基于CEV拓展模型下亚式期权定价的渐进法  

The Gradual Method of Asian Option Pricing Based on CEV Expansion Model

作　　者：于文明 王爱银[1] YU Wen-ming;WANG Ai-yin(School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830000,China)

机构地区：[1]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830000

出　　处：《数学的实践与认识》2021年第11期181-189,共9页Mathematics in Practice and Theory

基　　金：国家社会科学基金一般项目“基于CEV模型的中国居民金融资产投资-储蓄-增长策略研究”(18BJL072)。

摘　　要：运用渐进展开方法求解标的资产服从混合分数布朗运动和不变方差弹性(constant elasticity of variance,CEV)模型的亚式期权定价问题,首先通过Δ对冲策略求解抛物型偏微分方程,其次给出渐进展开方程,求出渐进解,并对渐进解给出收敛性,最后通过数值试验求解不同赫斯特指数H和渐进参数ε下的期权价值.研究得出,ε对期权价值影响较明显,选取ε是运用渐进展开法的关键.In this paper,the asymptotic method is used to solve the Asian option pricing problem of the underlying asset following the mixed fractional Brownian motion and constant elasticity of variance(CEV) model.First,the parabolic partial differential equation is solved by the Δhedging strategy,and then the progressive Expand the equation,find the asymptotic solution,and give the convergence of the asymptotic solution,and finally solve the option value under different Hurst exponent ε and asymptotic parameter W by numerical experiment.The research shows that ε has a significant effect on the value of options.Choosing ε is the key to applying the progressive development method.

关 键 词：混合分数布朗运动 CEV模型 亚式期权 渐进展开法 收敛性 

分 类 号：F830.9[经济管理—金融学] O175.2[理学—数学]