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AN APPROPRIATE APPROACH TO PRICING EUROPEAN-STYLE OPTIONS WITH THE ADOMIAN DECOMPOSITION METHOD

Part of: Equations and systems with constant coefficients

Published online by Cambridge University Press:  26 February 2018

ZIWIE KE Open the ORCID record for ZIWIE KE [Opens in a new window] ,
JOANNA GOARD Open the ORCID record for JOANNA GOARD [Opens in a new window]  and
SONG-PING ZHU Open the ORCID record for SONG-PING ZHU [Opens in a new window]
ZIWIE KE*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email zk990@uowmail.edu.au, joanna@uow.edu.au, spz@uow.edu.au
JOANNA GOARD
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email zk990@uowmail.edu.au, joanna@uow.edu.au, spz@uow.edu.au
SONG-PING ZHU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email zk990@uowmail.edu.au, joanna@uow.edu.au, spz@uow.edu.au
*
✉zk990@uowmail.edu.au
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Abstract

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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.

Keywords

Adomian decomposition methodEuropean optiondigital optionVasicek model

MSC classification

Primary: 35E15: Initial value problems
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 3 , January 2018 , pp. 349 - 369
Copyright
© 2018 Australian Mathematical Society 

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