标题： VIX期货的市场模型 显示英文标题

标题： A Market Model for VIX Futures

摘要： 本文提出了一种新的建模方法，该方法直接为VIX期货的期限结构规定动态。这种方法受到可以直接为VIX规定动态的模型的易处理性、利率建模中观察到的做法以及开发一个更好地理解VIX期权隐含波动率平台的愿望的启发。本文的主要贡献在于推导了VIX和股票衍生品联合市场之间不存在套利的必要条件。这些套利条件类似于利率建模中众所周知的HJM漂移限制。这些限制也解决了与现有建模方法相关的基本开放问题，其中VIX的动力学被直接指定。文章最后应用了主要结果，表明当直接对VIX期货进行建模时，相应的随机波动率模型的漂移和扩散必须受到限制以排除套利。 显示英文摘要

摘要： A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX, practices observed in interest-rate modelling, and the desire to develop a platform to better understand VIX option implied volatilities. The main contribution of the paper is the derivation of necessary conditions for there to be no arbitrage between the joint market of VIX and equity derivatives. The arbitrage conditions are analogous to the well-known HJM drift restrictions in interest-rate modelling. The restrictions also address a fundamental open problem related to an existing modelling approach, in which the dynamics of the VIX are specified directly. The paper is concluded with an application of the main result, which demonstrates that when modelling VIX futures directly, the drift and diffusion of the corresponding stochastic volatility model must be restricted to preclude arbitrage.