Option pricing under the subordinated market models
type: Item
instance of: scholarly article
title: Option pricing under the subordinated market models
zbMATH Open document ID: 1490.91216
DOI: 10.1155/2022/6213803
author: Changjuan Zheng
author: Luna Wang
author: Long-Jin Lv
published in: Discrete Dynamics in Nature and Society
publication date: 2022-02-02T00:00:00Z
review text: Summary: This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. The closed-form pricing formula for European options is derived. In the comparison with the classic Black-Sholes model, we find the option prices become higher, and the ``volatility smiles'' phenomenon happens in the proposed model. Finally, an empirical analysis is performed to show the validity of these results.
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 7468558
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/6213803
OpenAlex ID: W4206103454
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description: scientific article; zbMATH DE number 7468558