4/2随机波动率模型下的期权定价

Options on S&P 500 Index by Fundamental Transform Approach: 4/2 Stochastic Volatility Model

现有的随机波动率模型存在这样一个问题:给定一组参数,在一定的标的资产波动率水平下,单因子模型只能产生陡峭或平滑的期权隐含波动率曲线,而不能同时存在两种形态,这与实际观察的数据不符。为了更准确地刻画市场隐含波动率曲面,研究一种双因子4/2随机波动率模型,该模型结合了Heston模型和3/2模型。采用Lewis的基础变换法将期权定价问题转化为求解偏微分方程(PDE)的问题;利用标普500指数期权数据估计模型的参数,并且比较了不同模型在期权定价上的差异。结果表明,4/2模型的期权价格拟合误差小于另外两种模型,弥补了原模型的不足。

The existing stochastic volatility models have such a problem:A single-factor volatility model can generate steep curves or flat curves at a given volatility,but it cannot generate both for given parameters,which is inconsistent with the actual observed data.To precisely describe the market implied volatility curve,this paper studied a two-factor 4/2 stochastic volatility model that includes,as special instances,the Heston model and the 3/2 model.Besides,it applied Lewis’s fundamental transform approach to deduce the partial differential equation(PDE).In addition,by adopting the data on S&P 500,it estimated the parameters of the 4/2 model.Furthermore,it investigated the 4/2 model along with the Heston model and the 3/2 model,and compare their different performances.The results indicate that the option price fitting error of the 4/2 model is smaller than that of other two models.