股票价格遵循几何分式Brown运动的期权定价  

Pricing Options on Stocks Driven by a Geometric Fractional Brownian Motion

作　　者：闫海峰[1] 翟永会[2] 刘三阳[3] 

机构地区：[1]南京财经大学金融学院,江苏南京210046 [2]河南师范大学数学与信息科学学院,河南新乡453002 [3]西安电子科技大学应用数学系,陕西西安710071

出　　处：《数学的实践与认识》2006年第8期19-24,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(70471071);江苏省教育厅高校哲学社会科学基金(05SJD790056)

摘　　要：讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.The pricing European option on a stock whose price process is driven by geometric fractional Brownian motion is considered. Existing arbitrage opportunities for these process shows that option pricing is not possible with traditional financial asset pricing methods, such as capital asset pricing model, arbitrage pricing theory, dynamic equitable pricing theory. In this paper, the formulas of the pricing European option are obtained by insurance actuary pricing without any other market assumption. Then, the expand formulas are discussed under payment of a given stock dividends and stock yields during the effective date.

关 键 词：Black—Schole公式 几何分式Brown运动 保险精算定价 期权定价 

分 类 号：F830.91[经济管理—金融学] F224