论文标题
使用高斯多项式波动率模型的联合SPX-VIX校准：具有量化提示的深度定价
Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints
论文作者
论文摘要
我们考虑了一般的高斯多项式波动率模型中的联合SPX-VIX校准，其中SPX的波动率假定为高斯伏尔特拉过程的多项式函数，该过程定义为核和布朗尼运动之间的随机卷积。通过对2012年至2022年之间的每日SPX-VIX进行联合校准，我们比较了不同内核及其相关的马尔可夫和非马克维亚模型的经验性能，例如粗糙和非路径依赖性波动率模型。为了确保模型之间有效的校准和公平的比较，我们在我们的类模型类别中开发了一种通用统一方法，以基于功能量化和神经网络的SPX和VIX衍生物的快速准确定价。我们首次确定了\ textit {常规的一因子马尔可夫连续随机波动率模型}，该模型能够实现SPX和VIX的隐含波动率表面的显着拟合以及VIX期货的期限结构。更引人注目的是，我们常规的单因素马尔可夫连续的随机波动率模型在所有市场条件下都优于其粗糙和 与参数数量相同数量的非路径依赖性对应物。
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 2012 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. In order to ensure an efficient calibration and a fair comparison between the models, we develop a generic unified method in our class of models for fast and accurate pricing of SPX and VIX derivatives based on functional quantization and Neural Networks. For the first time, we identify a \textit{conventional one-factor Markovian continuous stochastic volatility model} that is able to achieve remarkable fits of the implied volatility surfaces of the SPX and 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.
