An ingenious, piecewise linear interpolation algorithm for pricing arithmetic average options

Tian-Shyr Dai*, Jr Yan Wang, Hui Shan Wei

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Pricing arithmetic average options continues to intrigue researchers in the field of financial engineering. Since there is no analytical solution for this problem until present, developing an efficient numerical algorithm becomes a promising alternative. One of the most famous numerical algorithms for pricing arithmetic average options is introduced by Hull and White [10]. In this paper, motivated by the common idea of reducing the nonlinearity error in the adaptive mesh model [7] and the adaptive quadrature numerical integration method [6], the logarithmically equally-spaced placement rule in the Hull and White's model is replaced by an adaptive placement method, in which the number of representative average prices is proportional to the degree of curvature of the option value as a function of the arithmetic average price. Numerical experiments verify the superior performance of our method in terms of reducing the interpolation error. In fact, it is straightforward to apply this method to any pricing algorithm with the techniques of augmented state variables and the piece-wise linear interpolation approximation.

Original languageEnglish
Title of host publicationAlgorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings
Pages262-272
Number of pages11
DOIs
StatePublished - 1 Dec 2007
Event3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States
Duration: 6 Jun 20078 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4508 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
CountryUnited States
CityPortland, OR
Period6/06/078/06/07

Keywords

  • Adaptive placement
  • Arithmetic average options
  • Logarithmically equally-spaced placement

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