AI 中文总结
该研究提出以VIX为核心的VDV模型，通过分离VIX与SPX的校准实现SPX-VIX联合建模，实验显示其可同时紧密拟合三类期权与期货市场，为金融建模提供一致可解释框架。
AI 中文摘要
我们提出了VIX衍生波动率（VDV）模型，这是一种以VIX为核心的SPX-VIX联合建模框架。在该模型中，我们为VIX过程定义了明确的动力学以对VIX期货和期权定价，从而得到与SPX动力学无关的VIX端校准。利用VIX的滚动窗口定义，我们推导了一个耦合函数，将SPX波动率过程作为与校准后的VIX动力学一致的潜过程，得到SPX的随机波动率表示，可进一步校准至SPX期权而不改变VIX动力学。相较于现有基于全局优化或高灵活性黑箱动力学的联合校准方法，该方法通过将VIX校准与SPX校准分离，提供了可解释且易处理的联合问题分解。在数值实验中，我们表明，具有局部波动率和均值回复动力学的VDV模型，同时实现了对VIX期货市场、VIX期权市场及SPX期权市场的紧密模型拟合，提供了一致的联合框架。
英文摘要
We propose the VIX-derived volatility (VDV) model, a VIX-first framework for joint SPXVIX modeling. In the model, we define explicit dynamics for the VIX process to price VIX futures and options, yielding a VIX-side calibration that is independent of the SPX dynamics. Using the rolling-window definition of the VIX, we then derive a coupling function to obtain the SPX volatility process as a latent process consistent with the calibrated VIX dynamics. This produces a stochastic-volatility representation for SPX that can be further calibrated to SPX options without altering the VIX dynamics. Relative to existing joint-calibration approaches based on global optimization or highly flexible black-box dynamics, the method offers an interpretable and tractable decomposition of the joint problem by separating the calibration of the VIX from the calibration of the SPX. In a numerical experiment, we show that a VDV model with local volatility and mean-reverting dynamics for the VIX achieves a close model fit to the VIX futures market, VIX option market, and the SPX option market at the same time, providing a consistent joint framework.
