Economic scenario generators are an essential tool for insurance companies. The production of market-consistent scenarios requires the models to be calibrated with the current market information. Within the generators, interest rate models focus the attention of practitioners. Their complexity has significantly increased over the last decade, along with the need for fast and accurate pricing methods for derivatives. This paper describes an efficient swaptions pricing method based on density approximation with Fourier series under the Libor market model with a displaced diffusion and stochastic volatility (DD-SV-LMM) framework. We discuss:

• Motivations for using this method
• The DD-SV-LMM
• Cosine expansion
• DD-SV-LMM calibration