Knight不确定环境下复式期权定价模型——在两种股权激励模式中的应用  

Compound Option Pricing Model Under Knight Uncertainty-Application in Two Equity Incentive Modes

作　　者：潘文强 孙莹 PAN Wen-qiang;SUN Ying(School of Mathematics and System Science,Shandong University of Science and Technology,Qingdao 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《数学的实践与认识》2023年第8期59-69,共11页Mathematics in Practice and Theory

基　　金：山东省自然科学重大研究计划项目“非线性随机系统的控制与对策”(ZR2019ZD42);青岛市哲学社会科学规划项目“数字经济对青岛市经济高质量发展的驱动机制与异质性影响研究”(QDSKL2201136)。

摘　　要：在分析我国上市公司实施股票期权激励模式和限制性股票股权激励模式时面临的定价问题.将两种激励模式视为特殊的复式期权,研究了Knight不确定环境下的金融市场,利用倒向随机微分方程(Backward stochastic differential equation,BSDE)以及时间-风险折现方法,构造复式期权动态定价模型.利用随机过程的有关知识求出该模型的显式解,得到两种股权激励模式的动态定价区间,并通过实验分析验证了该模型的适用性和准确性.This paper aims to analyze the pricing problems faced by China's listed companies when implementing stock option incentive model and restricted stock equity incentive model.This paper regards the two incentive models as special compound options,studies the financial market under Knight's uncertain environment,and constructs the dynamic pricing model of compound options by using backward stochastic differential equation(BSDE)and time risk discount method.Finally,the explicit solution of the model is obtained by using the knowledge of stochastic process,and the dynamic pricing range of the two equity incentive models is obtained.The applicability and accuracy of the model are verified through experimental analysis.

关 键 词：股权激励 复式期权定价 倒向随机微分方程 KNIGHT不确定性 

分 类 号：F272.92[经济管理—企业管理] F224[经济管理—国民经济] F832.5