基于量子模型的证券期权定价及实证分析  

Empirical Analysis of Stock Option Pricing Based on Quantum Model

作　　者：李星星 刘海军 LI Xing-xing;LIU Hai-jun(School of Education,Zhengzhou SIAS University,Zhengzhou 451150,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州西亚斯学院教育学院,河南郑州451150 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《数学的实践与认识》2020年第21期314-320,共7页Mathematics in Practice and Theory

摘　　要：首先,利用量子力学原理建立了证券市场的量子波动模型,它满足含有未知参数的薛定谔方程.其次,利用定价的风险中性理论给出了量子模型下的定价公式,它和传统的B-S公式有显著差异,主要表现为量子定价公式不仅和股票价格有关还和初态有关.最后,利用上海证券市场的数据进行了实证分析,分析表明量子的方法较传统的B-S方法更有效.Firstly,we establish quantum fluctuation model of securities market using the principle of quantum mechanics,which satisfies the Schrodinger equation with unknown parameters.Secondly,the pricing formula of the quantum model is given by the risk neutral theory,which is significantly distinguished with the traditional B-S formula.The difference mainly lies in that the pricing formula is not only concerned with the stock prices but also the initial states.Furthermore,empirical analysis is conducted by using the data in Shanghai stock market,and it shows that this method is more effective than the traditional B-S method.

关 键 词：量子模型 期权定价 B-S方法 实证分析 

分 类 号：O413.1[理学—理论物理] F832.51[理学—物理]