A PDE Software Framework in C++11 for a Class of Path-Dependent Options

• Published in: Financial Instrument Pricing Using C++ pp. 727 - 754
• Main Author: Duffy, Daniel J
• Format: Book Chapter
• Language: English
• Published: United Kingdom John Wiley & Sons, Incorporated 2018; Wiley
• Subjects: alternating direction explicit method; C++ software framework; FINANCE & ACCOUNTING; first‐order hyperbolic PDEs; Mathematica; numerical schemes; path‐dependent option
• ISBN: 0470971193; 9780470971192
• DOI: 10.1002/9781119170518.ch23

This chapter discusses how to analyse, design and implement a C++ software framework for a class of partial differential equations (PDEs) (an exemplar of which is discussed in Wilmott, Lewis and Duffy (WLD), 2014). The chapter applies the alternating direction explicit (ADE) method to model a special kind of path‐dependent option with one stochastic factor and one deterministic factor. The resulting PDE is similar to that used when pricing Asian options and in the Cheyette model. The results are reproduced in WLD that were computed using the NDSolve package in Mathematica. ADE is an efficient scheme and a possible project might be a feasibility study for calibration. From a numerical analysis perspective, the chapter considers some attention to the problem of choosing a stable and accurate finite difference scheme to approximate the first‐order hyperbolic part of the PDE. Then, it applies ADE to an analysis of numerical schemes for first‐order hyperbolic PDEs.