Marek Capinski, Tomasz Zastawniak - Mathematics for Finance: An Introduction to Financial Engineering

Description

Designed to form the basis of an undergraduate course in mathematical finance, this book builds on mathematical models of bond and stock prices and covers three major areas of mathematical finance that all have an enormous impact on the way modern financial markets operate, namely: Black-Scholes’ arbitrage pricing of options and other derivative securities; Markowitz portfolio optimization theory and the Capital Asset Pricing Model; and interest rates and their term structure. Assuming only a basic knowledge of probability and calculus, it covers the material in a mathematically rigorous and complete way at a level accessible to second or third year undergraduate students. The text is interspersed with a multitude of worked examples and exercises, so it is ideal for self-study and suitable not only for students of mathematics, but also students of business management, finance and economics, and anyone with an interest in finance who needs to understand the underlying theory.

Insufficient and disappointing. Not even a good introductury text.
As a graduate student in Financial Engineering I have found this book useless.
The title of the book is "Mathematics for Finance", but can you find in it even an elementary introduction to the stochastic processes? No. Ditto for the Ito's lemma and many other topics. The derivation of the Black Scholes formula is just sketched, and the insight that you can get from it is very limited.

I wouldn't mind the narrow breadth of topics covered and lack of mathematical depth if this was compensated by a simplicity in the explanations and solid financial intuition. Unfortunately this book is not good even in that. In comparison to other textbooks the theorems and definitions are convoluted and do not go straight to the point. For example, in many other textbooks such as Shreve's "Stochastic Calculus for Finance" or Baxter & Rennie "Financial Calculus" the Fundamental Theorem of Asset Pricing is stated in this way: "In a market with risk neutral probability there is no arbitrage". Can you find such a simple and explanatory definition in Capinski's book? Not at all. The theorem at page 83 (you can see it yourself by searching inside the book) basically says the same thing using 8 lines of text and little financial intuition.
The only good thing that I can say about this book is that all exercises are resolved.
Overall, "Mathematics for Finance" has been a big disappointment: it doesn't have either the mathematical depth of Shreve's books or the conciseness in explaining financial concepts of Baxter & Rennie.
Whatever is the level of education that you are pursuing I don't see any point in using it.

Great Book for Undergrad Quants
Mathematics for Finance (An Introduction to Financial Engineering) is a book intended for undergrad students "IN MATHEMATICS" or other discipline with a relative high mathematical content.

The book assumes some basic notion of Calculus and Probability Theory and it is focused more on the mathematics than in its theory and application of Finance. If you are looking to dwell into the mathematics (Proof of Equations) this is a great book, but if you are looking for a book that is rich in theory and in application then you should consider "Option, Future and Other Derivatives" or "Quantitative Methods for Finance" as an alternative. Both books are "a most" for any finance student and are of great help. Now if you want an introduction into the mathematics behind Finance then this book is a perfect purchase.

Important to state that all the problems presented in this book are solved meaning that it is great for self teaching. Marek Capinsi and Thomas Zastawniak have done a great job on this book.

I gave it four stars, because it has room for impovement.

Joining the chorus
I can only echo the other reviewers. As far as I can tell this book has no serious competition. This is an excellent introduction to mathematical finance for those with a solid undergraduate level understanding of higher math but without graduate level exposure. I agree that it is ideal for self study as that is exactly what I am using it for. The price is right especially in contrast with its overpriced brethren. Five stars!

The very best intro. . .Ideal for self-study
Part of my job is executing derivatives trades and doing risk management. This is the best introduction to financial engineering that I have seen. The authors explain their topic clearly. A major strength of the book is the numerous exercises, WITH WORKED SOLUTIONS. If you work through most of the exercises, your understanding of financial engineering will be greatly enhanced.

This book is ideal for self-study. At under $40, it is better than other books at twice the price. I recommend it without reservation.

Excellent Starting Place for Financial Software Developers
While shy on the mathematics for the would-be-quants, this treatment of mathematical financial is way beyond the mundane coverage typically seen in MBA-level texts, is widely accessible, and very well written.

The other reviewer's comments on Black-Scholes are wrong. Chapter eight is entirely devoted to the Black-Scholes formula and models and Chapter nine is a study in its applications (hedging the greeks, etc...)

Smarter than many of the more high-level math texts (Joshi, Willmott, Neftci, etc...) in that it is both an introduction to the financial topics as well as the mathematics and links the intuitive (and counter-intuitive) observations of how financial instruments should behave with the formal and mathematical discussion of how they really do behave.

Not nearly as good in the math as the others mentioned.