Financial Calculus : An Introduction to Derivative Pricing

Rating:
Summary: Hull is much better as a first book
Review: As a new person on the Wall Street, I picked this book after reading all reviews instead of Hull as my first book.

Reviews said undergraduates can handle this book. Wrong. Despite solid engineering background (IIT), I found this to be rather dry book. Certaily not the first book.

I have started Hull. And found that much more accessible and practically useful. Gets you into solving problems and getting answers.

Rating:
Summary: Substance with Style
Review: Baxter & Rennie are the clear descendents of Silvanus P. Thompson(Calculus Made Easy). A pair of Brits with an engaging style and clear expository prose. They take the reader on a tour of some heavy duty mathematics, without excessive formalism. The basics of arbitrage pricing, binomial branch models, the Ito calculus, and the martingale representation theorem are contained in 100 pages. The second hundred pages are devoted to the construction of models for contemporary financial derivatives in foreign exchange, stock, and fixed income markets. This book is a must read for practitioners of, and students in financial engineering.

Rating:
Summary: Excellent second introduction
Review: I'm not so sure that Baxter and Rennie's is an ideal first introduction to financial mathematics. But for those with a basic working knowledge of Black Scholes option pricing theory, or even an acquaintance with the basic concepts of replication and hedging, I believe that it could serve as an excellent way to get the reader as smoothly but as fast as possible to the more advanced aspects of derivatives theory, such interest rate theory. Even HJM and BGM are there, near the end.

I must say, though, that the book starts with "the parable of the bookmaker" that always put me off, because I found the point that the authors wish to make quite unclear. Now that I understand it, I'm not even so sure that it's really a good analogy of the use of the martingale measure vs the "objective" measure. Also, expressions such as "shortening the odds" are obscure to those of us who don't bet on horses, and it was never clear to me whether "shortening the odds" was analogous to anything in financial mathematics and thereby part of the discussion and the point that the authors wish to make -- I guess it's not. All in all, that was a far lessr than ideal way to start the book. However, once you get over that hurdle, the book is indeed very well written, though very concise.

Rating:
Summary: Best Introduction to Quantitative Finance--Ever
Review: This book is amazing. It's probably the best place to start if you want to learn quant finance. If you have a solid grasp of probability and calculus, you'll have little trouble following the text. You won't even need to know any measure theory.

The authors' expanations of even the toughest concepts (eg, Girsanov's Theorem and the Martingale Representation Theorem) are very clear and easy to understand. And their proofs and derivations of financial concepts give the reader a lot of valuable intuition. As I said, this book is a great place to start. After reading it, working through more advanced math books (like Oksendal) and more advanced finance books (like Duffie) is a lot easier.

Rating:
Summary: Nice, compact book on financial engineering
Review: 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. Recognizing that the Brownian motion they have defined is with respect to a given measure, they then ask the reader to consider the effect of changing the measure, thus motivating the idea of a Radon-Nikodym derivative. Their discussion is very intuitive and promotes a clear understanding rather than giving a mere formal measure-theoretic definition. Many interesting examples of changes are given. Portfolio construction and the Black-Scholes model follows. Basing their treatment of the Black-Scholes model of martingales gives an interesting and enlightening alternative to the usual ones based on partial differential equations (they do however later show how to obtain the usual equations). The next chapter discusses how to use the Black-Scholes equations to price market securities and how to assess the market price of risk. The discussion is very understandable but not enough exercises are given. Modeling interest rates is the subject of the next chapter. The mathematical treatiment is somewhat more involved than the rest of the the book. Several models of interest rate dynamics are discussed here very clearly, including the Ho/Lee, Vasicek, Cox-Ingersoll-Ross, Black-Karasinski, and Brace-Gatarek-Musiela models. A few of these models were unfamliar to me so I appreciated the author's detailed discussion. The book ends with a discussion of extensions to the Black-Scholes model. The emphasis is on multiple stock and foreign currency interest-rate models. A brief discussion of the Harrison/Pliska theorem is given with references indicated for the proof. An excellent book and recommended for beginning students or mathematicians interested in entering the field. My sole objection is the paucity of exercises in the last few chapters.

Rating:
Summary: Absolutely top-notch
Review: 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 http://easyweb.easynet.co.uk/~mw.baxter/book.html.

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.

Rating:
Summary: A tour de force in the world of derivative studies
Review: You may find the recent book by Paul Wilmott on option pricing a more comprehensive or a standard reference book by Hull a more direct accessible. However, by this small book, Baxter and Rennie has present the main theme of derivative pricing theory from a very elegant point of view. The reader can get a shortcut and clear insight of the state of modern derivative pricing theory which serious readers may have to consult in the old day the difficult seminal papers or a bunch of mathematical texts combined together. The authors has started with a 2 important concepts of modern pricing theory : no arbitrage and risk neutral approach. The concept of the abstract continuous time stochastic processes, filtration, change of measure, or Ito calculus are presented using a very touchable counter examples in a subsequent chapters. The authors also try devote a few lines to discuss a motive of underlying mathematical principles which is invaluable in a model ramification while most of the text largely ignore this. In the last chapters, the vast world of interest rate models especially in the HJM framework was impressively presented. All-in-all, the book successfully bridge a gap between elementary text and a more abstruse research works.

However, there is nothing perfect in this world. This beautiful book only skimmingly touch the concept of no-arbitrage condition. It also better serves a serious readers or gradute courses on derivatives rather than practitioners or model developers.