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http://www.amazon.com/Option-Theory-Wiley-Finance-Peter/dp/0471492892/ref=sr_1_1?ie=UTF8&s=books&qid=1252654148&sr=8-1
Option Theory takes the reader from first principles to thefrontiers of modern finance theory. The book is aimed at busy financialengineers at all levels, providing formulas and techniques that can bereadily applied to real life problems; yet the theoretical basis of thesubject is explored in detail so that the book will also appeal tostudents and researchers.
Written in a clear and accessible manner,the author covers the various approaches to option pricing: riskneutral expectations by integration, trees, analytical and numericalsolutions of partial differential equations and Monte Carlo methods,demonstrating the close relationship between them.
Structuredinto four parts, the mathematical tools used in the first three partsof the book are intermediate level "engineer's mathematics":differential and integral calculus, elementary statistical theory andsimple partial differential equations. In Part Three, the techniquesare systematically applied to all the standard exotic optionsencountered in the equity, foreign exchange and commodity markets. Itis shown that the exotics are not a large random collection ofunrelated instruments, but a few families which can be simply analysedusing the techniques developed in Parts One and Two.
Part Fourprovides a course in stochastic calculus that is specifically tailoredto finance theory and designed for readers with some previous knowledgeof options. It provides an active working knowledge of the subject andincludes coverage of:
- Martingales.
- Stochastic differential equations.
- Stochastic integration.
- The Feyman Kac theorem.
- Stochastic control.
- Local time.
- Girsanov's theorem.
Theaxiomatic approach to option theory using stochastic calculus iscompared in detail to the simpler and more intuitive approach usingclassical statistics, which was used in the first three parts of thebook. The analysis clearly shows where stochastic calculus providesvaluable insights and advances, and where it is mere window dressing. Thisis a no-nonsense professional book which demystifies and simplifies thesubject, and which will appeal to both practitioners and students.
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