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Financial Modelling With Jump Processes

Author: Peter Tankov
Publisher: CRC Press
ISBN: 0203485211
Size: 27.94 MB
Format: PDF
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WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Lévy processes are beyond their reach. Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations. Topics covered in this book include: jump-diffusion models, Lévy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms. This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.

Introduction To Stochastic Calculus Applied To Finance Second Edition

Author: Damien Lamberton
Publisher: CRC Press
ISBN: 142000994X
Size: 19.28 MB
Format: PDF, Kindle
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Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, Introduction to Stochastic Calculus Applied to Finance, Second Edition incorporates some of these new techniques and concepts to provide an accessible, up-to-date initiation to the field. New to the Second Edition Complements on discrete models, including Rogers' approach to the fundamental theorem of asset pricing and super-replication in incomplete markets Discussions on local volatility, Dupire's formula, the change of numéraire techniques, forward measures, and the forward Libor model A new chapter on credit risk modeling An extension of the chapter on simulation with numerical experiments that illustrate variance reduction techniques and hedging strategies Additional exercises and problems Providing all of the necessary stochastic calculus theory, the authors cover many key finance topics, including martingales, arbitrage, option pricing, American and European options, the Black-Scholes model, optimal hedging, and the computer simulation of financial models. They succeed in producing a solid introduction to stochastic approaches used in the financial world.

Mathematik In Der Modernen Finanzwelt

Author: Stefan Reitz
Publisher: Springer-Verlag
ISBN: 3834898600
Size: 52.30 MB
Format: PDF, ePub
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Ziel des Buches ist es, die mathematischen Methoden und deren Anwendung, welche heutzutage typischerweise in der Finanzwelt und bei der Beschreibung von Kapitalmärkten zum Einsatz kommen, in einem Band zusammenzufassen. Der Text kann etwa als Grundlage einer zweisemestrigen Vorlesung in einem Bachelor- oder Master-Studiengang (Wirtschafts-)Mathematik dienen, und gibt den Studenten, die bereits eine einführende Vorlesung zu den Themen der klassischen Finanzmathematik absolviert haben, einen Überblick über die konkrete Anwendung weiterführender mathematischer Methoden in der Finanzwelt. Es ist weniger theorielastig als viele vergleichbare Bücher und richtet den Fokus mehr auf das "tatsächlich vermittelbare und für die Praxis relevante" Wissen.

Kreditderivate Und Kreditrisikomodelle

Author: Marcus R.W. Martin
Publisher: Springer-Verlag
ISBN: 3658024003
Size: 24.29 MB
Format: PDF
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Ein einführendes Lehrbuch, dessen Adressaten Studierende und Praktiker sind. Die Autoren versuchen dabei, einen Mittelweg zu gehen zwischen Theorie und praktischer Anwendung von Kreditderivaten und Kreditrisikomodellen. Thematisch werden die für das tägliche Bankgeschäft relevanten Aspekte angesprochen. Studierende werden fundiert an ein hochaktuelles Anwendungsgebiet der Mathematik herangeführt. Für Praktiker bietet das Werk eine systematische Darstellung der methodischen Grundlagen ihrer täglichen Arbeit, z. B. in Bezug auf die Implementierung von Risikomesssystemen.

Option Pricing And Estimation Of Financial Models With R

Author: Stefano M. Iacus
Publisher: John Wiley & Sons
ISBN: 9781119990208
Size: 69.89 MB
Format: PDF, ePub, Mobi
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Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.

An Introduction To Exotic Option Pricing

Author: Peter Buchen
Publisher: CRC Press
ISBN: 1420091026
Size: 57.77 MB
Format: PDF, Kindle
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In an easy-to-understand, nontechnical yet mathematically elegant manner, An Introduction to Exotic Option Pricing shows how to price exotic options, including complex ones, without performing complicated integrations or formally solving partial differential equations (PDEs). The author incorporates much of his own unpublished work, including ideas and techniques new to the general quantitative finance community. The first part of the text presents the necessary financial, mathematical, and statistical background, covering both standard and specialized topics. Using no-arbitrage concepts, the Black–Scholes model, and the fundamental theorem of asset pricing, the author develops such specialized methods as the principle of static replication, the Gaussian shift theorem, and the method of images. A key feature is the application of the Gaussian shift theorem and its multivariate extension to price exotic options without needing a single integration. The second part focuses on applications to exotic option pricing, including dual-expiry, multi-asset rainbow, barrier, lookback, and Asian options. Pushing Black–Scholes option pricing to its limits, the author introduces a powerful formula for pricing a class of multi-asset, multiperiod derivatives. He gives full details of the calculations involved in pricing all of the exotic options. Taking an applied mathematics approach, this book illustrates how to use straightforward techniques to price a wide range of exotic options within the Black–Scholes framework. These methods can even be used as control variates in a Monte Carlo simulation of a stochastic volatility model.

Stochastic Finance

Author: Nicolas Privault
Publisher: CRC Press
ISBN: 1466594039
Size: 10.18 MB
Format: PDF, Docs
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Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.

Problems And Solutions In Mathematical Finance

Author: Eric Chin
Publisher: John Wiley & Sons
ISBN: 1119966086
Size: 34.46 MB
Format: PDF, ePub, Mobi
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Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance. Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance. This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance. Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.

Hedging Derivatives

Author: Thorsten Rheinlander
Publisher: World Scientific
ISBN: 981433880X
Size: 50.92 MB
Format: PDF, Kindle
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Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential L(r)vy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options. This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field."