Joint Modelling and Calibration of SPX and VIX by Optimal Transport
Mathematical Finance
2021-09-06 v3 Optimization and Control
Computational Finance
Abstract
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.
Keywords
Cite
@article{arxiv.2004.02198,
title = {Joint Modelling and Calibration of SPX and VIX by Optimal Transport},
author = {Ivan Guo and Gregoire Loeper and Jan Obloj and Shiyi Wang},
journal= {arXiv preprint arXiv:2004.02198},
year = {2021}
}