通过扰乱分析,探索伊万塞维奇期权定价模型中的混乱和敏感性
Adil Jhangeer1, Ali R Ansari2, Ariana Abdul Rahimzai3
1IT4Innovations, VSB - Technical University of Ostrava, Ostrava, Poruba, Czech Republic.
PloS one
|November 26, 2024
概括
这项研究引入了Ivancevic期权定价模型,一种基于波的新方法. 它分析了像单元和混乱这样的复杂动态,提供了超越Black-Scholes模型的新视角.
科学领域:
- 量化金融 量化金融
- 数学物理 数学物理
- 计算金融是指计算金融.
背景情况:
- 黑斯科尔斯模型是期权定价的基石.
- 需要替代模型来捕捉复杂的金融动态.
- 非线性波形方程为金融建模提供了一个新的框架.
研究的目的:
- 探索伊万切维奇期权定价模型作为基于非线性波动的替代方案.
- 用非线性施罗丁格方程分析模型的行为.
- 在模型中调查单子动力学,混乱模式和波浪结构.
主要方法:
- 应用波形转换来将PDEs转换为ODEs.
- 使用[公式:参见文本]方法来导出单离子溶液.
- 模拟的3D表面图和2D图表用于解决方案可视化.
- 在扰动力下分析动态行为,使用利亚普诺夫指数,分叉图和庞卡雷地图.
主要成果:
- 衍生出各种解决方案形式,包括单一扭曲,周期,过度,三角,指数和复杂的解决方案.
- 通过3D和2D图表可视化解决方案组件 (真实,想象的,模块).
- 确定了混乱模式,并分析了系统的灵敏度,多稳定性和波浪结构.
结论:
- 伊万切维奇期权定价模型为了解期权定价动态提供了一个全面的框架.
- 这项研究证明了模型捕捉复杂现象的能力,比如单元和混乱.
- 这些发现为模型的行为和金融市场的潜在应用提供了有价值的见解.
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