Time changes, Fourier transforms and the joint calibration to the S&P500/VIX smiles

Speaker: Prof. Laura Ballotta, Bayes Business School, City University of London

Abstract: We develop a model based on time changed Lévy processes and study its ability of reproducing the joint S&P500/VIX implied volatility smiles and the VIX futures prices – a problem known in the literature as the `joint calibration problem’. The model admits semi-analytical characteristic functions for the key quantities, and therefore efficient Fourier based pricing schemes can be deployed. We focus on a specification of the proposed general setting which uses purely discontinuous processes. Results from the application to market data show satisfactory performances in solving the joint calibration problem, and therefore demonstrate that the class of affine processes can provide a workable fit.