### Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation

LEI Ziqi1, ZHOU Qing1, WU Weixing2, WANG Zengwu3

1. 1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. Research Center of Applied Finance and School of Finance and Banking, University of International Business and Economics, Beijing 100029, China;
3. Institute of Finance and Banking, Chinese Academy of Social Sciences, Beijing 100029, China
• Received:2021-05-03 Revised:2021-12-24 Online:2023-01-25 Published:2023-02-09
• Supported by:
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.

LEI Ziqi, ZHOU Qing, WU Weixing, WANG Zengwu. Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation[J]. Journal of Systems Science and Complexity, 2023, 36(1): 328-359.

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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