C# for Financial Markets

Appendix 3

The Mathematical Background to the Alternating Direction Explicit (ADE) Method

A3.1 INTRODUCTION AND OBJECTIVES

In this appendix we give a mathematical overview of the ADE method that we introduced in Chapter 10. The goal is to describe the essential characteristics of the method and its applicability to option pricing in computational finance. We focus on one-factor equity problems in this appendix and we give some hints and guidelines on how to apply ADE to multi-factor problems.

ADE is a competitor to Alternating Direction Implicit (ADI) and Fractional Step (‘Soviet Splitting’) methods. The results to date look promising and we expect more interest in this area in the coming years. In particular, the method could form the basis for an MSc or PhD thesis and as an alternative to the hegemony of methods in computational finance, such as the Crank-Nicolson and ADI methods. The first applications of ADE to computational finance are discussed in Pealat and Duffy 2011.

In this appendix we focus on linear one-factor problems. We have included this detailed discussion of ADE because of the interest and requests from a number of quants and traders who develop software systems in computational finance.

Multi-factor and nonlinear problems will be discussed in future work. The ADE method was first applied to computational finance by Daniel J. Duffy.

A3.2 BACKGROUND TO ADE

The ADE method originated in the former Soviet Union (Saul'yev 1964) and, after its initial publication, ...