Thalesian Webinar: Daniel J. Duffy: PDEs and FDM for Computational Finance

Daniel Duffy

C++ author, trainer
25 August 2021



Thalesians

Partial Differential Equations (PDEs) and Finite Difference Method (FDM) for Computational Finance

Daniel J. Duffy, Datasim



In this talk we give an overview of the numerical solution of PDEs using finite difference methods. We focus on one-factor and two-factor PDEs and their applications to computational finance. In particular, we discuss the Black Scholes equation and its applications to equity, fixed income and hybrid models. Some common use cases between these models are:

. Option pricing and option sensitivities (“Greeks”).

. Early exercise features (American options).

. Calibration (Kolmogorov, Fokker-Planck PDE).

. The relationship between stochastic calculus and PDEs.



We address these use cases by modelling them as PDEs and subsequent approximation by various finite difference schemes that are unambiguously expressed in algorithmic form. We use a number of well-known schemes in finance as well as schemes that are less known in finance but which are nonetheless popular in other disciplines. We also some original schemes as developed in Duffy (2021):



. Crank Nicolson and extrapolation methods.

. Alternating Direction Explicit (ADE).

. Splitting Methods.

. Method of Lines (MOL).

. Front-fixing and variational methods.

. Some original results based on my research work.



We give guidelines on which scheme is optimal (in terms of accuracy, applicability, robustness and maintainability) for a given problem in computational finance.

We conclude the talk with a discussion of pricing a two-factor model with early exercise features in order to trace the steps from PDE specification through FDM algorithms and their design in C++.


This talk is aimed at a wide audience, but it should be of particular interest to MSc and MFE students as well as quants in computational finance. In particular, there are opportunities for new research projects and applications to production systems.



Reference

Duffy, Daniel J. (2021) NUMERICAL METHODS IN COMPUTATIONAL FINANCE A Partial Differential Equation (PDE/FDM) Approach (John Wiley & Sons).

(to appear November2021)



Daniel Duffy has a PhD in Mathematics from the University of Dublin (Trinity College).
 
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