[SEE ATTACHED FOR COMPLETE TEXT] In recent years stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This self-contained work examines that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. Key features of this work include: * accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis, * five introductory chapters on stochastic analysis, followed by