基于带跳分数Ornstein-Uhlenback过程的未定权益定价  

Pricing of contingent claim on the basis of Fractional Ornstein-Uhlenback process with jump

作　　者：秦进[1] 邓小华[2] 杨蓝[3] 

机构地区：[1]遵义师范学院数学系,贵州遵义563002 [2]棠湖中学外语实验学校,四川成都610225 [3]北京师范大学昆明附属中学,云南昆明650000

出　　处：《兰州理工大学学报》2010年第2期132-137,共6页Journal of Lanzhou University of Technology

摘　　要：考虑标的资产价格变动的非连续性、收益的时变性和波动的长期记忆性,建立带跳的分数O-U过程利用分数Girsanov定理,获得分数O-U过程的风险中性等价鞅测度,采用拟-鞅(quasi-martingale)定价方法,求出此环境下欧式看涨期权和两种奇异期权(复杂型的数据选择权和上限型买权)的定价公式,使得已有的一些模型和定价公式成为其特例.Considering the noncontinuous changes of underlying assets price,temporal variability of stock return,and long memory of volatility,a fractional O-U process with jump-diffusion was set up.The risk neutral equivalent measure was obtained with fractional Girsanov theorem.And then,with quasi-martingale method,the pricing formulas of European call option and two exotic options（complicated data option and capped calls option） were derived in this environment,so that a number of existing models and pricing formulas were made as their special cases.

关 键 词：分数布朗运动 O-U过程 跳-扩散过程 奇异期权 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]