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

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.