can be numerically implemented in a practical way. The book is aimed at undergraduate students, MBA students, and executives who wish to understand and apply financial models in the spreadsheet computing environment. The basic building block is the one-step binomial model where a known price today can take one of two possible values at the next time. In this simple situation, risk neutral pricing can be defined and the model can be applied to price forward contracts, exchange rate contracts, and interest rate derivatives. The simple one-period framework can then be extended to multi-period models. The authors show how binomial tree models can be constructed for several applications to bring about valuations consistent with market prices. The book closes with a novel discussion of real options. John van der Hoek is Senior Lecturer in Applied Mathematics at the University of Adelaide. He has developed courses in finance for a number of years at various levels and is a regular plenary speaker at major conferences on Quantitative Finance. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary. He is the author of over 300 research papers and several books, including Mathematics of Financial Markets, Second Edition (with P. Ekkehard Kopp), Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and Measure Theory and Filtering: Theory and Applications (with Lakhdar Aggoun). He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications, and the Canadian Applied Mathematics Quarterly.
This book presents the mathematics that underpins pricing models for derivative securities in modern financial markets, such as options, futures and swaps. This new edition adds substantial material from current areas of active research, such as coherent risk measures with applications to hedging, the arbitrage interval for incomplete discrete-time markets, and risk and return and sensitivity analysis for the Black-Scholes model.

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