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eBook: Peter James – Option Theory.pdf – (388pgs).

Option Theory: A Comprehensive Approach to Understanding and Pricing Options

This book offers a unified approach to the theory of options, presenting each methodology in its various forms and highlighting the equivalence between them. It simplifies complex topics, providing practical, actionable results using the theory, which is essential for problem-solving in financial practice. The book applies these results to the analysis and pricing of options across equity, currency, commodity, and interest rate markets. It equips readers with the analytical tools and technical language needed to comprehend current technical literature and serves as a user-friendly reference for investors and traders alike.

From the Back Cover

Option Theory guides readers from foundational principles to the cutting edge of modern finance theory. Written for financial engineers at all levels, the book presents formulas and techniques that can be easily applied to real-world problems while exploring the theoretical underpinnings in detail. It will also appeal to students and researchers who seek a deeper understanding of the subject.

The author addresses various approaches to option pricing, including risk-neutral expectations, integration, trees, analytical and numerical solutions of partial differential equations, and Monte Carlo methods. The relationship between these methods is explained clearly, demonstrating their interconnections.

The book is divided into four parts. The mathematical tools used in the first three sections are intermediate-level “engineer’s mathematics,” including differential and integral calculus, elementary statistical theory, and basic partial differential equations. Part Three applies these techniques systematically to all standard exotic options in equity, foreign exchange, and commodity markets. It shows that exotic options are not a random assortment of unrelated instruments but rather a few families that can be easily analyzed using the methods developed earlier in the book.

Part Four introduces stochastic calculus tailored specifically to finance theory. It is designed for readers who have some prior knowledge of options and provides a practical working knowledge of the subject. Topics covered include:

• Martingales

• Stochastic differential equations

• Stochastic integration

• The Feynman-Kac theorem

• Stochastic control

• Local time

• Girsanov’s theorem

The axiomatic approach to option theory using stochastic calculus is compared in detail with the more intuitive classical statistics approach used in the earlier parts of the book. The analysis highlights where stochastic calculus provides valuable insights and advances, and where it may merely serve as window dressing.

This straightforward, professional book demystifies and simplifies the subject of option theory. It is invaluable for both practitioners and students who wish to gain a deeper, more practical understanding of the topic.