引入Gamma-OU过程描述了股票市场中的跳跃噪音现象,并依此建立了含有跳跃噪音的股价模型。在股价模型基础之上利用蒙特卡洛模拟方法(MC)研究了跳跃噪音对欧式期权定价的影响。通过设计两个仿真实验发现跳跃噪音对期权定价的影响主要体现在两个方面:(1)噪音跳跃幅度对期权价格有一定的影响,大幅度的跳跃会抬高期权的价格;(2)期权合约的时间越长,期权价格的波动受噪音跳跃频率的影响越大,大大增加了期权定价的风险。
This paper introduces the Gamma-OU process to describe the jumping noise in the stock market, and a stock pricing model is established to study the influence on the noise to the European option pricing by using Monte Carlo simulation. Two experiments show that (1) the jump range increases the options prices~ (2) the long contract time strengthens the impact and increases the risk.