Joint SPX & VIX calibration with Gaussian polynomial volatility models: Deep pricing with quantization hints
研究了一类高斯多项式波动率模型，通过联合校准SPX和VIX隐含波动率曲面数据，发现传统一因子马尔可夫连续随机波动率模型在拟合效果上优于粗糙和非粗糙路径依赖模型。
Abstract We consider the joint SPX & VIX calibration within a general class of Gaussian polynomial volatility models in which the volatility of the SPX is assumed to be a polynomial function of a Gaussian Volterra process defined as a stochastic convolution between a kernel and a Brownian motion. By performing joint calibration to daily SPX & VIX implied volatility surface data between 2011 and 2022, we compare the empirical performance of different kernels and their associated Markovian and non‐Markovian models, such as rough and non‐rough path‐dependent volatility models. To ensure an efficient calibration and fair comparison between the models, we develop a generic unified method in our class of models for fast and accurate pricing of SPX & VIX derivatives based on functional quantization and neural networks. For the first time, we identify a conventional one‐factor Markovian continuous stochastic volatility model that can achieve remarkable fits of the implied volatility surfaces of the SPX & VIX together with the term structure of VIX Futures. What is even more remarkable is that our conventional one‐factor Markovian continuous stochastic volatility model outperforms, in all market conditions, its rough and non‐rough path‐dependent counterparts with the same number of parameters.