On the calibration of fractional two-factor stochastic volatility model with non-Lipschitz diffusions

Abstract

In this work, the volatility processes of the double Heston model are extended to treat the long memory property of the volatility. In this article, we study our presented model as a new version of the two-factor stochastic volatility model that it is proposed to model the volatility by a mean reverting equation driven by fractional Brownian motion named fractional Cox–Ingersoll–Ross process. Next, it is gone into the existence and uniqueness of the solution to this model dynamics which is defined by two independent variance processes with non-Lipschitz diffusions. Finally, by calibrating the model with real data, we examine the effect of the long memory property on the option prices and also, we confirm that the performance of the double Heston model will be improved under this property.

Keywords:

• Double Heston model
• Fractional CIR
• Long memory stochastic volatility
• Non-Lipschitz diffusion

MSC:

• 91Gxx
• 91G60