沃尔特拉-赫斯顿模型中的几何亚洲选项的定价
Florian Aichinger1,2, Sascha Desmettre1
1Institute for Financial Mathematics and Applied Number Theory, Johannes Kepler University of Linz, AT-4040 Linz, Austria.
概括
本研究介绍了沃尔特拉-赫斯顿模型中的亚洲几何选项的新定价公式,包括粗略的赫斯顿模型. 这些发现为期权定价提供了半封闭的解决方案,提高了金融建模的准确性.
科学领域:
- 量化金融 量化金融
- 随机模型建模 随机模型建模
- 金融衍生工具 金融衍生工具
背景情况:
- 几何亚洲期权取决于资产的几何平均值,需要复杂的定价模型.
- 随机波动模型,如沃尔特拉-赫斯顿和粗略的赫斯顿,对于现实的资产定价至关重要.
- 准确的外来期权定价对于风险管理和交易策略至关重要.
研究的目的:
- 根据沃尔特拉-赫斯顿模型来推导亚洲几何期权的半封闭定价公式.
- 将定价方法扩展到包括粗略的赫斯顿模型.
- 为估值这些复杂衍生品提供一种可计算的方法.
主要方法:
- 运用类似的沃尔特拉过程理论.
- 导出日志股价和日志几何平均值的条件联合里埃变换.
- 通过随机指数表示里埃变换,并解决里卡蒂-沃尔特拉方程.
主要成果:
- 获得了半闭式公式来定价具有固定和浮动罢工的几何亚洲期权.
- 衍生的公式适用于Volterra-Heston模型的类,包括粗略的Heston模型.
- 一项数值研究在粗略的赫斯顿模型框架内验证了结果.
结论:
- 该研究成功地在高级随机波动模型中为几何亚洲期权提供了新的定价公式.
- 该方法在异国情调选项的定价中提供了显著的进步,特别是在粗略的赫斯顿模型中.
- 衍生式和数值验证有助于量化金融技术的实际应用.
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