Title

An Appropriate Approach To Pricing European-style Options With The Adomian Decomposition Method

RIS ID

122615

Publication Details

Ke, Z., Goard, J. & Zhu, S. (2018). An Appropriate Approach To Pricing European-style Options With The Adomian Decomposition Method. Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 59 (3), 349-369.

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.

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Link to publisher version (DOI)

http://dx.doi.org/10.1017/S1446181117000438