Fourier-Laplace transforms in polynomial Ornstein-Uhlenbeck volatility models
The research extends Fourier inversion to complex polynomial Ornstein-Uhlenbeck volatility models, including quintic and one-factor Bergomi types, which are more flexible than standard affine models. It connects the joint Fourier-Laplace functional of log-price and variance to solving an infinite-dimensional system of Riccati equations. This allows for efficient pricing of options and volatility swaps using numerical schemes based on these transforms.