Mathematical Finance: Theory, Modeling, Implementation | 
 enlarge | Author: Christian Fries
Publisher: Wiley
Category: Book
List Price: $116.95
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Rating:  7 reviews
Sales Rank: 430210
Media: Hardcover
Pages: 544
Number Of Items: 1
Shipping Weight (lbs): 1.9
Dimensions (in): 9.5 x 6.1 x 1.3
ISBN: 0470047224
Dewey Decimal Number: 332.6015195
EAN: 9780470047224
Publication Date: August 24, 2007
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Product Description
This book concentrates on the theory of mathematical finance and the pricing of derivatives around the theory. The topics are presented from their mathematical foundations to their real-world implementation (through pricing models) using state-of-the art object oriented programming techniques. While a high standard of mathematical precision is retained throughout the book, the emphasis remains on practical motivations, interpretations, and results. The book harmonizes theory, practical modeling, and financial methods under one convenient cover.
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| Customer Reviews: Read 2 more reviews...
 This book is unbelievable precious June 5, 2008
Igor Cakulev (New York)
4 out of 5 found this review helpful
The book has so many nuggets of wisdom is hard to mention them all. I know I struggled with some concepts before and somehow they were explained in a remarkable way. So now I am just asking myself, was I so stupid before?
Perfect for practitioners, but not in the sense of generic cookbook like the Hull's book where the math is dangerously simplified.
The theory is explained with flawless clarity. Numerous tricks are given for free. For example, I always looked at interpolation as something trivial, however Fries explains arbitrage violations using different interpolation, i.e. negative probability density for smoothing interpolations, discrete for linear. This book is especially useful for somebody that is interested in Libor Market Model. There is also extension of it like the cross-currency version of it; I haven't seen it anywhere else (at least not in books).
From the negative side, I only wished more code posted, but that is just me being greedy. Given the amount spent on implementation issues, I would also like to see little bit more on calibration.
About this Book January 15, 2008
Christian Fries (Frankfurt am Main)
12 out of 14 found this review helpful
Disclaimer: As you can see from Amazon RealName (TM), I am the author of the book. The editorial review provided on the back of the book and reproduced on amazon was written by the publisher. However, that editorial review does not provide as much information about the book as I think is necessary. This review hopefully provides you with a more detailed description of the contents and objectives of the book, to help you finding the right book for your needs. [...]
The book's main objective is to provide an intuition for the theoretical concepts relevant for derivative pricing and to bridge from the more academic concepts (filtration, random variable, stochastic process) to their application in industry, most notably modeling, calibration and object oriented implementation. It comes with extensive additional material to further explore the key concepts. See the book's home page at christian-fries.de/finmath/book
The book starts like a textbook giving an introduction to probability theory and stochastic processes. However, instead of repeating "Definition-Theorem-Proof" the book often leaves out the proof and adds two special sections: "Motivation" and "Interpretation" (before and after a definition or theorem). The first part makes you acquainted with the mathematical theory and provides the intuition for the fundamental building blocks like random variable, brownian motion, drift and volatility, Ito process, measures, change of measure and numeraire, etc.
In the second part, first applications are, of course, the Black-Scholes model for a single asset. As an excursion important concepts like implied volatility, hedging and the greeks are presented. The results and graphs of these applications may be explored interactively in Java applets on associated web pages.
The third part introduces interest rates, interest rate products and further analytical pricing models. At first, this might come as an arbitrary choice of a specific asset class, namely to focus on interest rates in contrast then equity, foreign exchange (fx), or credit derivatives. However, there is a motivation on why interest rates are a natural choice if one wants to move to more complex derivatives like they have become popular recently: Derivatives feature payments or cash-flows (settlements) at different times, and interest rates are one way to describe the value of future payouts. Mathematically speaking, interest rate products (like bonds or money market accounts) are a natural choice for a numeraire. So interest rates are part of any model (e.g. the black-scholes model for equity and foreign exchange) and considering stochastic interest rates will make these models into hybrid interest rate models.
Before discussing interest rates models (part V) or hybrid models (part VI), the part IV of the book gives a treatment of the numerical implementation of such models. It focuses on Monte-Carlo simulations and their object oriented implementation. Monte-Carlo simulation is one of the most powerful tools in (numerical) derivative pricing. It is also a straight forward approach to implement models, making as few assumption as possible (for example: finite differences, like PDEs and trees are limited to low(er) dimensions). Despite its ubiquitous application, Monte-Carlo simulation brings several disadvantages: a) It is sometimes slower. Given the performance of todays computers, this disadvantage is becoming less important. b) Bermudan options are hard to price. This is solved in Chapter 15. Path-dependent bermudan options are even harder. This is solved in Chapter 16. c) Sensitivities are unstable. This is solved in Chapter 17 and 18.
Part V introduces bigger models, like the LIBOR Market Model, the classical Short Rate Models, Heath-Jarrow-Morton Framework, Cheyette Model and Markov Functional Models. This part focuses a bit on the LIBOR Market Model as it is our workhorse. The calibration of the LIBOR Market Model is discussed (e.g. the calibration to swaption volatility and swap rate covariance) and hints for fast, object oriented implementations are given. Object oriented designs are given in UML diagrams. In "Excursions" concepts like mean-reversion, instantaneous and terminal correlation, multi-factor model, etc. are discussed and illustrated. This part will both endow you with a solid intuition of important model aspects as well as the ability to actually implement such model.
Part VI builds upon the models presented in part V to introduce model extensions like credit spread (credit default) or hybrid models. Examples for hybrid-models are equity-interest rate hybrid model, fx-interest rate hybrid model, multi-currency model. The equity-interest rate hybrid model is essentially a Black-Scholes model (as it was discussed in the second part of the book) with stochastic interest rate modeled by a LIBOR market model (as it was discussed in the fifth part of the book). Since the numeraire is an interest rate product, a Black-Scholes model with stochastic interest rates becomes an interest rate model with an extension.
Part VII gives a short introduction to object oriented implementation.
A nice path through Mathematical Finance April 14, 2008
M. Paulsen
4 out of 6 found this review helpful
The subtitle of this book is Theory, Modeling and Implementation and this book has plenty of material on all these areas of Mathematical Finance. The author, who has a solid background in mathematics and is a succesful professional in the finance industry, is very generous with the tricks of the trade. To my knowledge, there is no other book who takes the reader (preferably someone with a good working knowledge in university mathematics) on a path from the mathematics of Ito calculus to models of volatility and interest rate derivatives and then to numerics and object oriented programming. For a commited reader this book will be very rewarding, since it has so much to offer. It should be excellent preparation for e.g. an internship in a quantitative team at a bank (especially for derivatives) or could serve as course literature for a university course in applied financial modeling (the examples from industry will motivate the students, believe me). All in all, this is an excellently versatile book with such a richness concerning the material.
An excellent quant book February 6, 2008
The Wizard
8 out of 10 found this review helpful
The book starts with discussing basic mathematical finance such as Ito's lemma and Black-Scholes theory. This is a rather compact summary without proofs and I therefore believe a novice reader first should read an introductory book such as the one by Baxter & Rennie. The main part of the books is then devoted to various issues that one encounters in the implementation of financial models. I found this part very useful and I guess most quants have encountered the interesting problems that the author discusses such as: calculation of greeks in Monte-Carlo implementations, backward pricing of path-dependent products, implementation of Markov models, etc.
strong buy April 25, 2008
Dr. Joerg Wackertapp (London)
5 out of 7 found this review helpful
There are a couple of good mathematical finance books and this is for sure one of them. The important thing is that this book doesn't just repeat what you can find in other books, but very often gives you a different view on problems. A lot intuition and explanation of concepts is provided in a clever, unique and new way (even if you've read and thought already a lot about it). That implementation issues are discussed in this book makes it clear that this book is perfect for practitioners and I could make a lot use of it even though I'm not new to the field (I work as a quant for 10y now).
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