Symmetry Methods for the Quadratic Gaussian Libor Model

This article describes the expectation and measure groups of the quadratic Gaussian algebra, and considers their application in the pricing of interest rate and cross asset derivatives. The discussion is motivated by the desire to construct consistent, arbitrage-free, term structure pricing models, that incorporate multi-factor decorrelation and credible smile dynamics in a robust and easy to implement framework. The article concludes with the application of symmetry techniques in the construction of the quadratic Gaussian Libor model.