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Option Pricing under the Subordinated Market Models

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  • Longjin Lv
  • Changjuan Zheng
  • Luna Wang
  • Benjamin Miranda Tabak

Abstract

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.

Suggested Citation

  • Longjin Lv & Changjuan Zheng & Luna Wang & Benjamin Miranda Tabak, 2022. "Option Pricing under the Subordinated Market Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-8, January.
    • Handle: RePEc:hin:jnddns:6213803
    DOI: 10.1155/2022/6213803
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    Cited by:

    1. Zhi Liu, 2022. "Testing for the Presence of the Leverage Effect without Estimation," Mathematics, MDPI, vol. 10(14), pages 1-16, July.

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