Wang Jixia, Zhang Yameng
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan Province, China.
Entropy (Basel). 2018 Oct 28;20(11):828. doi: 10.3390/e20110828.
This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman-Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for which can fit the real stock data, and the result shows that investors underestimate the risk using the Black-Scholes model compared to our model.
本文致力于研究非广延统计力学下时变系数扩散模型的几何平均亚式看涨期权定价。我们采用非广延的Tsallis熵分布来对标的资产价格的运动进行建模，该分布能够描述收益的尖峰厚尾特征。考虑到经济变量随时间变化，我们允许模型中的漂移项和扩散项为时变函数。我们使用伊藤公式、费曼 - 卡茨公式和帕德近似法，得到了具有时变模型且支付股息收益率的几何平均亚式期权定价的闭式解。此外，模拟研究表明，我们的方法所得到的结果比赵等人的方法更符合模拟数据。通过对实际数据的分析，我们确定了能够拟合实际股票数据的最佳值，结果表明，与我们的模型相比，投资者使用布莱克 - 斯科尔斯模型低估了风险。
