Itô Process and Diffusion Models

Abstract

In this chapter we will introduce a general framework of financial market. In the first section we present some basic concepts and fundamental results on martingale methods in the pricing and hedging of European contingent claims under the Itô process setting. In Sect. 7.2 we show that within the diffusion process framework, the pricing and hedging of European contingent claims can be done through a PDE approach. In Sect. 7.3 we present two probabilistic methods for closed-form pricing of European options and illustrate these methods through examples. In the fourth section we briefly address the problem of pricing American contingent claims in diffusion models.