Lattice Models Applications to Computational Finance

• Published in: Financial Instrument Pricing Using C++ pp. 367 - 394
• Main Author: Duffy, Daniel J
• Format: Book Chapter
• Language: English
• Published: United Kingdom John Wiley & Sons, Incorporated 2018; Wiley
• Subjects: Bernoulli paths; binomial method; C++ features; FINANCE & ACCOUNTING; finite difference methods; lattice abstract data type; lattice models applications; option dividends; option sensitivities; Pascal's triangle; price options
• ISBN: 0470971193; 9780470971192
• DOI: 10.1002/9781119170518.ch12

This chapter concerns with the analysis and application of the basic software framework to price European and American options using lattice models. It focuses on testing the reliability, accuracy and functionality of the code in the framework. In doing so, the chapter first discusses how to create and test the properties of Pascal's triangle using the lattice abstract data type (ADT). In some cases (for example, non‐path‐dependent European options), it is possible to compute call and put prices as a sum using Bernoulli paths. The chapter shows how to compute option prices using Bernoulli paths. It then helps the readers to compute option sensitivities and dividends. After this, an abridged numerical analysis of the binomial method is also carried out. Furthermore, the chapter discusses the transition from lattice methods to explicit finite difference methods. Finally, it explores the features in C++ to allow the software to be adapted to new situations.