An appropriate approach to pricing European-style options with the Adomian decomposition method

Authors

  • Ziwei Ke School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522. http://orcid.org/0000-0002-1666-3592
  • Joanna Goard School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522.
  • Song-Ping Zhu School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522.

DOI:

https://doi.org/10.21914/anziamj.v59i0.11573

Keywords:

Adomian decomposition method, European option, digital option, Vasicek model.

Abstract

We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black–Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black–Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results. doi:10.1017/S1446181117000438

Published

2018-04-04

Issue

Section

Articles for Printed Issues