Lévy Processes in Finance: Pricing Financial Derivatives 1st Edition by Wim Schoutens (PDF)

Description

Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of Lévy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. Lévy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of Lévy-based models, and features many examples of how they may be used to solve problems in finance. * Provides an introduction to the use of Lévy processes in finance. * Features many examples using real market data, with emphasis on the pricing of financial derivatives. * Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling. * Includes many figures to illustrate the theory and examples discussed. * Avoids unnecessary mathematical formalities. The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers.

User’s Reviews

Editorial Reviews: From the Inside Flap Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of Lévy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. Lévy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of Lévy-based models, and features many examples of how they may be used to solve problems in finance. * Provides an introduction to the use of Lévy processes in finance. * Features many examples using real market data, with emphasis on the pricing of financial derivatives. * Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling. * Includes many figures to illustrate the theory and examples discussed. * Avoids unnecessary mathematical formalities. The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers. From the Back Cover Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of Lévy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. Lévy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of Lévy-based models, and features many examples of how they may be used to solve problems in finance. * Provides an introduction to the use of Lévy processes in finance. * Features many examples using real market data, with emphasis on the pricing of financial derivatives. * Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling. * Includes many figures to illustrate the theory and examples discussed. * Avoids unnecessary mathematical formalities. The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers. About the Author WIM SCHOUTENS has a degree in Computer Science and a PhD in Science, Mathematics. He is a research professor in the Department of Mathematics at the Catholic University of Leuven, Belgium. He has been a consultant to the banking industry and is author of the Wiley book Lévy Processes in Finance: Pricing Financial Derivatives. His research interests are focused on financial mathematics and stochastic processes. He currently teaches several courses related to financial engineering in different Masters programmes. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Levy statistics has seen much success in multiple areas; earthquakes, solar flares, derivatives – phenomenological time series in general. The author attempts to convince the reader that Levy stats is a powerful model of market dynamics. This is done using actual market data focusing on financial derivatives. The author includes many examples and his presentation of Levy Theory is done quite well and should be appreciated by the reader.This is a practical, user friendly introductory text and I found the mathematics to be quite understandable and well presented for the practitioner. As such it is not the most rigorous text for physicists however, for those needing to learn the chaos aspects of market theory, it provides a welcome introduction to basic market ideas and gives a sense via the mathematics as to how the market may really work.Again, the book is primarily aimed at researchers and practitioners in market finance and economics. The many examples utilizing levy statistics surely makes the text a valuable reference source for market and finance practitioners.DebL

⭐I like this book very much. It is clear and brings you upto date with the theory in less than 200 pages. No technical details, clear style, a lot of real world examples. In contrast to other very mathematically oriented books (like Bertoin’s and Boyarchenko-Levendorvski’s), I must say that after reading it you can start applying the models to real world situations.

⭐This is a good book about Levy processes. The first few chapters are clear enough but after that the subject and the book gets difficult. Levy processes are a half-way house between compound poisson or counting discrete time processes and brownian motion continuous time process and both of these are hard enough in their own right. The book makes it clear that the key to understaning these processes is the notion that the moment generating function (mgf) of a compound poisson process is the n-th power of the mgf of the process being compounded. Combining these allows continous time models to be developed which also allow for randomly occurring level changes and shocks. The book uses the resulting processes to build a stochastic calculus that generalises the Ito calculus. This book not for the novice but for those who already have a strong grasp of stochastic processes. It will best suit advanced actuarial graduates working in financial mathematics who are comfortable with counting processes for tracking lifetimes and Ito calculus for diffusions. While Levy processes unify discrete and continuous time processes the author does not provide examples that show a motivation for linking the two. As a consequence I was left unclear about how to apply the process outside finance and say go from a counting process for lifetimes or a continuous time diffusion like population model to the marriage of a Levy process that might have an evolving population that is affected by an influx of migrants or deaths from an epidemic.

⭐The problem is: This book is expensive, and you don’t find illegal copies on the web that could help you decide if it’s worth its price. I would say it’s not, though it’s certainly useful.My main point of criticism is that it doesn’t really cover equivalent martingale measures. Schoutens introduces one martingale measure, but it’s not clear if it’s an equivalent measure. It doesn’t cover mean variance hedging or local risk minimization, the Föllmer-Schweizer measure or the minimal entropy measure. There is a very useful little volume by Yoshio Miyahara which covers these aspects (and of course they are found in Cont Tankov). With Schoutens, you could as well say you don’t care about the physical measure and you just formulate your model under the pricing measure. But the nice thing about exponential Levy models is that you can calibrate them to historic returns and they still give accurate option prices, unlike diffusion-based models.What is good about Schoutens’s Book is that he discusses jump models with stochastic volatility. However, you can’t rely on the book for simulation. For example, Schoutens suggests that simulating a square root diffusion is easy, just apply an Euler or Milshtein scheme… yeah, you can do that, but it’s a horrible method (you get negative volatilities and the convergence is sloooow). Better methods are known these days.It’s not bad for a first overview, plus the appendix on special functions is useful. But you end up with a somewhat incomplete picture.For exponential Lévy models, I find the book by Miyahara actually more useful. For Computational matters, check out Ali Hirsa‘s volume. Also the papers of Carr, Madan and various co-authors are very well worth reading.

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