Option Pricing in Non-Gaussian Ornstein-Uhlenbeck Markets

Non-Gaussian Ornstein-Uhlenbeck processes allow to model several distributional features of assets’ returns, including volatility clustering, fat tails and leverage. The most common specifications however do not allow to model long range dependence in the volatility process or self-exciting dynamics. Here we focus on the recently introduced class of Volatility Modulated non-Gaussian Ornstein-Uhlenbeck (VMOU) processes, that introduce a Stochastic Volatility of Volatility (SVV) component, allowing for richer dynamics for the processes, while maintaining good analytical properties. We present the framework, showing how to introduce SVV and how to compute structure preserving equivalent martingale measures. We also recall the Fourier transform option pricing setting, showing an implementation based on Non-Gaussian Ornstein-Uhlenbeck processes. Finally, we run a simulation study to highlight the empirical properties of VMOU processes, with particular attention to the clustering of volatility of volatility.