Advanced Ordinary Differential Equations and Method of Lines

• Published in: Financial Instrument Pricing Using C++ pp. 781 - 818
• Main Author: Duffy, Daniel J
• Format: Book Chapter
• Language: English
• Published: United Kingdom John Wiley & Sons, Incorporated 2018; Wiley
• Subjects: barrier options; Boost odeint library; C++ projects; exponential fitting; FINANCE & ACCOUNTING; first‐order ordinary differential equations; matrix differential equations; method of lines; option pricing
• ISBN: 0470971193; 9780470971192
• DOI: 10.1002/9781119170518.ch25

This chapter deals with a discussion of the numerical solution of systems of first‐order ordinary differential equations (ODEs). In doing so, the Boost odeint library is used. There are several solvers in the library. Next, the chapter introduces the method of lines (MOL) that allows the developers to approximate the solutions of the time‐dependent parabolic partial differential equations (PDEs). It then provides generic examples of the Boost odeint library and their applications to computational finance. The exponentially fitted schemes are ideal for approximating the solution of PDEs that describe barrier options. Exponential fitting is used in the space S direction and implicit Euler time marching in the t direction. If needed, the developers can employ extrapolation techniques in the time direction in order to promote accuracy. Finally, the chapter concludes with a number of exercises and C++ projects that have been discussed in the preceding chapters of this book.