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Option pricing for an uncertain stock model with jumps

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Abstract

By means of uncertain differential equation, an uncertain stock model usually describes the evolution of the stock price which highly depends on human uncertainty. Considering the sudden drifts on the stock price which might be caused by war, policy or technology, this paper proposes an uncertain stock model with both positive jumps and negative jumps in form of uncertain differential equation with jumps. European option pricing formulas for the proposed stock model are derived, and its monotonicity with respect to the parameters such as initial price, expiration date, and strike price is also studied.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 71171191 and 71272177), and National Social Science Foundation of China (Grant No. 13CGL057).

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Authors and Affiliations

  1. School of Business, Renmin University of China, Beijing, 100872, China

    Xiaoyu Ji

  2. School of Management, Shanghai University, Shanghai, 200444, China

    Jian Zhou

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  1. Xiaoyu Ji
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  2. Jian Zhou
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Correspondence to Jian Zhou.

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Communicated by E. E. Pap.

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Ji, X., Zhou, J. Option pricing for an uncertain stock model with jumps. Soft Comput 19, 3323–3329 (2015). https://doi.org/10.1007/s00500-015-1635-3

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  • DOI: https://doi.org/10.1007/s00500-015-1635-3

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