Quantitative finance has become an integral part of today's assessment of risk in the financial derivatives market. It is an indispensable tool for risk managers and investors. The field is relatively new, but nevertheless we can find adequate literature and tools to be able to assess risk in a timely fashion. With the increase of computer power and availability of large amounts of data, there is even more emphasis on mathematical methods in quantitative finance. The book under review introduces quantitative finance using the benchmark approach.
Efficient use of methods of quantitative finance requires quite a good knowledge of probability, statistics and stochastic processes and methods. Due to this, the book is naturally divided into two parts.
The first part covers important concepts from graduate level probability, statistics and stochastic processes. There is also a chapter on Itô's formula and stochastic differential equations. The reader should already be somewhat familiar with all of these concepts; it is very hard to learn stochastic processes or SDEs from one chapter, especially as only the main concepts are presented. The authors try to connect the theoretical exposition of Part I to finance so that the text is not completely a dry account of probability, statistics and stochastic processes. Even though the first part of the book serves as an introduction of higher level theory the reading is quite pleasant, i.e., it is not as technical as it could be. It is quite a nice blend of narrative and mathematics. There are also some bigger examples which contribute nicely to the overall presentation. The authors did a really good job with this part of the book, particularly in making connections to finance. Many books avoid this and just introduce the plain theory and the reader is left to make the connections on his own.
The second part of the book deals with actual mathematical models used to price financial derivatives. Naturally, the first part of the book serves as a base. Chapters 8 and 9 are an introduction to pricing methods covering option pricing and real world asset pricing. The chapters 10, 11 and 12 deal with the new concepts and ideas of the benchmark approach. A general unified framework for modeling continuous financial markets is developed. The text is a bit more technical in the second part of the book. However, the narrative style is still present, which makes it much easier to follow.
Exercises are provided at the end of each chapter. The authors even provide solutions to exercises. This is extremely useful to students who wish to use this book. All of the exercises are theoretical. Lastly, the authors provide quite a nice reference list enabling further research and exposure to the subject. Even though the book presents something new in the field of quantitative finance I think it could be quite useful for students, because of the first part of the book, and to practitioners, due to the exposition in the second part of the book.
Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold 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.
Preliminaries.- Statistical Methods.- Modeling via Stochastic Processes.- Diffusion Processes.- Martingales and Stochastic Integrals.- The Ito Integral or Stochastic Chain Rule.- Stochastic Differential Equations.- Continuous Benchmark Models.- Introduction to Option Pricing.- Various Approaches to Asset Pricing.- Numerical Methods for Derivatives Pricing.- Pricing of Derivatives.- Benchmark Models with Jumps.