广义CEV模型下分数阶BS方程的亚式期权定价及反问题
Pricing and Inverse Problem of Asian Options for Fractional Order BS Equations under the Generalized CEV Model
DOI: 10.12677/AAM.2024.136286, PDF, 下载: 53  浏览: 82  国家自然科学基金支持
作者: 沈诺晨, 许作良*：中国人民大学数学学院，北京
关键词: 广义CEV模型；分数阶BS方程；期权定价；反问题；Generalized CEV Model； Fractional Order BS Equation； Option Pricing； Counterproblem
摘要: 本文主要研究广义CEV模型下分数阶 Black-Scholes 方程的亚式期权定价及反问题。首先介绍了广义CEV模型下分数阶 Black-Scholes方程结合亚式期权的定价问题，根据Cox和Jumarie提出的带有分红的广义CEV波动率模型，推导出算术平均亚式期权满足的定价公式，其次在空间和时间上进行差分离散，并根据数值模拟验证了模型有效性。最后研究了时间分数阶广义CEV模型下亚式期权定价的反问题，在正问题的基础上，结合一种稳健的预测 -校正线性化算法，对波动率进行反演，根据数值实验验证算法的有效性及稳定性。
Abstract: This article mainly studies the pricing and inverse problem of Asian options for frac- tional order Black Scholes equations under the generalized CEV model. Firstly, the pricing problem of fractional order Black Scholes equations combined with Asian op- tions under the generalized CEV model is introduced. Based on the generalized CEV volatility model with dividends proposed by Cox and Jumarie, the pricing formula satisfied by arithmetic mean Asian options is derived. Secondly, the difference is separated in space and time, and the effectiveness of the model is verified through numerical simulation. Finally, the inverse problem of Asian option pricing under the time fractional generalized CEV model was studied. Based on the forward problem, a robust prediction correction linearization algorithm was combined to invert volatil- ity. The effectiveness and stability of the algorithm were verified through numerical experiments.
文章引用：沈诺晨, 许作良. 广义CEV模型下分数阶BS方程的亚式期权定价及反问题[J]. 应用数学进展, 2024, 13(6): 2996-3014. https://doi.org/10.12677/AAM.2024.136286

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