随机利率条件下的欧式期权定价  

Pricing European options under stochastic interest rate

作　　者：周海林[1] 吴鑫育[2] 高凌云[3] 陆凤彬[4] 

机构地区：[1]安徽财经大学金融学院,蚌埠233030 [2]湖南大学工商管理学院,长沙410082 [3]中国社会科学院世界经济与政治研兖所,北京100732 [4]中国科学院数学与系统科学研究院,北京100190

出　　处：《系统工程理论与实践》2011年第4期729-734,共6页Systems Engineering-Theory & Practice

基　　金：NSFC/RGC of Hong Kong(70731160635);国家自然科学基金(71003004)

摘　　要：分别选择标的资产价格和零息债券价格为计价单位,给出了利率和标的资产价格的漂移系数和扩散系数为适应随机过程的条件下、在期权生命期内任意时刻的欧式期权价格的一般形式.当利率和标的资产价格的波动率过程为时间t的非随机函数时,欧式期权价格具有解析形式.给出了一个标的资产价格服从几何布朗运动、利率服从HJM模型的欧式期权定价的例子,并导出期权价格的解析式.With the assumption that the underlying asset price and interest rate follow diffusion process, the structure of the price of European option is obtained by choosing the underlying asset price and zero coupon price as numeraires respectively.A sufficient condition that the volatility processes of interest rate and the price of underlying asset are deterministic function of time is also derived,under which the price of European option has a close-formed structure.A case of European option pricing is presented with assumption that the underlying asset price follows a Geometry Brownian Motion and the interest rate follows a HJM model and the closed-form price of the option is obtained.

关 键 词：期权定价 随机利率 计价单位转换 解析解 

分 类 号：F224[经济管理—国民经济]