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Financial Calculus: An Introduction to Derivative Pricing Hardcover – September 28, 1996

ISBN-13: 978-0521552899 ISBN-10: 0521552893 Edition: 1st

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Financial Calculus: An Introduction to Derivative Pricing + Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance) + Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (Springer Finance)
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Product Details

  • Hardcover: 233 pages
  • Publisher: Cambridge University Press; 1 edition (September 28, 1996)
  • Language: English
  • ISBN-10: 0521552893
  • ISBN-13: 978-0521552899
  • Product Dimensions: 6 x 0.8 x 9 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (36 customer reviews)
  • Amazon Best Sellers Rank: #103,765 in Books (See Top 100 in Books)

Editorial Reviews

Review

"...a rigorous and accessible account of the probabilistic structure behind the pricing, construction, and hedging of derivative securities....Real examples from stock, currency, and interest rate markets are used. The text also gives a clear view and introduction to modern mathematical finance for probabilists and statisticians."
The Journal of the American Statistical Association

"This is an excellent book for anyone who want an intuitive understanding of the use of stochastic calculus in financial engineering."
riskbook.com

Book Description

Here is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts are described with mathematical precision in a style tailored for market practitioners. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations. A full glossary of probabilistic and financial terms is provided.This up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees in investment banks in the major financial centres throughout the world.

Customer Reviews

The authors have managed to clearly explain a topic that is very difficult and unclear to begin with.
N. Shah
An excellent book and recommended for beginning students or mathematicians interested in entering the field.
Dr. Lee D. Carlson
My recommendation for those learning mathematical finance is to buy both Baxter/Rennie and Shreve Vol. II.
longhorn24

Most Helpful Customer Reviews

66 of 67 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on March 10, 2001
Format: Hardcover
This book is an introduction to financial engineering from the standpoint of martingales, and assumes the reader knows only elementary calculus and probability theory. After giving a motivating example entitled "the parable of the bookmaker" the authors clarify in the introduction the difference between pricing derivatives by expected value versus using the concept of arbitrage. Vowing then never to use the strong law of large numbers to price derivatives, discrete processes are take up in the next chapter. The authors do an excellent job of discussing the binomial tree model using only elementary mathematics. Interestingly, they introduce the concept of a filtration in constructing the binomial tree model for pricing. Filtrations are usually introduced formally in other books as a measure theory concept. They then define a martingale using a filtration and a choice of measure. The use of martingales pretty much dominates the rest of the book. They emphasize that a martingale can be a martingale with respect to one measure but not to another. Continuous models are the subject of the next chapter, where the ubiquitous Brownian motion is introduced. The discussion is very lucid and easy to understand, and they explain why the conditions in the definition of Brownian motion make its use nontrivial; namely, one must pay attention to all the marginals conditioned on all the filtrations (or histories). The Ito calculus is then appropriately introduced along with stochastic differential equations. The authors do a good job of discussing the difference between stochastic calculus and Newtonian calculus.Read more ›
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44 of 47 people found the following review helpful By A Customer on June 1, 1999
Format: Hardcover
This is an elegant book for students of financial mathematics. You won't see the tedious Theorem/Proof format so common in other similar textbooks. But what it lacks in rigor it more than makes up for in other more important areas: superb writing, clear explanations and brilliant insight into the most popular valuation models. For instance, the concise but very clear derivation of the Black-Scholes formula should impress anyone who has studied the PDE-based derivation covered by Hull and others.
There is little discussion of empirical issues. This, in my opinion, was a wise choice by the authors. Any such discussion would severely dilute the strength of the book -- namely, the fundamentals of stochastic calculus applied to arbitrage pricing. For those interested in empirical features of the markets, I'd suggest "Econometrics of Financial Markets" (Andy Lo, et al).
I find it ironic that the punchline for the whole book -- a chapter on exotic option valuation where probabilistic techniques such as the reflection principle naturally come into play -- did not make it to production. But this excellent chapter is available on the errata Web page under [...]
This book is a great place to begin study for quantitative MBA students or math students with an interest in option valuation. Supplement this book with Oksendal or Karatzas / Shreve, perhaps, for more in-depth material on stochastic calculus.
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50 of 55 people found the following review helpful By A Customer on March 1, 2000
Format: Hardcover
Having been a student of this subject for a short 18 months now, and having looked at many books on the same subject, this is by far THE BEST. What this book does is simple. It lays the groundwork for pricing derivative securities using stochastic calculus. It helps build the intuition behind the stochastics. Then, from this intuition and foundation, you are equipped to read more advanced treatments of the subject.
This is not a book on solving partial differential equations, nor is it supposed to be. If you are looking for a book on solving and creating financial PDE's, then buy Wilmott's books. Rather, this book uses discounted expectations under the risk neutral measure to price securities. What does that mean? Well, all I can say is "READ THE BOOK".
The first three chapters of this book are so fundamental and necessary to building a firm and solid intuition that I have read them over three or four times now. The reason I have read it so many times is because it is so well written and new things pop out at you every time. It really is a delight to read.
Moreover, the section on fixed income models is extremely well written as well.
I can't stress enough how great this text is.
You should buy it even if you already know the material.
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26 of 27 people found the following review helpful By longhorn24 on June 23, 2005
Format: Hardcover
Baxter/Rennie deserves its reputation as the best introductory book to modern financial engineering because of its terse, elegant description of the martingale approach to asset pricing. The basic machinery of financial engineering comes from fields in applied analysis such as stochastic calculus and martingale theory, whose presentation is often weighed down with overbearing technical considerations. While necessary from a mathematician's perspective (and often relevant even in many real-world cases), a reader with mathematical maturity but without formal training in measure theory or probability can nonetheless appreciate and understand the basic tools used over and over again in Black-Scholes, and more generally, in martingale methods for pricing.

The quantitative analyst often needs to thorougly understand both the theory and the techical aspects of implementation of these models, and often studies these subjects in graduate programs. Many participants in quantitative fields such as fixed income and derivative trading/pricing often want an intuitive notion of what these "quants" are doing. Baxter/Rennie serves as a good book that is far more advanced than the excellent book by Hull; the latter is a wonderful introduction to quantitative fields, but Baxter/Rennie is the first book that truly introduces the math in a unified presentation that encompasses the three most important tools of mathematical finance (assuming, of course, the Ito-Doeblin calculus driven by Brownian motion); the Cameron-Martin-Girsanov (CMG) Theorem that permits changes of measure, the Feynman-Kac formula and the Martingale Representation Theorem.
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Financial Calculus: An Introduction to Derivative Pricing
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