In traditional pricing of financial assets, the impact of drift rate and volatility rate on asset prices are often not paid enough attention. It is better to reflect the impact of the stock price drift rate and volatility on the asset price. Through the solution of stochastic differential equations containing the drift rate and volatility rate, the drift rate and volatility along with the martingale method was added to traditional asset pricing, and measure change was used to determine asset prices. As a result, a stochastic ARIMA-GARCH process was jointly set up based on the classical random processes of ARIMA and GARCH, reflecting non-linear characteristics of stock price, thereby improving its accuracy in exotic option pricing. From past information, an exchange option with a linear power-type was priced with high-precision.%为了更好地体现现实的股价中漂移率和波动率对其资产价格的影响,利用随机微分方程和其解中都含有的漂移率和波动率,在传统的资产定价中加入漂移率和波动率的鞅表示算法,利用测度变换确定资产价格.最终在经典的ARIMA和GARCH过程基础上联合建立了一个反映股价非线性特点的随机过程ARIMA-GARCH过程,对奇异期权定价提高精度,通过过去信息对具有线性幂型交换期权进行高精度定价.
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