Prices in Financial Markets de Michael U. Dothan

Prices in Financial Markets

Michael U. Dothan

This book offers a unified treatment of selected topics in the theory of financial markets. Starting with discrete time models, Dothan introduces discrete time stochastic calculus and discrete martingale methods of intuitive simplicity to characterize attainability, completeness, pricing, and
the relationship between risk and return in financial markets. Subsequently, he uses the intuition developed in conjunction with the discrete time theory to introduce continuous time calculus for continuous, jump, and mixed continuous-jump processes, and to deal with attainability, completeness,
pricing, and the relationship between risk and return in general continuous time models. Throughout, the exposition of the continuous time theory emphasizes the analogies between discrete time and continuous time methods and results. The book includes many examples, applications to the pricing of
options and other derivative securities, and an extensive discussion of the Black-Scholes model and its most general theoretical extension.

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Descriere

This textbook on financial markets has two purposes: one is to introduce students to the latest theory of financial markets, and the other is to explain the advanced mathematics that is the language of this theory. It requires students to have a familiarity with the elementary ideas of ordinary calculus, linear algebra, probability, and microeconomics. The theory in the book is the basis for some very successful applications to a large and growing segment offinancial markets: futures markets in commodities, interest rates, and stock indexes; and the options markets in the same areas.

Cuprins

Introduction to models of financial markets; One-period equilibrium price measures; A discrete multi-period model; Multi-period equilibrium price measures; Discrete stochastic calculus; Extensions of the discrete multi-period model; The Wiener process; Ito Calculus; The Black-Scholes model; Local martingales and semimartingales; General stochastic calculus; A continuous multi-period model

Recenzii

'The great strengths of the book are its logical development of very sophisticated concepts and the examples and exercises. Each major definition and theorem is followed by a simple example. This makes the early chapters on the discrete model, in particular, very useful for teaching at the PhD level.'Richard Stapleton, University of Lancster, Economica, 2/92