(A) structural understanding of american option dynamics and application to deposit insurance

Abstract

Abstract This dissertation deals with the nature of American option pricing. First, it explores the nature of the American options dynamics and introduces a general methodology to derive the analytic valuation formula of the American options on the same basis of Black-Scholes model using the knowledge with diffusion theory. The formula is derived from the analysis of the structural mechanics between early exercise premium and the European options. The whole information on the dynamics of the American options is provided while deriving the formula. And the reason why the optimal exercise boundary has to be determined in the solution process of the valuation formula is explained and the basic characteristics of early exercise boundary are reviewed in diffusion framework. The analytic valuation formula of American options can be obtained by using the general methodology developed in Chapter 2. The chapter expands the general methodology to be applied to several other American options.