A Short History of Computational Finance 1990-2020, a Partial Differential (PDE/FDM) Approach

Daniel J. Duffy's historical review focuses on the applicability of partial differential equation (PDE) techniques and related numerical methods, particularly Finite Difference Method (FDM) that are applied to option pricing and hedging applications.

This article traces the development of computational finance during the period 1990–2020. The views and conclusions are based mainly on the author’s involvement in this area. We focus on the mathematical and numerical models that form a crucial part of this field. Special attention areas are option pricing, partial and stochastic differential equation, and their numerical approximation. We take what we could call a lifecycle approach by tracing the evolution of computational finance, from problem description to design and implementation. The presentation is semi-technical, and it should appeal to a wide range of readers.


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A Short History of Computational Finance 1990-2020, a Partial Differential (PDE/FDM) Approach