Numerical Partial Differential Equations in Finance Explained: An Introduction to Computational Finance

This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach.  In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient.

The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.

Table of Contents

Chapter 1 Financial Option Valuation
Chapter 2 Partial Differential Equations
Chapter 3 Spatial Discretization I
Chapter 4 Spatial Discretization Ii
Chapter 5 Numerical Study: Space
Chapter 6 The Greeks
Chapter 7 Temporal Discretization
Chapter 8 Numerical Study: Time
Chapter 9 Cash-Or-Nothing Options
Chapter 10 Barrier Options
Chapter 11 American-Style Options
Chapter 12 Merton Model
Chapter 13 Two-Asset Options
Appendix A: Wiener Process
Appendix B: Feynman–Kac Theorem
Appendix C: Down-and-Out Put Option Value
Appendix D: Max-of-Two-Assets Call Option Value