论文标题
通过最佳运输对SPX和VIX的联合建模和校准
Joint Modelling and Calibration of SPX and VIX by Optimal Transport
论文作者
论文摘要
本文解决了SPX选项和VIX选项或期货的联合校准问题。我们表明，本以[Arxiv：1906.06478]的精神，可以在有限数量的离散限制下以有限数量的离散约束来表达该问题。我们引入了PDE配方及其双重配方。该溶液是校准的扩散过程，可以通过双重配方引起的汉密尔顿 - 雅各布贝尔曼方程的溶液表示。该方法对模拟数据和市场数据进行了测试。数值示例表明，可以同时将模型准确地校准为SPX选项，VIX选项和VIX期货。
This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE formulation along with its dual counterpart. The solution, a calibrated diffusion process, can be represented via the solutions of Hamilton-Jacobi-Bellman equations arising from the dual formulation. The method is tested on both simulated data and market data. Numerical examples show that the model can be accurately calibrated to SPX options, VIX options and VIX futures simultaneously.
