Black-Scholes模型和GARCH模型下的隐含波动率研究

Researches on Implied Volatility under Black-Scholes Model and GARCH Model

在标的股票支付红利的条件下,分别讨论Black-Scholes模型与GARCH模型中隐含波动率的性质。在两个模型中使用了泰勒逼近,得到隐含波动率满足的二次方程,并讨论系数对隐含波动率的影响。然后,通过数值算例研究不同参数对应的隐含波动率的性态,同时分析了隐含波动率随着参数的变化趋势。

In the premise of the underlying stock dividend payment,the properties of the implied volatility were discussed in Black-Scholes model and GARCH model. Using the Taylor approximation in the two model,quadratic equation implied volatility were obtained,and the influence coefficients of the implied volatility were discussed. By numerical examples,different parameters corresponding to the hidden state volatility were investigated,the implied volatility trend with parameters were analyzed.