Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation

LEI Ziqi, ZHOU Qing, WU Weixing, WANG Zengwu

系统科学与复杂性(英文) ›› 2023, Vol. 36 ›› Issue (1) : 328-359.

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系统科学与复杂性(英文) ›› 2023, Vol. 36 ›› Issue (1) : 328-359. DOI: 10.1007/s11424-023-1140-1

Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation

    LEI Ziqi1, ZHOU Qing1, WU Weixing2, WANG Zengwu3
作者信息 +

Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation

    LEI Ziqi1, ZHOU Qing1, WU Weixing2, WANG Zengwu3
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摘要

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.

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.

关键词

α-path / uncertainty / uncertain fractional differential equation / vulnerable option pricing

Key words

α-path / uncertainty / uncertain fractional differential equation / vulnerable option pricing

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LEI Ziqi , ZHOU Qing , WU Weixing , WANG Zengwu. Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation. 系统科学与复杂性(英文), 2023, 36(1): 328-359 https://doi.org/10.1007/s11424-023-1140-1
LEI Ziqi , ZHOU Qing , WU Weixing , WANG Zengwu. Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation. Journal of Systems Science and Complexity, 2023, 36(1): 328-359 https://doi.org/10.1007/s11424-023-1140-1

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基金

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.
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