<p>Cumulative-Parisian options are a special type of barrier options, where the knock-in or knock-out feature is triggered based on whether the cumulative time spent beyond the barrier level exceeds a fixed delay period. This paper studies the pricing of cumulative-Parisian options using uncertainty theory and derives pricing formulas for four types of options, including up-and-in call, down-and-in put, up-and-out put, and down-and-out call. The pricing formulas are further extended to an uncertain mean-reverting stock model. Parameters are estimated using the least squares method, and the fitted uncertain differential equations are validated through uncertain hypothesis testing. In addition, an empirical analysis based on Tesla stock data is conducted to show the practical use of the pricing formulas and to examine how option prices respond to changes in key factors such as barrier levels, delay periods, and interest rates.</p>

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Cumulative-Parisian Option Pricing in Uncertainty Theory

  • Zhihan Shi,
  • Yaodong Ni,
  • Xiangfeng Yang

摘要

Cumulative-Parisian options are a special type of barrier options, where the knock-in or knock-out feature is triggered based on whether the cumulative time spent beyond the barrier level exceeds a fixed delay period. This paper studies the pricing of cumulative-Parisian options using uncertainty theory and derives pricing formulas for four types of options, including up-and-in call, down-and-in put, up-and-out put, and down-and-out call. The pricing formulas are further extended to an uncertain mean-reverting stock model. Parameters are estimated using the least squares method, and the fitted uncertain differential equations are validated through uncertain hypothesis testing. In addition, an empirical analysis based on Tesla stock data is conducted to show the practical use of the pricing formulas and to examine how option prices respond to changes in key factors such as barrier levels, delay periods, and interest rates.