随机波动率模型下离散几何平均亚式障碍期权定价
Pricing of Discrete Geometric Average Asian Discrete Barrier Option under Stochastic Volatility Model
DOI: 10.12677/OJNS.2019.76054, PDF,   
作者: 陈有杰：广西师范大学数学与统计学院，广西 桂林
关键词: Heston模型；障碍期权；Fourier反变换；几何平均；Heston Model； Barrier Option； Fourier Inverse Transform； Geometric Average
摘要: 本文在标的资产价格满足Heston随机波动率模型下讨论基于资产价的离散几何平均情形的亚式离散障碍期权定价。应用半鞅Itô公式、多维联合特征函数、Girsanov测度变换和Fourier反变换等随机分析方法，推导出了基于资产价的亚式几何平均离散障碍期权的定价公式，最后给出了数值计算实例，并分析了波动率参数对障碍期权价格的影响。
Abstract: In this paper, the pricing of Asian barrier options for discrete time scenarios based on the discrete geometric average of asset price is discussed under the model of Heston stochastic volatility which is discussed in the underlying asset price. Some stochastic analysis approaches such as the semi-martingale Itô formula, multidimensional federated characteristic functions, Girsanov theo-rem and Fourier inverse transform technique are to derive the pricing formula for the Asian dis-crete barrier call option. And finally, numerical examples are given by us, and the impacts of some parameters in stochastic volatility process on the values of the barrier option values are examined by this numerical example.
文章引用：陈有杰. 随机波动率模型下离散几何平均亚式障碍期权定价[J]. 自然科学, 2019, 7(6): 447-455. https://doi.org/10.12677/OJNS.2019.76054

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