Accuracy and Reliability Considerations of Option Pricing Algorithms

✍ Scribed by Yue-Kuen Kwok; Ka-Wo Lau

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 297 KB
• Volume: 21
• Category: Article
• ISSN: 0270-7314
• DOI: 10.1002/fut.2001

✦ Synopsis

Abstract

A wide variety of computational schemes have been proposed for the numerical valuation of various classes of
options. Experiences in numerical computation have revealed that the details of the implementation of the
auxiliary conditions in the numerical algorithms may have profound effects on numerical accuracy. Difficulties
in designing algorithms that deal with the path‐dependent payoffs, monitoring features, etc., have been
well reported in the literature. In this article, the theoretical issues on the assessment of numerical schemes
with regard to accuracy of approximation of auxiliary conditions, rate of convergence, and oscillation phenomena
are reviewed. In particular, the oscillation phenomena in bond‐price calculations and the intricacies in
implementing the auxiliary conditions in barrier options, proportional step options, and lookback options are
discussed. With different types of options and modes of monitoring (continuous or discrete), the
optimal method of placing the lattice nodes with reference to the boundary (absorbing or reflecting)
are examined in order to achieve linear temporal rate of convergence. © 2001 John Wiley & Sons, Inc.
Jrl Fut Mark 21:875–903, 2001