Boundary, Terminal and Interface Conditions and their Influence

The differential equation itself is not sufficient to valuate a financial instrument; in order to do so, we additionally need final conditions, boundary conditions and sometimes also interface conditions. This chapter deals with the formulation of such conditions for specific examples. There are quite a few financial instruments with more or less heavily path‐dependent payoffs available, and this path‐dependence may be arbitrarily complicated. Therefore, the chapter concentrates on specific aspects that are fundamental from the authors point of view. It focuses on the terminal conditions for equity options, and examines the terminal conditions for fixed income instruments. The chapter briefly talks about the callability and Bermudan options. It also deals with snowballs and tarns. The chapter concludes with a discussion on boundary conditions, and deals with the interface conditions of two groups of exotic instruments with a strong path dependence.