Libor Market Model and Gaussian HJM explicit approaches to option on composition

The twin brothers Libor Market and Gaussian HJM models are investigated. A simple exotic option, floor on composition, is studied. The same explicit approach is used for both models. Using an approximation the LLM price is obtained without Monte Carlo simulation. The results of the approximation are very good, with an error well below the uncertainty due to the simulation. The appendices proves the existence of the (modified) normal and shifted log-normal LLM used in the pricing. The link of the latter with the Ho and Lee continuous time model is described.