不同利率下服从混合分数布朗运动的亚幂期权定价  

Asian power option pricing model in mixed fractional Brownian motion environment under different interest rates

作　　者：李丽梅[1] 胡华[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《中国科技论文》2016年第17期2008-2013,共6页China Sciencepaper

基　　金：国家自然科学基金资助项目(11361044);宁夏自治区软科学计划项目(20151003);宁夏大学研究生创新项目(GIP201621)

摘　　要：Black-Scholes期权定价模型的2个重要假设是标的资产服从几何布朗运动和利率为不变的常数,这不符合实际的金融市场环境,针对此问题,将利率分别为常数、非随机函数和服从Hull-White利率模型的随机函数,应用到混合分数布朗运动驱动的Black-Scholes模型中,基于风险中性等价鞅测度得到亚幂期权的定价公式,从而推广了Black-Scholes模型的应用。Two key assumptions for Black Scholes option pricing model, the underlying asset follows a geometric Brownian motion and interest rates are constant, are not match the actual financial market environment. To solve this problem, the interest rate is constant, non random function and obey the Hull-White rate model of random function, which are respectively applied to Black Scholes model driven by mixed fractional Brownian motion. The pricing formula of Asian power option is obtained based on the risk-neutral equivalent martingale measure, which promots the application of Black Scholes model.

关 键 词：Black—Scholes期权定价模型 随机函数 混合分数布朗运动 鞅 亚幂期权 

分 类 号：F830.9[经济管理—金融学] F224