基于O-U过程的幂函数族期权定价

为了使股票模型更加接近市场实际情况,文章针对股价波动的几何布朗运动模型对收益率假设的缺陷,对该模型进行了改进,假设股票价格遵循能反映股票预期收益率波动变化的指数O-U过程,利用Girsanov定理获得了指数O-U过程模型的唯一等价鞅测度。利用期权定价的鞅方法,得到了指数O-U过程随机模型下具有连续红利支付的幂函数族期权的定价公式。

Pricing Power-function Options Under the Ornstein-Uhlenbeck Process

In order to make the stock market model closer to the actual situation,we assume that stock-price process is driven by O-U process,which can reflect fluctuation in the appreciation rate of the stock.Exponential O-U process model can overcome some defects of traditional exponential Brownian motion model,and stains some more graceful properties.The unique equivalent martingale measure of this model is found by using the Girsanov theorem.Under the stochastic model of exponential O-U process,the pricing formulas of power-function options with continuous dividend are obtained by martingale method.