Smiles & Smirks: a tale of factors

We offer a general framework based on time changed Lévy process for modelling the joint evolution of stock log-returns and their volatility, which includes risk factors of both diffusive and jump nature, and leverage effects... [ view full abstract ]

We offer a general framework based on time changed Lévy process for modelling the joint evolution of stock log-returns and their volatility, which includes risk factors of both diffusive and jump nature, and leverage effects originated by both factors. The proposed setting encompasses a large number of the most commonly used stochastic volatility models, allows for the construction of new potential alternative models, and enables a comparative study of their features in terms of volatility, volatility of volatility and correlation processes. We analyse the performance in terms of calibration, fit of the volatility surface, hedging and forward volatility.