Customer Reviews

Derivative Securities and Difference Methods (Springer Finance)

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This is a GREAT book... if you are looking for treatment of "options pricing" from 2 specific perspectives.

In the first half of the book, the authors tackle the pricing issue using PDEs only, paying little attention to the Martingale approach. The treatment is VERY detailed, starting with the Ito Lemma (one dimension and n-state variables), and gradually moving from Vanilla to Exotic options. There is also a shorter chapter on Interest Rate Derivatives.

The greatest thing about the book is that every result is either proved or strongly justified, and that each section nicely builds on previous results. The Barrier & Lookback options pricing formulas are thoroughly developped and the authors do not try to skate around more complicated aspects of the theory. The sections on American options (Linear Complementarity & Free Boundary Formulations, location of the free boundary) are gems! The book is obviously math intensive and sometimes a little dry, but efforts to go through all the sections are well rewarded.

In a second part, specific numerical techniques for solving the PDEs are thoroughly explained. First, numerical techniques are reviewed in a very tight chapter, swiftly and clearly presenting all one needs to know to efficiently tackle solving PDEs numerically. Then, specific option problems are discussed in details. No code is provided, but the mathematical procedures are very well laid out.

Overall, I found the monograph a lot more mathematically detailed than most other books on the market (Hull, Wilmott, etc...), while being relatively good at clearly highlighting why certain issues are problematic and constantly keeping the big picture in perspective.

Somewhat surprisingly for a first edition and given the sometimes complex equations, the editing is VERY tight (good English, few typos) and the incremental steps are well balanced in terms of providing enough information for reader to easily fill the gaps. The only suggestion for further editions would be to collate ALL the pricing formulas (some, when replicating calculations already presented, are left to be demonstrated as an exercise) in an Annex for quick reference. More coverage of Interest Rate models using the same detailed approach would also definitely add value.

In all, a very good book.
Kudos !!

Very good book.
First chapter shows the basics of derivatives (someone would like Hull's for more detail).
Second is what I look for. Introduces derivatives pricing and stochastic processes by example.
From Black-Sholes to exotics and interest rate options, the reader will find PDE equation, boundary conditions and (a lot of) closed formulas.
Everything step-by-step. It is not a formula reference (like Haug's) but a book you will study in order to take practice to construct your own models.
Second half of book is about numeric solution. Well explained, a lot of case studies, but no pseudo-code or source code CD. Buy a Numerical Analysis book to support you with algorithm and coding if you need.

So far, I have read/bought more than 30 books on Derivatives while studying for a Master's in Fin.Eng. and this book is by far one of the best in terms of introducing someone in a clear and concise manner to how to value and interpret many derivatives securities.

The other 2 reviews have clearly laid out the structure of the book, so I won't redo it here.

However, I wish to state how mathematically sound are the methods for exotic options (chap 3), for deriving the four one-factor interest models (chap 4) and most importantly, the critical reformulation of the American-style derivatives as a Linear Complementarity problem and the carefully and sound discussion of the free-boundary for such derivatives.

Also, the numerical section (chap 5 to 8 ) is very well laid out -again I possess more than a few books on the subject- and you end up with the ability to solve most of the PDE that you model, if you carefully write the appropriate code, and understand the meaning of the coefficients of the PDE, which takes time and experience.

An excellent book!