具有时变参数的分数布朗运动环境下欧式缺口期权定价  

Pricing of European gap options under fractional Brownian motion with time- varying parameters

作　　者：白婷[1] 李翠香[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024

出　　处：《商丘师范学院学报》2015年第3期19-21,26,共4页Journal of Shangqiu Normal University

基　　金：国家自然科学基金资助项目(10771049);河北省自然科学基金资助项目(A2012205028)

摘　　要：经典的期权定价模型假设股票价格服从标准几何布朗运动,但金融实证表明用分数布朗运动描述股票价格过程更贴近市场.本文假设标的资产服从几何分数布朗运动,且无风险利率r(t),红利率q(t),波动率σ(t)均为随时间变化的确定函数,运用拟鞅方法求出了欧式缺口期权的定价公式,推广了相关结果.In the classical option pricing model stock price was supposed to follow standard geometric Brownian motion. However financial evidence shows that using fractional Brownian motion to describe the process of stock price is more closer to the market. In this paper,we assume that underlying asset price follows geometric fractional Brownian motion,the riskless interest rate r（ t）,dividend rate q（ t）,and the volatility q（ t） of the stock are all time- varying certain functions. Using quasi- martingale method,we get the pricing formulas of European gap option. The results extend the related results.

关 键 词：分数布朗运动 拟鞅 时变参数 欧式缺口期权 

分 类 号：O211.6[理学—概率论与数理统计]