时间分数阶 CIR 模型下回望期权的定价问题
Pricing of Lookback Options under the Time-Fractional CIR Model
DOI: 10.12677/FIN.2024.144159, PDF,    国家自然科学基金支持
作者: 杜云康, 许作良*：中国人民大学数学学院，北京
关键词: CIR 模型；时间分数阶；期权定价；数值方法；CIR Model； Time-Fractional； Option Pricing； Numerical Methods
摘要: 本文主要研究了时间分数阶 CIR (Cox-Ingersoll-Ross) 模型下回望期权的定价问题。传统的 CIR 模型由于其对长期记忆效应的忽视，已无法充分描述金融市场中的一些复杂现象。因此，本 文引入了时间分数阶导数，以捕捉金融市场中更为复杂的动态特性。在研究过程中，本文首先利 用 It^o 引理和 ∆-对冲原理对时间分数阶 CIR 模型进行了数学推导，建立了回望期权定价的理论 框架。然后，本文在时间方向与空间方向上使用了有限差分方法对定价公式进行了数值离散处理。 最后，本文进行了数值实验，数值实验的结果验证了所提出方法的有效性。
Abstract: This paper primarily studies the pricing problem of lookback options under the time-fractional CIR (Cox-Ingersoll-Ross) model. The traditional CIR model, due to its neglect of long-term memory effects, can no longer fully describe some complex phenomena in financial markets. Therefore, this paper introduces the time-fractional derivative to capture more complex dynamic characteristics in financial markets. In the research process, this paper first uses Ito’s lemma and the Delta-hedging principle to mathematically derive the time-fractional CIR model, establishing the theoretical framework for lookback option pricing. Then, the paper uses the finite difference method in both the time and space directions to numerically discretize the pricing formula. Finally, numerical experiments are conducted, and the results of these ex- periments validate the effectiveness of the proposed method.
文章引用：杜云康, 许作良. 时间分数阶 CIR 模型下回望期权的定价问题[J]. 金融, 2024, 14(4): 1539-1551. https://doi.org/10.12677/FIN.2024.144159

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