Synopses & Reviews
The objective of this book is to give a self-contained presentation to the theory underlying the valuation of derivative financial instruments, which is becoming a standard part of the toolbox of professionals in the financial industry. Although a complete derivation of the Black-Scholes option pricing formula is given, the focus is on finite-time models. Not going for the greatest possible level of generality is greatly rewarded by a greater insight into the underlying economic ideas, putting the reader in an excellent position to proceed to the more general continuous-time theory. The material will be accessible to students and practitioners having a working knowledge of linear algebra and calculus. All additional material is developed from the very beginning as needed. In particular, the book also offers an introduction to modern probability theory, albeit mostly within the context of finite sample spaces. The style of presentation will appeal to financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to become acquainted with this modern applied topic; and mathematicians, physicists or quantitatively inclined economists working in the financial industry.
Review
"This is probably the best written book on discrete-time models of mathematical finance. It is self consistent, all notions used in it are carefully defined. That is a mathematical book - by mathematicians and for mathematicians, which also means that its practical applications are restricted. The bibliography is complete. I strongly recommend that title as an introduction to mathematical finance." -- Darius Gatarek (Control and Cybernetics) "The style of presentation will appeal to anyone who is seeking an elementary but rigorous introduction to the pricing of derivative securities. The book is written carefully and is very readable." --Mathematical Reviews "The book offers a self-contained elementary but rigorous and very clear introduction to the pricing of derivative instruments in discrete time. . . . For the interested reader who has not been exposed to modern probability theory before, the book provides an excellent starting point for studying the theory of derivative pricing. In particular, for a rigorous course on derivative pricing in an economics department or at a business school this introduction seems to be well-suited." --Zentralblatt Math "The book presents the part of mathematical finance devoted to the pricing of derivative instruments; its basic theme is the study of prices in securities markets in an uncertain environment. . . As the objective of the book is to provide a sound understanding of important issues of modern approaches to mathematical finance, several mathematical models are developed and examined in detail. The focus is on finite-time models and the highest level of generality is frequently sacrificed for the sake of a greater insight into the underlying economic ideas. Even when the problems are approached from the mathematical point of view and almost all results are strictly proved, the financial interpretation is always stressed. . . The style of presentation is aimed at students of financial economics, mathematics and physics and at mathematicians, physicists and economists working in financial industry." --APPLICATIONS OF MATHEMATICS
Synopsis
On what grounds can one reasonably expect that a complex financial contract solving a complex real-world issue does not deserve the same thorough scientific treatment as an aeroplane wing or a micro-proces sor? Only ignorance would suggest such an idea. E. Briys and F. De Varenne The objective of this book is to give a self-contained presentation of that part of mathematical finance devoted to the pricing of derivative instruments. During the past two decades the pricing of financial derivatives - or more generally: mathematical finance - has steadily won in importance both within the financial services industry and within the academic world. The complexity of the mathemat ics needed to master derivatives techniques naturally resulted in a high demand for quantitatively oriented professionals (mostly mathematicians and physicists) in the banking and insurance world. This in turn triggered a demand for university courses on the relevant topics and at the same time confronted the mathematical community with an interesting field of application for many techniques that had originally been developed for other purposes. Most probably this development was accelerated by an ever more applied orientation of the mathematics curriculum and the fact that finance institutions were often willing to generously support research in this field."
Synopsis
This self-contained book presents the theory underlying the valuation of derivative financial instruments, which is becoming a standard part of the professional toolbox in the financial industry. It provides great insight into the underlying economic ideas in a very readable form, putting the reader in an excellent position to proceed to the more general continuous-time theory.
Table of Contents
Introduction .- A Short Primer on Finance .- Positive Linear Functionals .- Finite Probability Spaces .- Random Variables .- General One.-period Models .- Information and Randomness .- Independence .- Multi.-period models: The Main Issues .- Conditioning and Martingales .- The Fundamental Theorems of Asset Pricing .- The Cos.-Ross.-Rubinstein Model .- The Central Limit Theorem .- The Black Scholes Formula .- Optimal Stopping .- American Claims