Standard Methods for Standard Options

Abstract

We now enter the part of the book that is devoted to the numerical solution of equations of the Black-Scholes type. Here we discuss “standard” options in the sense as introduced in Section 1.1. Accordingly, let us assume the scenario characterized by the Assumptions 1.2. In case of European options the function V (S, t) solves the Black-Scholes equation (1.2). It is not really our aim to solve this partial differential equation because it possesses an analytic solution (#x2192; Appendix A4). Ultimately it is our intention to solve more general equations and inequalities. In particular, American options will be calculated numerically. The goal is not only to calculate single values V (S₀, 0) —for this purpose binomial methods can be applied— but also to approximate the curve V (S, 0), or even the surface defined by V (S, t) on the half strip S > 0, 0 ≤ t≤ T.