Riding on the smiles
用主要股指的普通期权数据，通过快速傅里叶变换定价，研究多因子随机波动率模型的校准性质，特别关注Wishart类模型如何分别控制微笑和偏斜效应，对定价奇异期权和篮子期权的风险管理很有用。
Using a data set of vanilla options on the major indexes we investigate the calibration properties of several multi-factor stochastic volatility models by adopting the fast Fourier transform as the pricing methodology. We study the impact of the penalizing function on the calibration performance and how it affects the calibrated parameters. We consider single-asset as well as multiple-asset models, with particular emphasis on the single-asset Wishart Multidimensional Stochastic Volatility model and the Wishart Affine Stochastic Correlation model, which provides a natural framework for pricing basket options while keeping the stylized smile–skew effects on single-name vanillas. For all models we give some option price approximations that are very useful for speeding up the pricing process. In addition, these approximations allow us to compare different models by conveniently aggregating the parameters, and they highlight the ability of the Wishart-based models to control separately the smile and the skew effects. This is extremely important from a risk-management perspective of a book of derivatives that includes exotic as well as basket options.