Fourier-Laplace transforms in polynomial Ornstein-Uhlenbeck volatility models: theory and practice

In this thesis we want to explore the application of Fourier-Laplace transforms in the context of polynomial Ornstein-Uhlenbeck volatility models, making a connection with an infinite dimensional system of Riccati equations. It is then shown a numerical implementation of such model to price options, specifically in the framework of the quintic Ornstein-Uhlenbeck volatility model.