On the calibration of rough Heston model using Quasi-linearization and Spectral Collocation

The rough Heston model has become very popular among both nancial researchers and practitioners, since the characteristic function of the log-price process is available in closed form [1]. This allows the use of Fourier transform techniques to price options. However, the characteristic function is given in terms of the solution of a parametric nonlinear fractional Riccati equation, for which the classical methods such as fractional Adams scheme don t work e ciently. In this work, we introduce a new method based on quasi-linearization and fractional spectral collocation to solve the above mentioned Riccati equation and discuss its error analysis. The e ciency of the method is illustrated by calibrating the model parameters for a sample of market data.