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This book studies pricing financial derivatives with a partial differential equation approach. The treatment is mathematically rigorous and covers a variety of topics in finance including forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, lookback options, interest rate models, interest rate derivatives, swaps, caps, floors, and collars. Each chapter concludes with exercises.
- Sales Rank: #7656816 in Books
- Published on: 2010-10-20
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.20" w x 6.10" l, 1.62 pounds
- Binding: Paperback
- 513 pages
Review
From the reviews:
"This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities... the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS
"This book is devoted to pricing financial derivatives with a partial differential equation approach. It has two parts, each with four chapters. … The book covers a variety of topics in finance, such as forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, barrier options, lookback options, multi-asset options, interest rate models, interest rate derivatives, swaps, swaptions, caps, floors, and collars. The treatment is mathematically rigorous. There are exercises at the end of each chapter." (Elias Shiu, Zentralblatt MATH, Vol. 1061 (12), 2005)
From the Back Cover
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This book is devoted to determining the prices of financial derivatives using a partial differential equation approach. In the first part the authors describe the formulation of the problems (including related free-boundary problems) and derive the closed form solutions if they have been found. The second part discusses how to obtain their numerical solutions efficiently for both European-style and American-style derivatives and for both stock options and interest rate derivatives. The numerical methods discussed are finite-difference methods. The book also discusses how to determine the coefficients in the partial differential equations.
The aim of the book is to provide readers who have some code writing experience for engineering computations with the skills to develop efficient derivative-pricing codes. The book includes exercises throughout and will appeal to students and researchers in quantitative finance as well as practitioners in the financial industry and code developers.
Most helpful customer reviews
5 of 5 people found the following review helpful.
Well Done
By Michel Trudelle
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 !!
2 of 2 people found the following review helpful.
Best Buy
By Piter Dias
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.
0 of 0 people found the following review helpful.
An excellent book on derivative pricing
By James D
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!
See all 3 customer reviews...
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