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Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation

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Abstract

This paper presents two new versions of uncertain market models for valuing vulnerable European call option. The dynamics of underlying asset, counterparty asset, and corporate liability are formulated on the basis of uncertain differential equations and uncertain fractional differential equations of Caputo type, respectively, and the solution to an uncertain fractional differential equation of Caputo type is presented by employing the Mittag-Leffler function and α-path. Then, the pricing formulas of vulnerable European call option based on the proposed models are investigated as well as some algorithms. Some numerical experiments are performed to verify the effectiveness of the results.

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Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Ziqi Lei & Qing Zhou

  2. Research Center of Applied Finance and School of Finance and Banking, University of International Business and Economics, Beijing, 100029, China

    Weixing Wu

  3. Institute of Finance and Banking, Chinese Academy of Social Sciences, Beijing, 100029, China

    Zengwu Wang

Authors
  1. Ziqi Lei
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  2. Qing Zhou
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  3. Weixing Wu
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  4. Zengwu Wang
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Additional information

The work of ZHOU Qing is supported by the National Natural Science Foundation of China under Grant Nos. 11871010 and 11971040, and by the Fundamental Research Funds for the Central Universities under Grant No. 2019XD-A11. The work of WU Weixing is supported by the National Natural Science Foundation of China under Grant No. 71073020.

This paper was recommended for publication by Editor YUAN Zhongyi.

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Lei, Z., Zhou, Q., Wu, W. et al. Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation. J Syst Sci Complex 36, 328–359 (2023). https://doi.org/10.1007/s11424-023-1140-1

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  • DOI: https://doi.org/10.1007/s11424-023-1140-1

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