Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options

By Jean-Pierre Fouque 3, Yuri F. Saporito. 2017

46 citations recorded by the source corpus.

A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al [Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, 2011, Cambridge University Press] to derive a first-order approximation of the price of options on a stock and its volatility index. This approximation is given by Heston’s quasi-closed formula and some of its Greeks. It can be efficiently calculated since it requires to compute only Fourier integrals and the solution of simple ODE systems. We exemplify the calibration of the model with S&P 500 and VIX data.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/e34a969e1a7be836799984f22ccdd7a32567e821

Citations in the corpus

• Joint calibration to SPX and VIX options with signature‐based models (2023, unknown): “For instance, in Fouque and Saporito (2018) a Heston model with stochastic vol-of-vol has been calibrated, however only for maturities above 4 months where VIX options are less liquid.”