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Pricing problem, sensitivity analysis and empirical analysis of exchange options under uncertainty

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  • Gao, Yin
  • Yin, Xiangqian
  • Tang, Han

Abstract

In the high-risk modern financial markets under uncertainty, exchange options including exchange call and put options as an effective tool can be applied to hedge the risks, which means that the buyer of the options has the right to convert one asset into another asset within a certain period of time according to the agreed proportion in advance. This paper derives the ordinary price of exchange call and put options by means of uncertain differential equations. As a special kinds of uncertain differential equations, the asset value are described by Liu’s stock model, the certain price of exchange call and put options are given successfully. By means of the ordinary and certain pricing formulas, the sensitivity analysis of exchange call and put options are presented respectively. Moreover, the algorithms for the ordinary and certain pricing formulas of exchange call and put options are designed, and the numerical examples of exchange call and put options are discussed. Besides, the empirical research of exchange call and put options are discussed based on the stock price of BABA and JD from December 26, 2023 to June 26, 2024 in the NASDAQ stock market.

Suggested Citation

  • Gao, Yin & Yin, Xiangqian & Tang, Han, 2026. "Pricing problem, sensitivity analysis and empirical analysis of exchange options under uncertainty," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 571-582.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:571-582
    DOI: 10.1016/j.matcom.2026.04.046
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