Fourier Integration and Stochastic Volatility Calibration

Abstract

We look at recent algorithms to compute Vanilla option prices under the stochastic volatility models with a known characteristic function, focusing on Heston, Bates, Double-Heston, Schobel-Zhu and study how they behave in the calibration of a real-world implied volatility surface example. We consider local minimization based on Levenberg-Marquardt and a smart initial guess, as well global minimization based on differential evolution.

Keywords: Heston, Bates, Schobel-Zhu, Double Heston, COS method