双分数跳-扩散Ornstein-Uhlenback过程下的后定选择权定价

摘要

In order to make the stock price closer to the actual price of financial markets,the stock price satisfies the stochastic differential equation driven by bi-fractional Brownian and jump process in this paper,the expected return rate and volatility rate are constant.The financial market mathematical model under bi-fractional Ornstein-Uhlenback process and jump-diffusion process is built by the stochastic analysis on bi-fractional Brownian motion. Using the actuarial approach,the explicit expression of European call or put options price and the parity relation are obtained,and the pricing formula of the chooser option is obtained.%为了使股票价格更接近金融市场的实际价格,考虑了股票价格服从双分数布朗运动和泊松过程共同驱动的随机微分方程,股票预期收益率和股价波动率均为常数,根据双分数布朗运动随机分析理论,建立双分数Ornstein-Uhlenback过程下跳-扩散模型金融市场数学模型,运用保险精算方法,获得欧式看涨和欧式看跌期权定价公式及平价关系,并得到了后定选择权定价公式.