Exact solutions of transaction cost nonlinear models for illiquid markets

Volume 23, Issue 3, pp 263--278 http://dx.doi.org/10.22436/jmcs.023.03.08

Publication Date: November 22, 2020 Submission Date: September 04, 2020 Revision Date: September 23, 2020 Accteptance Date: September 28, 2020

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Authors

Javed Hussain - Department of Mathematics, Sukkur IBA University, airport road Sukkur, Sindh, Pakistan.

Abstract

The aim of this study is to show that the Reduced Differential Transform Algorithm (RDTA) can be applied to highly nonlinear evolution equations appearing in quantitative finance. In particular, we compute exact solutions of nonlinear PDEs arising by relaxing the transaction-cost assumption in the illiquid Black-Scholes market. Moreover, we also aim to study the impact of the absence and presence of price slippage impact in the illiquid Black-Scholes model with transaction-cost.

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Keywords

• Option pricing
• relaxed Black-Scholes assumptions
• evolution equation
• differential transform

MSC

•  35Q91
•  91G80

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