Finite Difference Methods for Financial PDE Pricing

Summary

This article surveys five books on finite difference methods (FDM) and partial differential equations used in quantitative finance, especially for solving Black–Scholes pricing problems. It distinguishes texts that emphasize mathematical foundations, practical implementation, or both. Topics across the books include stability analysis, sparse linear systems, multidimensional and multi-factor models, boundary conditions, and numerical schemes such as Crank–Nicolson and iterative matrix methods.

The comparisons help readers choose references by purpose: Duffy’s theory text pairs with his C++ implementation book, while Tavella and Randall connect stochastic pricing theory to numerical solutions. Smith and Evans, Blackledge, and Yardley offer broader, more theoretical PDE coverage, with less emphasis on desk-ready implementation. The article gives qualitative assessments rather than comparative experiments or performance benchmarks. Its recommendations reflect the author’s view of the books’ usefulness and currency; some methods and implementation discussions are described as dated, and the list is focused on FDM rather than numerical methods generally.

Key ideas

• Finite difference methods approximate derivatives in pricing models expressed as partial differential equations.
• The reviewed books vary in emphasis from PDE theory and stability to practical C++ solver design.
• Stability analysis and sparse linear system methods are recurring foundations for numerical PDE work.
• Duffy’s theoretical and implementation texts are presented as complementary references.
• The guide offers qualitative book-selection advice, not evidence from comparative testing.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.