Tools for Computational Finance is a book on numerical methods for pricing financial derivative products. It is already in its third edition. There are plenty of books in the market on the theoretical concepts of financial derivatives; however, there are not so many on the computational techniques needed to price and analyze such products.
The book is divided into four parts:
- Financial and Stochastic Background
- Tools for Simulation
- Partial Differential Equations for Options <
- Further Requisites and Additional Material
Since the main focus is on the numerical methods there are almost no detailed theoretical expositions on financial derivatives, stochastic processes, martingales, etc. Hence, the reader should have some prior knowledge on both financial derivatives, probability theory, and stochastic processes.
Computational finance is growing immensely as we speak. With the complexity of financial markets and hence its products, the volumes of trade, efficient computational and numerical methods are required. What is nice about the current times is the fact that quite powerful computers can be purchased, which gives students a remarkable advantage and allows them to practice the methods presented in the book.
To introduce the book, the author prepared a well organized first chapter in which he explains the basic concepts of option theory, risk-neutral valuation and stochastic differential equations. Discussion on random numbers and simulation follows. The discussion is concentrated on the most important concepts only. There is also a very short variance reduction section. Rest of the book deals with pricing, mainly, the American options. The last chapter discusses how to price exotic options. Asian options are used. The book ends with a collection of appendices covering financial as well as stochastic and numerical topics.
As this is more of a finance oriented text, the technical details of stochastic tools are not presented in any detail. Rather, the author concentrates on how to provide numerical solutions to the problem of pricing. Exercises are provided at the end of each chapter and they follow and complement the text very well. In my opinion the book is more for practitioners than for academics, given the very brief theoretical presentation of the material. However, it does guide us in a right direction and as such I think it could be valuable even for an academic.
Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.