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

Ting Jin, Xiangfeng Yang (), Hongxuan Xia () and Hui Ding ()
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Ting Jin: School of Science, Nanjing Forestry University, Nanjing 210037, Jiangsu, P. R. China
Xiangfeng Yang: ��School of Information Technology & Management, University of International Business and Economics, Beijing 100029, P. R. China
Hongxuan Xia: ��College of International Education, Nanjing Forestry University, Nanjing 210037, Jiangsu, P. R. China
Hui Ding: �College of Economics and Management, Nanjing Forestry University, Nanjing 210037, Jiangsu, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-21

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.

Keywords: Fractional-Order Differential Equations; α-Path; Predictor–Corrector; First-Hitting Time Model; Barrier Option; Reliability Index (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500122

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