A Logistic Black-Scholes Partial Differential Equation with Stochastic Volatility, Transaction Costs and Jumps

Journal article

Authors/Editors

DAWUD THONGTHA

Strategic Research Themes

Other (Strategic Research Themes)

Publication Details

Author list: Kankullanat Arnuphap and Dawud Thongtha

Publication year: 2024

Volume number: 19

Issue number: 1

Start page: 57

End page: 74

Number of pages: 18

ISSN: 18140424

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85172357995&partnerID=40&md5=5f19a81c803b3d84171b0d5e376515fe

Languages: English-Great Britain (EN-GB)

Abstract

In this paper, we introduce a new differential form of an asset price. This form is proposed by considering various factors such as demand and supply on the asset, stochastic volatility, transaction costs and jumps. The new differential form extends an original logistic geometric Brownian motion by adding transaction cost and jump terms. More-over, we find a solution for the asset price related to the proposed form. Furthermore, we derive Black-Scholes partial differential equations based on the proposed price process. ฉ (2024). All Rights Reserved.

Keywords

Black-Scholes Model, Logistic Geometric Brownian Motion, Option pricing model, Stochastic volatility, Transaction costs