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      RELIABILITY INDEX AND OPTION PRICING FORMULAS OF THE FIRST-HITTING TIME MODEL BASED ON THE UNCERTAIN FRACTIONAL-ORDER DIFFERENTIAL EQUATION WITH CAPUTO TYPE

      1 , 2 , 3 , 4
      Fractals
      World Scientific Pub Co Pte Lt

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          Abstract

          Since the ability to control the investor’s income or loss within a certain range, barrier option has been among the most popular path-dependent options where its payoff depends on whether or not the underlying asset’s price reaches a given “barrier”. First, assuming the underlying asset as an uncertain variable for the case that the Caputo fractional-order derivative is adopted instead of the ordinary derivative, the real financial market is better modeled by the uncertain fractional-order differential equation with Caputo type. Then, a first-hitting time model which can measure the exercise ability is innovatively presented. Second, based on the first-hitting time theorem of the uncertain fractional-order differential equation, the reliability index (including validity and survival index) for the proposed model is obtained, and four types of European barrier option (including up-and-in call, down-and-in put, up-and-out put, and down-and-out call options) pricing formulas are obtained accordingly. Lastly, applying the predictor–corrector method, numerical algorithms are provided for calculating European barrier and the reliability index, numerical experiments and corresponding sensitivity analysis are also illustrated concerning various conditions.

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          Author and article information

          Contributors
          Journal
          Fractals
          Fractals
          World Scientific Pub Co Pte Lt
          0218-348X
          1793-6543
          February 2021
          January 23 2021
          February 2021
          : 29
          : 01
          : 2150012
          Affiliations
          [1 ]School of Science, Nanjing Forestry University, Nanjing 210037, Jiangsu, P. R. China
          [2 ]School of Information Technology & Management, University of International Business and Economics, Beijing 100029, P. R. China
          [3 ]College of International Education, Nanjing Forestry University, Nanjing 210037, Jiangsu, P. R. China
          [4 ]College of Economics and Management, Nanjing Forestry University, Nanjing 210037, Jiangsu, P. R. China
          Article
          10.1142/S0218348X21500122
          fc724a28-8a2b-4631-929b-a47f10a1047b
          © 2021
          History

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