Zhao Pan, Zhou Benda, Wang Jixia
College of Finance and Mathematics, West Anhui University, Lu'an 237012, China.
Financial Risk Intelligent Control and Prevention Institute of West Anhui University, Lu'an 237012, China.
Entropy (Basel). 2018 Jan 18;20(1):71. doi: 10.3390/e20010071.
In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.
在本文中，我们考虑非高斯模型下几何平均亚式期权的定价问题，其中标的股票价格由基于非广延统计力学的过程驱动。该模型可以描述收益的峰值和肥尾特征。因此，对标的资产价格的描述和期权定价更加准确。此外，使用鞅方法，我们得到了几何平均亚式期权的封闭形式解。此外，数值分析表明，相对于布莱克-斯科尔斯模型，该模型可以避免低估风险。
