欧式期权和交换期权在随机利率及O-U过程下的精算定价方法  

Actuarial pricing approach to Europe option and exchange option under stochastic interest rates and O-U process

作　　者：刘坚[1,2,3] 文凤华[2,3] 马超群[1,3] 

机构地区：[1]湖南大学工商管理学院,长沙410082 [2]长沙理工大学经济与管理学院,长沙410114 [3]湖南省金融工程与金融管理研究中心,长沙410114

出　　处：《系统工程理论与实践》2009年第12期118-124,共7页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70971013;70701035);湖南省杰出青年基金(09JJ1010);湖南省普通高等学校哲学社会科学重点研究基地开放基金(09FEFM04)

摘　　要：引入随机利率及股价服从O-U过程的市场模型,研究了精算定价法在上述模型下的期权定价问题.根据精算定价法的定价定义,利用随机微分方程的相关理论,得到了欧式看涨看跌期权和交换期权的精确定价公式,并由此得到了欧式买权卖权的平价公式;进而推出有红利率的欧式看涨看跌期权的精算定价公式.最后,对上述结果与B-S定价公式进行了数值模拟比较分析,显示出了精算法下的定价与B-S定价的差异.所有结果均适用于复杂的不完全市场.This paper discusses an actuarial approach to the option pricing problem for a market model where the interest rates are stochastic and the stock prices are driven by generalized Exp-Ornstein-Uhlenback process.According to the definition of actuarial pricing approach,the exact solutions of the general European option and the exchange option are obtained with the help of the related theory of stochastic differential equation.Then the European call-put parity relation is derived naturally.Furthermore,the new prices of European call option and the put option with continuous dividend yield are deduced from the above results. At last,a comparative analysis of numerical simulation is made between the above-mentioned results and the B-S pricing formula.All the results are applicable to complex incomplete markets.

关 键 词：精算定价 ORNSTEIN-UHLENBACK过程 Hull-White利率模型 交换期权 

分 类 号：F224.7[经济管理—国民经济]