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Compound option pricing problem in uncertain environment

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Abstract

A compound option, or option on option, is a kind of option that gives the investor a right to obtain the underlying option. Unlike the European option, pricing the compound options involves two periods and two kinds of underlying assets, which will be more complex. This paper researches the compound options based on the general uncertain stock model and derives the general pricing formulae for four types of compound options. Based on the general pricing formulae, two examples of the mean-reverting process are shown in this paper. The paper also designs related numerical algorithms for computing the price in these examples.

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Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 62303115), the Fundamental Research Funds for the Central Universities in UIBE (No. 22QN03) and the Scientific Research Laboratory of AI Technology and Applications in UIBE.

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Authors and Affiliations

  1. School of Information Technology and Management, University of International Business and Economics, Beijing, 100029, China

    Huadong Wu, Yaodong Ni & Xiangfeng Yang

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  1. Huadong Wu
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  2. Yaodong Ni
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  3. Xiangfeng Yang
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Correspondence to Xiangfeng Yang.

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Wu, H., Ni, Y. & Yang, X. Compound option pricing problem in uncertain environment. J Ambient Intell Human Comput 15, 593–605 (2024). https://doi.org/10.1007/s12652-023-04716-4

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