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American Rainbow Option Pricing Formulae in Uncertain Environment

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Abstract

American rainbow option is a compound option on multiple underlying assets and its gain depends upon the variations of these assets’ prices. This option can entitle investors a right that this option be traded and waived at the discretion of investors. Considering the flexibility of exercising time of American option and the investment preferences of purchasing multiple underlying assets, this paper predominantly discusses American rainbow option pricing under the framework of uncertainty theory. Assuming that independent stock prices obey the corresponding uncertain differential equations, we derive the option pricing formulae. They are American rainbow call on max option, American rainbow call on min option, American rainbow put on max option, American rainbow put on min option, American rainbow put 2 and call 1 option, and American rainbow better of assets option, respectively. Moreover, we verify that the option pricing formulae is valid through some numerical examples. And the effect of relevant parameters on option price is also analyzed.

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Acknowledgements

This work was funded by National Natural Science Foundation of China (Grant No. 72101080), Natural Science Foundation of Hebei Province (Grant No. F2020202056), and the Key Project of Hebei Education Department (Grant No. ZD2020125).

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  1. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, China

    Rong Gao & Xiaofang Yin

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  1. Rong Gao
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  2. Xiaofang Yin
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Correspondence to Rong Gao.

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This paper, in whole or in part, has not been previously published and is not under consideration of any other journal. There is no competing interests involved with this submission. The authors declare that there are no financial or non-financial interests that are directly or indirectly related to the work submitted for publication. All co-authors agree to the submission.

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Communicated by Rosihan M. Ali.

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Gao, R., Yin, X. American Rainbow Option Pricing Formulae in Uncertain Environment. Bull. Malays. Math. Sci. Soc. 46, 190 (2023). https://doi.org/10.1007/s40840-023-01581-4

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